Integration of probabilistic costing and scheduling. in management and control of infrastructure projects. Jordi Sergio Wong

Transcription

1 Integration of probabilistic costing and scheduling in management and control of infrastructure projects Jordi Sergio Wong

2 Colophon Thesis Integration of probabilistic costing and scheduling in management and control of infrastructure projects Location Delft Date April 2015 Pages 101 Author J.S. (Jordi) Wong Student number University Delft University of Technology Master Construction Management and Engineering Graduation committee Prof. dr. ir. A.R.M. Wolfert Delft University of Technology Faculty of Civil Engineering and Geosciences Ir. E.J.C. Dupuits Delft University of Technology Faculty of Civil Engineering and Geosciences Ir. R. Berkelaar Volker InfraDesign bv.

3 Preface This report is the result of my master thesis at TU Delft, that constitutes the final step in completing the Construction Management and Engineering MSc program. It has been a learning experience during which I became familiar with the concepts of risks and uncertainties in management and control of infrastructure projects. It helped me to obtain specific knowledge on the statistical modelling of uncertainties in the areas of cost, time and risk management. I believe that these statistical models, if correctly applied, are powerful tools that will contribute to project success. This thesis was performed in the form of an internship at VolkerInfra. I would like to thank the people from VolkerInfra, who have facilitated me with a comfortable environment to conduct my research. In addition to VolkerInfra, my thanks go to Han Pekelharing for his external view on my thesis and for introducing me to the world of tendering and contracting. I would like to specifically thank my graduation committee for their scientific view, which helped me succeed in the final part of my studies. Rogier Wolfert, for pointing out this interesting topic, your constructive criticism, and for chairing the graduation committee. Guy Dupuits, for your clear feedback and for your methodological advice that allowed me to turn this report into an academic writing. And Robert Berkelaar, for your guidance during my internship and for your on-going day-today enthusiasm that kept me motivated during this research. Finally, I would like to thank my parents and friends for their patience and trust in me while conducting this research. With this thesis, an end has come to a valuable period at TU Delft and to great student days in Delft. On to the next challenge! Jordi Wong 2 Preface

4 Table of content Preface... 2 Table of content... 3 List of abbreviations... 4 Summary Introduction Research background Problem analysis Research Objective and Questions Report outline Methodology Definition and key topics Strategy Phases Theoretical framework Project uncertainty Methods Mechanism Simulation experiment Set-up cases Cost diversion diagrams Evaluation Conclusions & Recommendations Conclusions Recommendations Literature List of figures List of tables Appendices Appendix A: Overview of distribution functions Appendix B: Statistical dependence Appendix C: Analytic method for probabilistic analysis Appendix D: Simulation experiments Table of content

5 List of abbreviations D&C DBFM NASA DACE MC AACE SIG PRA IPA method SPA method DA method SAA WBS SE TI TD CPM PMS EMAS RMP MOM JCL Design and Construct Design, Build, Finance and Maintain National Aeronautics and Space Administration Dutch Association of Cost Engineers Monte Carlo American Association of Cost Engineering Special Interest Group Probabilistic Risk Analysis as part of DACE Integrated Probabilistic Assessment method Separated Probabilistic Assessment method Deterministic Assessment method Schiphol-Amsterdam-Almere Work Breakdown Structure Systems Engineering Time-Independent Time-Dependent Critical Path Method Project Master Schedule Economically Most Advantageous Solution Risk Management Plan Methods of Moments Joint cost-schedule Confidence Level 4 List of abbreviations

6 Summary Problem analysis Advancements in statistical modelling and the need to assess uncertainty in project schedule and budget has led to frequent employment of probabilistic methods in management and control of projects. These methods are effective tools to apply uncertain information, which is common in infrastructure projects, in the estimate of construction costs and time. The application of integrated and complex contracts, that are of long duration and have a high degree of exposure both political and related to stakeholders, has increased in recent years. Most risks in these contracts are typically made a full responsibility for the contractor. As a result, contractors aim to control the project schedule and budget by implementing probabilistic methods in the planning of infrastructure projects. These methods statistically analyze project uncertainty, in order to predict the end-delivery date or budget within a certain marginal probability value. A common technique in the application of probabilistic methods is the Monte Carlo simulation. These simulations often run a separate analysis on costing and scheduling in a different environment, despite the interconnection of cost items, schedules and risk registers (Gilmer & Druker, 2012; Isidore & Back, 2002). These separated analysis cannot evaluate the impact of schedule uncertainty on time-dependent cost items, which is defined as the cost effect of schedule uncertainty in this thesis. The lack of a complete assessment of this effect in project planning is indicated as a limitation to the cost estimate (AACE, 2011). In order to resolve this limitation, the American Association of Cost Engineering contributes to the direction of an integral probabilistic approach. This has led to the development of an integrated cost-schedule probabilistic approach. The development of probabilistic methods is broadly discussed in scientific literature, and is therefore, no part of this research (AACE, 2011; Hulett, 2011). A challenge exists in the practical application of these methods in the infrastructure industry. This requires understanding about the combined effects of cost and schedule uncertainty. It is on this area that this thesis would like to give a contribution to the knowledge. Methodology The aim of this thesis is to explore, compare and evaluate the separated cost-schedule probabilistic approach (SPA method) and the integrated cost-schedule probabilistic approach (IPA method) in management and control of projects. It is expected that only differences exist in the cost estimate between the probabilistic methods, since probabilistic scheduling in the IPA method is no different from probabilistic scheduling in the SPA method. A comparison between the two probabilistic methods and the deterministic method is no part of this thesis, because the latter does not specify uncertainty explicitly in project planning. This study analyzes the difference in cost outcomes between the IPA and SPA methods and the mechanisms behind it. The results of this analysis indicates what limitations in the SPA method are identified and which forms of uncertainty are not covered with this method. In relation to the 5 Summary

7 objective, the research question formulated is What is the added value of the integrated costschedule probabilistic approach in terms of cost and schedule quality in management and control of infrastructure projects?. This thesis consists of two main parts, that is the qualitative and quantitative study on the methods to assess uncertainty in project costs and schedules. In the theoretical framework the cost, time and risk management process are described, including the interaction between them. Furthermore, in this part forms of uncertainty that are related to the management processes are classified. These forms, i.e. inherent, event and systemic uncertainty, serve as input for the probabilistic analysis in this thesis. In the simulation experiments the numerical differences in cost estimates between the IPA and SPA methods are evaluated. A simplified project in these experiments is developed with branch specific figures from the infrastructure industry. This project involves different schedule variants, cost ratios and forms of uncertainty. The cost confidence intervals, that is the outcome of both methods, are compared on basis of derived contingency costs 1 and probabilities of completing the project within budget. Conclusions and Recommendations The results from the qualitative and quantitative study in this thesis demonstrate that the SPA method takes into account the combined effects of cost and schedule uncertainty on a rudimentary level. However, the SPA method does not evaluate the complete impact of uncertainty in infrastructure projects. It ignores the impact of schedule uncertainty in the indirect cost estimate. This is concluded on basis of the obtained insight from results of the literature review and simulations with the IPA method, in which the functional cost-schedule dependence is included. This functional dependence is defined in a cost-resource loaded schedule. The added value of the IPA method is described by three essential findings, that are derived from literature review and the comparison of the methods in the simulation experiments. 1. The first finding is derived from joint cost-schedule probability distributions in the IPA method. These distributions illustrate a difference in marginal and conditional probabilities of completing a project within budget and time objectives. This difference statistically proves that probabilistic costing and scheduling are dependent and therefore should be analyzed with the IPA method. This method shows that completion within time objective, increases the level of confidence related to completion within project budget. Vice versa, a completion within budget increases the level of confidence related to completion within time objective. The SPA method cannot estimate conditional probabilities and constructs a joint costschedule distribution from marginal probabilities. However, such a joint distribution excludes the dependence between cost and time aspects. 2. The second finding is derived from the difference in contingency costs between the IPA and SPA methods. It is found that the SPA method underestimates contingency costs up to a maximum of 1.9% of deterministic budget, due to the limitation of evaluating the impact of 1 Contingency costs are defined in this thesis as the difference between the probabilistic costs including uncertainties at a Pxx level (xx = level of certainty) and the deterministic costs excluding uncertainties. 6 Summary

8 schedule uncertainty in the cost estimate. Under current Dutch competitive market conditions this figure is of the same order of magnitude (or even higher) than the profit margins. The IPA demonstrates a qualitative improvement to the cost estimate, by adding the statistically analyzed cost effect of schedule uncertainty in contingency costs. 3. The third finding is derived from the analysis of risk mitigating measures on time. The results of the IPA method show that effective mitigating measures on schedule risks, in addition to time reduction, pay off in a cost effect as well. This cost effect is covered by the IPA method, because the functional cost-schedule dependence is included in the analysis. The development of a cost-resource loaded schedule in the IPA method requires understanding about time-dependent and time-independent cost items, which are distributed over direct and indirect costs. Coordination about the level of detail is required in project planning, in order to enable the linkage between costing and scheduling. Direct cost items are linked to activities and indirect cost items are linked to hammock activities in the integrated schedule. Further research into the statistical analysis of finalized bids and/or projects in the infrastructure industry is required, in order to establish general acceptance about the added value of the IPA method. Moreover, such studies should indicate when to adopt the IPA method in management and control of projects. Finally, management should consider that statistical dependence between events in the risk register and unidentified forms of uncertainty in project planning are not assessed in the SPA and IPA methods. These items form subjects for further studies and until fully resolved, a combination of deterministic and probabilistic methods is still recommended in the infrastructure industry. 7 Summary

9 1. Introduction 8 Introduction

10 1.1 Research background Public construction projects, in particular large-scale infrastructure projects, imply the development of unique and complex products to boost national economy and enhance urban environment. Such projects are initiated in the Netherlands by the executive agency of the Ministry of Infrastructure and the Environment Rijkswaterstaat (Rijkswaterstaat, 2012). Lately, the changed outsourcing strategy of Rijkswaterstaat have shifted infrastructural contracts from traditional and detailed specification into Design and Construct (D&C) and Design, Build, Finance and Maintenance (DBFM) variants. These integrated contracts aim to utilize the knowledge and creativity of the private sector by generally allocating more risks and responsibilities in the asset life cycle to the contractor (Rijkswaterstaat, 2011). It becomes possible for the contractor to optimally coordinate the planning of design, execution and maintenance on each other. One associated aspect of these integrated contracts is the requirement of a probabilistic schedule within the delivery of the bid package (Projectgroep PPI, 2001). Probabilistic methods have been recommended as an alternative to deterministic approaches to evaluate uncertainty in scheduling of large-scale and complex projects (Goodpasture, 1999; Hulett & Campell, 2002; Kindinger, 1999; Vrijling & van Gelder, 2009). Probabilistic scheduling recognizes schedule variation and enables management to deal with uncertainties prior to the start of the project. It provides a basis for decision-making about the assignment of a project-specific time plus contingency estimate for competitive bidding in the infrastructure industry. The required estimate of project cost still has to be expressed in one single deterministic bid price ( ). Therefore, discrepancies between the initial estimate and the finally realised cost cannot be avoided (Vrijling & van Gelder, 2009). Public employer Prorail has launched a pilot on probabilistic costing and contracting (Prorail, 2013). It is expected that in the near future a deterministic and fixed price will no longer be the only bid selection criteria, but besides probabilistic scheduling also probabilistic values for costing as average and spread will be differentiators. With respect to the outsourcing strategy of unique and complex projects, the National Aeronautics and Space Administration (NASA) handles a different policy for project selection. The agency, responsible for space programs of United States, was increasingly experiencing cost and time overruns due to a lack of clear understanding about combined effects of cost and schedule uncertainty (GAO, 2004). In order to establish priorities, asses uncertainty and make investment decisions, NASA adopted an integrated cost-schedule probabilistic approach as part of project controls requirements. This method enables to combine probabilistic costing and scheduling into a single cohesive approach. Since this integrated cost-schedule probabilistic approach is mandated by policy for NASA budgeting and scheduling, it is quickly gaining traction in other industries in the United States such as the oil and gas, defence, shipbuilding, mining and construction (Druker & Gilmer, 2013). The Dutch infrastructure industry is more conservative and is just starting to adopt probabilistic methods in project planning. In that respect, understanding the principles of this new practise can lead to new insight in project uncertainty and its impact on project cost and schedule objectives. 9 Introduction

11 1.2 Problem analysis Over the years many Dutch contractors used predetermined percentages of the base estimate as project cost and schedule contingency. When more complex integrated contracts were put out to tender, the drive to explore and understand the impact of project uncertainty on cost and schedule performance increased. Advancements in statistical modelling provided management with an increasing power for making decisions under uncertainty. The probabilistic cost and schedule analysis are effective tools to apply existed uncertain information in project planning. Input data for the probabilistic analysis is derived from the project base plans in the cost, time and risk management process. The output of a probabilistic analysis is a confidence interval for the expected project performance, which is used to predict an end-delivery milestone or cost target within a certain probability value. Moreover, the interval enables more reliable decision-making with respect to cost and schedule contingency planning (Isidore et al., 2001). A popular technique for the probabilistic analysis is the Monte Carlo (MC) simulation. The MCsimulations on time and cost are usually conducted separately in different software, despite the interconnection of cost estimates, schedules and risk registers (Gilmer & Druker, 2012; Isidore & Back, 2002; Shr & Chen, 2006). This isolated approach is identified as a serious limitation, because it is common knowledge in the infrastructure industry that project cost is affected by the chosen schedule (Time is Money). Besides the fact that preparing two MC-simulations can be time consuming, ignoring the relationship between cost and time aspects is substantially underestimating total cost and schedule uncertainty (Isidore & Back, 2002; Isidore et al., 2001). Especially in a competitive environment, every improvement with respect to schedule, cost and resource requirements can result in winning or losing an infrastructure tender. This lack of optimization emphasises on the challenge to integrate cost, time and risk management in project planning. The first attempts to develop an integrated cost-schedule probabilistic approach were focused on combining the results of two independent MC-simulations on project cost and duration (Isidore et al., 2001). In order to improve this approach, further studies investigated the interaction between cost and time on work task level (Poh & Tah, 2006). This research has led to the development of a cost-resource loaded schedule, which represents the relation among the duration and cost aspects of a construction activity. This integrated schedule is used as platform for modern simulation software (e.g. Booz Allen s Polaris and Oracle Primavera Risk Analysis). Simultaneously with the development of modern software, research was conducted about the impact of schedule uncertainty on the project cost assessment (Hulett, 2011). In order to study this linkage, schedule uncertainty results were incorporated into the cost assessment. Therefore, a distinction was made between time-dependent and time-independent cost items. Consequently, cost items that are dependent on time will tend to vary if schedule uncertainty occurs. According to this research (Hulett, 2011), the integrated cost-schedule probabilistic approach provides the most accurate information about project uncertainty. Moreover, it reveals the most important risk and opportunity events that affect project cost and duration. The aforementioned studies resulted in a recommended practice authored by the American Association of Cost Engineering (AACE). This practice acknowledges the need for an integrated 10 Introduction

12 approach on cost, time and risk management. It describes the integrated cost-schedule probabilistic approach and executes an example cost and schedule contingency calculation (AACE, 2011; Hollmann, 2010). In the view of the AACE, the integration of time, cost and risk management is important because: Most risks have impact on the project schedule that are expressed as delays. Many cost items are time dependent such as labour and project management. Cost and time aspects are trade-offs and therefore important for risk response strategy. The Special Interest Group Probabilistic Risk Analysis (SIG PRA) of the Dutch Association of Cost Engineers (DACE) recognizes that the mathematical background of the probabilistic methods are well developed. In order to provide insight into the added value of the probabilistic methods, the SIG PRA clarifies the statistical analysis of uncertainty in reference project. They consider the practical application and demonstration of benefits as an essential challenge (Schoevers, 2013). These benefits are expressed in cost and schedule terms, and enhanced project control and decision-making about the effects of project uncertainty. However, the lack of reference projects make it very challenging for the SIG PRA to objectively evaluate probabilistic methods. The drive to assess project uncertainty in a more integral approach has led to different policies for budgeting and scheduling around the world. In this thesis, the methods to assess project uncertainty are grouped in three categories (Figure 1). The DA method is in traditional and specified contracts applied, whereas the SPA method is used in more complex integrated contracts in recent Dutch infrastructural tenders 2. NASA is leading the way in the development of the IPA method and has applied as first organization this method as standard policy in their project selection process (Gilmer, 2011; Hulett & Druker, 2014). 1. Integrated cost-schedule Probabilistic Assessment Method (IPA method). 2. Separated cost-schedule Probabilistic Assessment Method (SPA method). 3. Deterministic Assessment Method (DA method). IPA Method SPA Method DA Method Cost-resource loaded schedule Base schedule Base cost Base schedule Base cost Project uncertainty Project uncertainty Historical Data % schedule % cost MC-analysis on cost-resource loaded schedule MC-analysis on schedule MC-analysis on cost Cost and time contingency plan Time contingency plan Cost contingency plan Time contingency plan Cost contingency plan Figure 1 Methods to assess project uncertainty on cost and time estimates 2 Frame of reference made by management of VolkerInfra. 11 Introduction

13 1.2.1 Practical relevance As a contractor working in a competitive environment, VolkerInfra focuses on efficiently and effectively acquiring, executing and managing large-scale multidisciplinary infrastructural projects. In order to succeed in their mission, VolkerInfra applies an integral approach in the field of tender- and design management. An integrated probabilistic approach on costing and scheduling, and their interconnection in project planning will therefore fit in with the method of working of VolkerInfra. In project planning, updates and adjustments originating from information and characteristics gathered in the tender phase potentially have impact on several management processes. These updates and adjustments can refer to new or revised cost estimates, activity sequences, schedule dates, resource requirements and risk responses. This progressive optimization indicates the iterative feature of a tender and emphasizes on the need of integral management on planning processes (Project Management Institute, 2008). The level of interaction between management processes is dependent upon project characteristics and context. With respect to projects in which VolkerInfra is involved, probabilistic analysis (IPA and SPA method) are extremely useful to support decision making in tenders. These analysis include the variety of values in the cost, time and risk management process and statistically analyzes the impact of this variety on project objectives. The deterministic analysis (DA method) is a more straightforward approach and is an effective tool to determine cost and time contingency (Burroughs & Juntima, 2004). It is however less suitable to support decision-making, related to the progressive optimization of an infrastructural tender. Hence, the analysis is only based on historical data and gut feeling. There is no project-specific uncertainty included in this analysis (Figure 1). Until now, the SPA method has been applied by VolkerInfra in the Dutch infrastructure industry (e.g. project Schiphol-Amsterdam-Almere A1-A6, SAAone consortium) to assess project uncertainty on time and cost in isolation. Therefore, effects of uncertainty are only analyzed that restrict their impact only to one specific management process (e.g. price uncertainty on budget estimate in cost management). As mentioned, interconnection exists between planning processes (Gilmer & Druker, 2012; Isidore & Back, 2002). This causes some forms of uncertainty to have impact on multiple management processes (e.g. Heavy weather conditions that cause a delay in the duration of demolishing works and consequently increases cost to rent heavy equipment). This example illustrates a cost effect of schedule uncertainty and requires a more integrated approach in the processes of costing, scheduling and risk assessment. This integrated approach allows management to initiate risk responses, based on the strategic trade-off among the competing project objective time and cost. So far, the cost effect of schedule uncertainty can only be fully captured with the IPA method (Hulett, 2011). The lack of knowledge about the cost effect of schedule uncertainty reflects the practical relevance of this thesis Scientific relevance The topic of statistical modelling of cost and time performance is broadly discussed in scientific literature. Unfortunately little data have been published on how successful these methods have been in contingency estimating. DACE emphasizes on the lack of literature about this practical application, but acknowledge the fact that total project cost and duration cannot be exactly predicted on beforehand (Schoevers, 2013). 12 Introduction

14 The available literature presented over the years did however initiate the development of modern software to conduct an integrated cost-schedule probabilistic approach. Since this planning software became available, the AACE published a recommended practice in which a case study is simulated with the IPA method (AACE, 2011). The result indicates that 57% of the cost contingency at the P-80 point originates from schedule uncertainty. It illustrates the statistically analyzed cost effect of schedule uncertainty. Although the AACE admits these results depend on case study assumptions, they believe that the majority of cost uncertainty arises from uncertainty in the scheduling process. All together the aforementioned, make it very difficult to determine if the Dutch infrastructure industry should adopt the IPA method as an essential technique in project planning. It is commonly agreed that variables in the planning of large-scale projects are unique, making statistical evaluation on a small set of reference projects not feasible (Schoevers, 2013). Nevertheless an objective assessment of the presented methods is imperative at the present juncture, in order to increase understanding about the combined effects of cost and schedule uncertainty. 1.3 Research Objective and Questions The aim of this graduation research is to explore, compare and critically evaluate the separated costschedule probabilistic approach (SPA method), the integrated cost-schedule probabilistic approach (IPA method) and the deterministic approach (DA method) (Figure 1). This is done in terms of quality and required level of effort, in order to examine the added value of the IPA method in management and control of infrastructure projects. It is expected that the exploration of project uncertainty plays an important role, in particular the cost effect of schedule uncertainty. The comparison between the IPA, SPA and DA methods in quality terms is made on basis of statistically analyzed data. This involves cost and schedule information obtained from the analysis, which supports decision-making in project planning. This study will analyze the possible quantitative difference in outcomes between the IPA and SPA methods and the mechanisms behind it. In particular, these findings should indicate from which form of uncertainty in the cost, time and risk management process the different outcomes tend to increase. A quantitative comparison between the probabilistic and deterministic methods is no part of this thesis, because the latter does not explicitly specify uncertainty. This research will formulate suggestions on how to improve the cost, time and risk management process related to the cost effect of schedule uncertainty. This is done on basis of the results of the IPA method, which is the most integrated approach to estimate construction costs and schedules. In relation to the objective, the main research question has been formulated and together with the sub-questions has to be answered in the final chapter of this report. The main research question is: What is the added value of the integrated cost-schedule probabilistic approach in terms of cost and schedule quality in management and control of infrastructure projects? 13 Introduction

15 The main research question (RQ) is supported by the following four sub-questions (SQ): SQ1. SQ2. SQ3. SQ4. What forms of uncertainty are identified and assessed in the planning of infrastructure projects? What are the limitations and benefits of the IPA, SPA and DA methods in relation to the assessment of project uncertainty and the required level of effort? What mechanism behind the IPA and SPA methods evaluates the cost effect of schedule uncertainty in infrastructure projects? In what ways can the cost, time and risk management process be improved with respect to the insight obtained from the IPA method? The first two sub-questions are aimed to explore and compare the methods to assess uncertainty in management and control of infrastructure projects. In essence, these questions reflect the theoretical background of this thesis. The third sub-question elaborates on the cost effect of schedule uncertainty. It describes a context in which these cost effects have a significant impact on project cost objectives. The last sub-question evaluates all forms of uncertainty in the cost, time and risk management process and translates these findings into recommendations applicable in the Dutch infrastructure industry. 1.4 Report outline Following the introduction of this thesis, the second chapter unfolds the research methodology to achieve the formulated research objective. The third chapter elaborates on the required literature, that is divided in three main sections, in order to obtain insight in the key theories an concepts of this research. In the first section, the nature of uncertainty in management and control of infrastructure projects is discussed. The second section studies the methods to assess uncertainty, with emphasis on the explicit cost-schedule relationship. The last section presents an initial comparison between the probabilistic methods. The fourth chapter presents an extensive quantitative comparison between the probabilistic methods. This includes a variety in variables in the cost, time and risk management process, in order to design a set of project scenarios. Finally, in chapter five the conclusions and recommendations of the report are presented, along with suggestions for further research. 14 Introduction

16 2. Methodology 15 Methodology

17 This chapter describes the developed methodology, involving the definition of key terms, research strategy and phases, in order to achieve the formulated research objective and answer the research questions. First, an overview of the key terms is established to determine the boundaries of this thesis. Second, the research strategy elaborates on the approach to execute this research such as the handling of research data. Finally, three research phases are described. The developed methodology is based on recommended literature (Verschuren & Doorewaard, 1998) of the Delft University of Technology. 2.1 Definition and key topics This section clarifies specific topics that are relevant for this practice-oriented research. These are recurrent topics throughout this report, which require an exact description based on PMBOK principles (Project Management Institute, 2008). Therefore, four topics are defined and narrowed down to indicate the limitation and coverage of the study area. 1. Project planning: A key concept of this study is project cost and duration estimation, which is conducted in the planning phase of the project lifecycle. These estimations become more accurate as time passes. The focus of this study is on the estimating methods in project planning, in particular probabilistic cost and schedule results prepared to be applied as bid proposal. The level of detail is on project management level and involves a certain degree of project uncertainty, which is further defined throughout this report. 2. Planning processes: An initial exploration of the methods to assess project uncertainty (Figure 1), delimits the study area into three methods. These methods are applied in the following planning process groups: Cost management, Time management and Risk management. It is of special interest for this research to examine the statistical analysis of uncertainty in these processes. 3. Project Uncertainty: Project uncertainty manifest itself by an infinite amount of sources that potentially impact construction costs and duration. These sources of uncertainty can be interpreted and classified in many ways. It is not feasible to map out all these sources in detail, but instead the focus should be on the dominant sources of uncertainty in project planning. Branch specific figures of the infrastructure industry are applied to specify uncertainty in this thesis. 4. Estimating and Tendering: A competitive tender process regarding the final bid of cost performance involves input from the risk management, costing and scheduling disciplines, as well as from the commercial management of the project. These commercial considerations reflect the trade-off between winning a tender and making a reasonable profit. The focus of this study is purely on the mathematical modelling of cost estimate, so the comparison and evaluation between the probabilistic methods will mainly be based upon a fixed percentile of the confidence level. The 70 th percentile (P70) is generally approved by management in a competitive tendering environment (CROW, 2010). The deterministic method calculates contingency with an across-the-board percentage on the base estimates. The percentages to be applied within this study are presented in chapter Methodology

18 2.2 Strategy The research strategy involves a set of coherent decisions about the approach to execute this research. These decisions refer to the choice of an in-depth or broad analysis of the study area, and whether results are interpreted as quantitative or qualitative data. These decisions are often interrelated (Polit & Beck, 2010), as illustrated in Figure 2. This study has the characteristic of a qualitative as well as a quantitative research, to the extent of understanding the mathematical modelling of uncertainty. Figure 2 Qualitative and Quantitative research The examination of the integrated probabilistic approach in management and control of projects is a complex problem, that in order to be solved requires more than an indication of the numerical differences between outcomes. Therefore, the mechanism of probabilistic costing and scheduling is more important than the possible outcomes. These are prepared as the project cost and duration estimates. An in-depth research is proposed to enable the analysis of the mechanism behind the IPA, SPA and DA methods and investigate what sources of uncertainty tend to trigger differences. Furthermore, the large amount of variables in the planning of infrastructure projects would not allow for generalized results and quantitative research alone (Schoevers, 2013). The problem of studying the added value of the IPA method is context-specific. This means that the size of project, the type of contract and the way the responsibilities are organized are of influence. A combination of a theoretical framework (qualitative) and simulation experiments (quantitative) is proposed, to exploit the strengths of both a qualitative and quantitative research strategy. The theoretical framework is applied to in-depth understand the context, while simulation experiments aim to get insight into the mechanism of the methods of interest. Figure 3 illustrates the iterative model of the combined strategies, that facilitates handling of the complexity of the present problem. Theoretical framework Branch specific figures Simulation experiment Project uncertainty Cost, Time and Risk management Cost and Time probability figures Methods Gain insight in mechanisms Figure 3 Iterative model of research strategy (modified) (Hellström & Nilsson, 2006) 17 Methodology

19 Starting from a theoretical framework perspective, the typical forms of uncertainty in project planning are explored and classified. The costing, scheduling and risk assessment process are described in the framework, that serves as detailed input for the simulation experiments. It is important to acquire branch specific knowledge about the variety of cost and schedule figures and their interrelation to develop a consistent reflection of a Dutch infrastructure project. Forms of uncertainty are assessed in these projects by the IPA, SPA and DA methods in the simulation experiments, in order to obtain cost and schedule probability figures. The ability to experiment with uncertainty, cost, schedule and methods demonstrates the motivation for the simulation strategy. Combining the qualitative knowledge gained from the theoretical framework with the quantitative cost and time probability figures from the simulation experiments, should lead to an in-depth evaluation of the IPA, SPA and DA methods in project planning. 2.3 Phases The research is divided into three phases: exploration, comparison and evaluation. These phases are a repeating process with the aim to achieve the formulated research objectives Exploration phase In the exploration phase, the subjects of project uncertainty and planning processes are studied and categorized. In order to obtain knowledge about project planning, a desk research is executed in practical project documents (schedules, risk registers, breakdowns structures, course books) and scientific literature (reports, books). Furthermore, practical observations and conversations with experts should provide key cost and schedule figures. The same principle applies for the classification of project uncertainty. The key planning figures should help to develop a simplified infrastructure project based on typical schedule, resource and activity features for Dutch infrastructure projects. Variants should be derived from this simplified project to take into account the dynamics of planning figures. The main focus of the exploration phase is on the development of theoretical framework Comparison phase The comparison phase aims to make a comparison between the cost and schedule estimates of the IPA, SPA and DA methods by analyzing the marginal impact of the forms of uncertainty in the management processes. This comparison is performed on different cost structures and schedule logics of a simplified project. The essence of the comparison phase is to identify forms of uncertainty that tend to increase the difference in cost and schedule estimates between the presented methods. Therefore, simulation experiments are part of the comparison phase Evaluation phase In the evaluation phase, the obtained knowledge and simulated figures are combined and evaluated. New insight from this evaluation is derived, in order to predict the combined effects of cost and schedule uncertainty. With respect to the forms of uncertainty, project figures and methods, a contextualized analysis is preferred. Basically, this means that the evaluation of the methods in management and control of infrastructure projects will be context-specific. The level of effort of the methods, such as the required time or information to execute the analysis, is also used as criteria in the final evaluation of the IPA, SPA and DA methods. 18 Methodology

20 3. Theoretical framework 19 Theoretical framework

21 In this chapter the theoretical framework is developed, in order to qualitatively study the IPA, SPA and DA methods. This framework explores theories and concepts related to the statistical analysis of project uncertainty and helps to compare and evaluate the methods on quantitative basis in the next chapter. This chapter start with the classification of project uncertainty and describes the mathematical problems encountered in the cost, time and risk management process. Next, the probabilistic and deterministic methods that manage and deal with uncertainty are presented. The process of these methods is described step by step, based on the classified forms of uncertainty. Finally, an initial comparison between the IPA and SPA methods is executed, so insight is obtained in the mechanism behind each method. This section ends with some assumptions that are tested in the simulation experiments. Figure 4 illustrates the structure of this chapter, in which each step requires understanding from the previous section. Project uncertainty Methods Mechanism Figure 4 Structure of theoretical framework 3.1 Project uncertainty A project is an endeavour in which human, material and financial resources are organized in a novel way, to undertake a unique scope of work of given specification, within constraints of cost and time, so as to achieve unitary, beneficial change, through the delivery of quantified and qualitative objectives. (Turner, 1992) The change-inducing nature of projects stated in Turner s definition highlights the inevitability of project planning, in which a variety of resources under significant constraints should be organized in order to achieve the formulated objectives. It also suggests the intrinsic uncertainty related to a novel organization and a unique scope of work. Uncertainty in project planning can be divided in two categories (Gelder, 1999): 1. Epistemic uncertainty as scientific uncertainty in the model of the process. 2. Aleatoric uncertainty representing randomness of a stochastic process. Epistemic uncertainty is caused by a lack of knowledge and arises since relevant information is not always available nor stable (Chapman & Ward, 2011). It may change as knowledge increases. Aleatoric uncertainty is defined by a lack of a specific pattern, such as variation in a process, and cannot be reduced by extra knowledge. As central part of project planning epistemic uncertainty should be reduced in time by collecting more data, while aleatoric uncertainty should be analyzed with standard probability theory. Project uncertainty is defined as the effect of future uncertainty on realizing objectives cost, time and quality performance (Figure 5) (Chapman & Ward, 2011). This thesis focuses on cost and time uncertainty. Project uncertainty related to quality performance is kept constant, in order to study the 20 Theoretical framework

22 interaction between cost and time uncertainty. In order to discern between the different forms of uncertainty, an overview of project uncertainty is presented below. Figure 5 Project uncertainty This thesis subdivides the aleatoric and epistemic uncertainty in four forms of uncertainty based on literature (Chapman & Ward, 2011) and (CROW, 2010). Recognizing these four forms will help to manage the sources of uncertainty more effectively. 1. Ambiguity uncertainty (beslisonzekerheid) is the dominant form of all sources of uncertainty in the early phase of the asset life cycle and involves a lack of knowledge which, in principle, could be completed. This epistemic uncertainty reduces over time as part of project planning and occurs when parameters and distribution types are determined from limited number of data. Several reasons for this form of uncertainty are lack of agreed contracts, structure, data and specifications. This form of uncertainty is typically in the span of control of the client, such as the decision about multiple design alternatives. 2. Inherent variability (kennisonzekerheid) originates from the spread or bandwidth on duration and costs of activities. The cause may lie in productivity and efficiency uncertainties, such as spread on the amount of sand to be excavated or spread on the price of sheet pile walls. This aleatoric uncertainty cannot fully be reduced by obtaining more data. 3. Event uncertainty (toekomstonzekerheid) involves events which may or may not occur that have impact on project objectives. An example is the event of encountering unidentified archaeologically remains during the construction phase of an infrastructure project. This form of uncertainty is referred to as risks and opportunities and is categorized as aleatoric uncertainty. 4. Systemic uncertainty (Afhankelijkheid) involves simple forms of dependences, such as the rise of materials and labour prices when markets seriously overheat, but also more complex relationships between delay in activities and total cost increase. Further studies into the dependences of variables reduces this epistemic uncertainty. Often the assumption of independence is adopted in the infrastructure industry (de Ridder, 2011). Uncertainty in and around projects can hardly be associated with only one form of uncertainty, so a composite of two or more forms is usually more common. A baseline for the statistical analysis of uncertainty is developed, by the identification and quantification of these forms of uncertainty in project planning (Chapman & Ward, 2011). The statistical analysis in this thesis addresses all aspect of uncertainty in performance terms time and cost. Therefore, as illustrated in Figure 6, a statistical analysis is required in three management processes (Project Management Institute, 2008): cost, time and risk management. Each process forms a separate engineering discipline in project planning. 21 Theoretical framework

23 Probability of occurence Statistical dependence Risk management Event uncertainty Consequence Inherent variability Project uncertainty Statistical dependence Time management Activity duration Inherent variability Functional dependence Unit Inherent variability Statistical dependence Cost management Price Inherent variability Figure 6 Classification of project uncertainty in the cost, time and risk management process The dominant form of project uncertainty in the risk management process is event uncertainty. The consequences of these events are often subjected to inherent variability. In addition, systemic uncertainty expressed as statistical dependence is the lack of knowledge about the underlying relationship between the occurrence of events in risk management. The dominant form of uncertainty in both the cost and time management process is inherent variability and involves variation in activity durations, units and prices. The lack of knowledge about the mutual dependences of materials and prices expresses the systemic uncertainty in these processes. Systemic uncertainty between the outcomes of the cost, time and risk management process is defined as a functional dependence. It reflects the lack of knowledge about the combined effect of cost and schedule uncertainty in a project. Hence, the focus of this study is on the quantification process of this form of uncertainty and its impact on project objectives. Ambiguity uncertainty is involved in all processes to the extent that forms of inherent, event and systemic uncertainty have not been identified and appropriate data has not been available or analyzed. It stimulates the idea for effective consideration of trade-offs within tenders, which involves stretching to do best with limited time, knowledge and other resources. Therefore, an iterative approach to continuously assess uncertainty about the achievement of objectives is required. This helps to spend time efficiently on data acquisition and to reduce epistemic uncertainty that matters. Ambiguity uncertainty should be distinguished because, unlike other forms of uncertainty, it originates from the decision-making process of the client. It often involves uncertainty about the specification in the project scope. This form of uncertainty is analyzed by estimating multiple design variants. This form of uncertainty is not in the scope of this thesis. The first part (3.1) of this chapter describes the assessment of the forms of uncertainty in the management processes (Figure 6). Furthermore, mathematical formulas are introduced that lend themselves to be solved with probabilistic uncertainty analysis. 22 Theoretical framework

24 3.1.1 Inherent variability The statistical analysis of project uncertainty within the cost and time estimating process is an integral part of project planning, in which activity duration, unit and price estimates are affected by inherent variability. These estimates are predictions and their exact values are uncertain in nature. They are only known when the project is completed. Therefore, these estimates are not well represented by a single number and instead should be expressed by a random variable (Covert, 2013). This random variable represents a distribution of possible estimates. A probability distribution is used to provide a statistical meaning to the estimates. A random variable (X) defined by the use of a probability distribution can either be continuous or discrete. A continuous random variable can attain an infinite number of values and is expressed by a probability density function (1), while a discrete random variable will attain a specified finite or a numerable list of values and is defined by a probability mass function (2) (Dekking et al., 2005). (1) In the infrastructure industry, historical data about activity duration, units and prices is limited and enlarging the amount of data is not always possible, nor economically feasible (Gelder, 1999). Exact determination of the probability distribution is, therefore, often not possible and epistemic uncertainty is included in the applied analysis. Still, the simplest form of probability distribution is preferable to one-dimensional deterministic point estimates (Hubbard, 2009). In order to construct a probability distribution, a range of estimates is required with at least a lowest (L) and upper (U) value and if possible a most likely top (T) value as well. Appendix A elaborates on the different ways to model these distributions, based on the 3-point estimates derived from expert opinion. The 3-point estimates is common and well accepted when historical data are not available (Hulett, 2011). The probability distributions described in the appendix are: 1. Uniform distribution 2. Triangular distribution 3. Beta-PERT distribution 4. Normal distribution Although the use of different distributions has impact on the outcome of a probabilistic analysis, several studies (Back et al., 2000; Fente et al., 2000; Touran, 1997) concluded that beta and triangular distributions are the most suitable in project planning. A more recent study (Hulett, 2011) prefers the use of a triangular distribution, which conveys a great degree of uncertainty. Moreover, it has the benefit that it can easily be collected from discipline experts. This study recommends to focus on the correct extreme and most likely values of the probability distribution, rather than the precise type of distribution. This thesis mainly examines the application of a triangular and normal distributions, with respect to the comparison and evaluation of the IPA and SPA methods. (2) 23 Theoretical framework

25 Cost management Cost management is the process in which contractors estimate the project cost and determine project overheads, in order to formulate the total price of a bid (Figure 7). The study area of this research is limited to the cost estimating process and the required contingency level derived from this process. It is however good to understand that working in a competitive environment requires experiences, with respects to the decisions being made about project cost and suitable overheads. A final bid price should be low enough to win and, at the same time, high enough to make acceptable profit. Profit General overhead Contingency Cost Direct Indirect Further detailing Figure 7 Development total price of bid (Maylor, 2010) Basically there are two approaches to prepare project costing information, that is bottom-up and top-down estimating (Project Management Institute, 2008). The application of the different approaches is dependent on the level of project definition, project type and complexity of the project. This research only applies the detailed bottom-up approach, as presented in the cost estimating guideline SSK-2010 (CROW, 2010). This approach is typically done at a low level of detail and is applied once the project is decomposed into manageable work packages in the Work Breakdown Structure (WBS). This decomposing is done with the Systems Engineering (SE) (Figure 8). Figure 8 Work package in WBS (Modified) (Rijkswaterstaat & Prorail, 2009) 24 Theoretical framework

26 Framework for integrated analysis: SE focuses on the required functionalities of the project and its context. Moreover, it ensures that all likely aspects of the projects are consider and integrated. The scope of the project is then defined as the activities of all the work packages. A work package consist of a cluster of activities that are linked to a physical element from the object tree. Therefore, as a whole, these activities should fit within the project budget and schedule. Each work package also entails relevant information about its functions and related risks, as illustrated in Figure 8. SE provides the framework for an integrated environment to manage the interfaces between risk management, costing and scheduling (Rijkswaterstaat & Prorail, 2009). The total project cost estimate is represented by a summation of the individual direct and indirect cost components. In deterministic costing these components are presented as single values. If probabilistic costing is applied, then direct (X) and indirect cost items with a potential for variability are modelled as continuous random variables. The total project cost estimate (Z) is then illustrated with a probability distribution. Indirect costs can be calculated by an additional percentage (j) over the direct costs (Vrijling & van Gelder, 2009). Branch specific percentages are presented in chapter The project cost formula is formulated as equation 3. In which: (3) In order to produce an realistic cost model, besides inherent variability, also systemic uncertainty defined with the Pearson correlation between cost variables should be consider in cost management (CROW, 2010). This form of uncertainty is discussed in chapter Further decomposition of direct and indirect costs items is described in the next section Direct cost Direct cost are the expenses that are directly linked to the production or delivery of a product or service involved. The work packages in the WBS are used as baseline for the direct cost estimate (Rijkswaterstaat & Prorail, 2009). These costs make up the bulk of any infrasteructure project cost estimate with material, labour, equipment, and subcontractor work among the largest components of direct cost (Bennett, 2003). Historic cost records, project databases and the market are used as source of information for the direct cost estimate. 1. Materials include all physical objects that become part of the complete structure. In order to determine the price per unit, the contractor will request material suppliers for a price specification. Consequently, the cost for a task item can be calculated as the product of its estimated quantity (Q) and its price (P) per unit. These resource units and prices are potentially subjected to inherent variability, and should be expressed by continuous random variable. 25 Theoretical framework

27 2. Labour is more difficult to estimate accurately due to productivity, defined as the factor at which employees complete the work task (Bennett, 2003). Productivity varies with the size and experience of the team, availability of equipment, weather, coordination etc. Besides productivity, also the price (P) per time unit can vary. The measure of quantity (Q) is expressed in man-hour (mh), indicating that this cost item is dependent on the duration of an activity. 3. Equipment is used to install the various materials into the structure. Equipment may be owned by the contractor, rented (short-term) or leased (long-term) for the project. Estimating equipment cost is often done on daily basis, which is similar to the process of labour cost estimating (Bennett, 2003). 4. Subcontractors are selected on their reputation, qualification and lowest price. The subcontract offers may be provided to the general contractor on a lump-sum or unit-price basis. A lump-sum contract (ls) is simply added to other items. A unit-price contract applies the same principles as material cost estimating, the proposed price (P) times the estimated quantity (Q). Time-Dependent and Time-Independent direct cost: Modelling project cost items and activity durations as stochastic quantities as opposed to fixed, requires understanding on how uncertainties between costing and scheduling interact. This interaction is expressed on work package level as a functional relationship, in particular for the linkage of direct cost items labour and equipment with their activities in the WBS. These items are defined as Time-Dependent (TD) and will vary if duration uncertainty in these activities occurs. If activities will take longer than initially planned, due to schedule uncertainty, TD direct cost will increase. Likewise, if activity durations take shorter than expected, cost will decrease. Time-Independent (TI) cost items are not related to the project schedule. These cost may be uncertain, but not because of time (AACE, 2011). In order to conduct the simulation experiments in the next chapter, key direct cost figures are presented in Table 1. These ranges are used to develop a set of fictive infrastructure projects. Table 1 Key direct cost figures civil engineering projects (Potts & Ankrah, 2008) Direct cost Description Proportion range to direct cost Material and Subcontractor Time-independent TI 80% - 90% Labour and Equipment Time-dependent TD 10% - 20% Indirect cost Indirect cost are expenses incurred, in order to manage and deliver the elements of direct cost items that are employed on the job. These costs, defined in this report as project overheads, are not directly associated with one specific work package in the WBS. 1. Project overheads consists of types of cost such as job supervision, site office facilities, temporary utilities, permits and fees. Most of these cost are related to a group of activities or total project duration, and are defined as TD indirect cost items (Bennett, 2003). 26 Theoretical framework

28 Time-Dependent and Time-Independent indirect cost: In principal, a similar functional relationship between TD indirect cost items and a group of activities/project duration exist. These items are not directly linked via work packages in the WBS, making the analysis of the cost effect of schedule uncertainty more difficult. It is examined in this thesis whether an inconsistent direct and indirect cost estimate will be estimated, if the functional relationship between probabilistic costing and scheduling is ignored. This is done by the assignment of cost items to activities in the schedule. It is considered that the IPA method demonstrates a qualitative improvement to probabilistic costing (AACE, 2011). The key indirect cost figures are shown in Table 2. These cost vary between 12% (e.g. quay-wall delivery) and 25% (e.g. complex projects) as the ratio of indirect cost to direct cost. Table 2 Key indirect cost figures civil engineering projects 3 Indirect cost Description Proportion range to indirect cost Site overheads Time-independent TI 15% - 20% Site overheads Time-dependent TD 80% - 85% Further detailing A detailed cost estimate in a D&C or DBFM type tender often includes a further detailing cost element. This element defines the incompleteness of information in the early planning phases, related to not completely work out parts of the design. This element is estimated based on reference projects or as percentages of the direct costs. Common percentages in D&C projects are between 1% and 5% (Schenk, 2014), depending on level of detail of design Contingency cost Contingency cost is the amount of money that experience has demonstrated must be added to base cost estimate (sum of Direct, Indirect and Further detailing costs in Figure 7) to cover project uncertainties (Burroughs & Juntima, 2004). Contingency costs are defined in this report as the difference between probabilistic costs including uncertainties at a Pxx level (xx = level of certainty) and deterministic costs excluding uncertainties. These costs are used as measure to numerically compare the results of the IPA and SPA methods Time management Time management is the process in which contractors develop the project schedule. This schedule represents the plan for executing activities including durations, dependences and other planning information (Pekelharing, 2014b). Traditional scheduling has been around since Henry Gantt developed the first Gantt chart for the construction of the Hooverdam and American Interstate highway in The Gantt chart is a graphical representation in time, in which a list of activity durations are showed in horizontal bars. It provides an proper overview of the sequence and timing of activities, and insight into the total required and available project duration (Mubarak, 2010). The introduction of milestones, as diamond shapes, concluded Gantt s view of project control. As schedules became more extensive and complex, examination of the project was accomplished through SE (Figure 8). In project scheduling usually not all activities succeed each other in time, and 3 These figures are typical for construction projects, in which VolkerInfra is involved (Schenk, 2014). 27 Theoretical framework

29 logical relationships were identified between activities. This led to the development of the Critical Path Method (CPM), which calculates the longest, or critical path, between the start of the project and it s last activity (Mubarak, 2010). Hence, the CPM determines the earliest possible delivery of the project. Other activities in the project, whilst not being part of the critical path, could after analysis be delayed in time without impact on the end date. This delay is expressed as float in time. A total float of 0 days is the basis for the critical path. Logical relations between activities are represented in a network structure. The total duration of a simple project (D t ) with two sequences of activities is a combination of the calculation rules for serial and parallel systems (4). (4) It is evident that an estimate of total project duration is subjected to various forms of uncertainty (Pekelharing, 2014b). The Programme Evaluation and Reviewing Technique (PERT) was initially developed to include uncertainty into the schedule estimate, by calculating average activity durations from optimistic, most likely, and pessimistic values. This type of scheduling is still referred to as deterministic scheduling, because the end-delivery milestone is represented as a single number. Further development of the PERT led to the introduction of probabilistic scheduling. The optimistic, most likely, and pessimistic values are then used to statistical analyze inherent variability in activity duration. This form of uncertainty is caused by the size and experience of the team, availability of equipment, weather, coordination etc (Mubarak, 2010). There are two fundamental differences between probabilistic scheduling and costing (Covert, 2013). First, activity durations are often measured in workdays and second, total project duration cannot be calculated by adding together durations of all activities. Therefore, the logical time distributed network needs to be analyzed. An important aspect of project planning is the optimization of the project schedule. Efficient use of time can improve the quality of a bid significantly. Most contractors will utilize the same cost specifications from subcontractors, equipment and material suppliers. So one of the few ways to distinguish oneself in the bid is by considering alternative methods of construction, sequence of construction and the level of utilization of resources to reduce project duration (Potts & Ankrah, 2008). An effective schedule will substantially save project cost, because time is money. Project uncertainty makes it difficult to optimize the project schedule on beforehand, due to the arrangement of activities. It treats every activity duration as a random variable, making it difficult to determine the critical path. Project scheduling software takes into account the variance of activities in a MC-simulation and determines for each iteration the critical activities. At the end of the simulation the criticality index expresses the probability that a particular path (Y) will have a longer duration than the other paths (5) (Covert, 2013). It also measures the probability that an activity lies on the critical path. (5) 28 Theoretical framework

30 The criticality index is useful information for the project team before project execution starts. The statistical analysis on project uncertainty in scheduling and the insight in the arrangement of activities in the network structure is necessary, in order to continuously optimize the project schedule until project time objectives are met. The probability of completing the project on time can be calculated with the following equation (6) (Covert, 2013). Project schedules are developed for various participants in the contract, which all have different requirements and levels of interest (AACE, 2010). The correct level of detail in the schedule allows the user to understand the information and enables communication and reporting. The schedules applied in the simulation experiments in this thesis are with the same level of detail as the Project Master Schedule (PMS) as shown in Table 3. In practice, a Project Coordination Schedule (PCS) is preferred to simulate a probabilistic planning and highlight strategic project elements (Hulett, 2011). With respect to this thesis, the amount of activities in a PCS are too time-consuming to develop. The PMS still provides high-level information, in order to evaluate the IPA and SPA methods. Table 3 Schedule levels of detail (Pekelharing, 2014a) Level of Detail Description Range of max. defined activities 1 Project Master Schedule PMS Summary Master Schedule SMS Project Coordination Schedule PCS Working Level Schedule WLS 400x 1200x In a consistent project schedule dependences exist between activities, due to the implementation of logical relationships in the schedule. A type of relationship between two finish dates, that are related to each other, can be caused by sharing a common predecessor (Covert, 2013). Systemic uncertainty between activity durations, expressed with the Pearson correlation, is often caused by mutual environmental and spatial factors (Mubarak, 2010). Systemic uncertainty in probabilistic scheduling is explained in section Contingency time The scheduling of project uncertainty, in order to estimate time contingency, provides insight into the complexity of the forms of uncertainty and their impact on the critical path. The estimated time buffer on the critical path ensures that a certain amount of project uncertainty can be absorbed (Pekelharing, 2014b). This provides the contractor a level of certainty that contractual milestones are achieved Event uncertainty The application of project uncertainty within the risk management process focuses on the assessment of event uncertainty (Chapman & Ward, 2011). Event uncertainty is defined by a set of individual risk and opportunity events (E i ), which have a probability of occurrence and an associated impact. The probability distribution is expressed with the Bernoulli distribution and has two possible states (7) (Dekking et al., 2005). 29 Theoretical framework (6)

31 A state in which the event actually occurs and has impact ( ) on project objectives with a specific probability ( ) and a state in which the event doesn t occur with the residual probability ( ). More precise, it means there is a probability that some estimate of additional cost or time will be added or subtracted. Historical data can be used to assess the probability and impact of risk and opportunity events. (7) This form of uncertainty becomes more interesting when multiple events are identified, since the statistical analysis of event uncertainty then becomes combinatory (Covert, 2013). Any combination of risk and opportunity events that potentially could occur should be taken into account. In case of multiple events, the possible states (S) are defined by 2 n. An example of three risks is illustrated in Figure 9. Risk 1 Risk 2 S1 S4 S2 S5 S7 S6 S3 Risk 3 S0 Figure 9 Venn diagram of multiple events (Covert, 2013) A probabilistic analysis on cost related risks and opportunity events is usually executed simultaneously with inherent variability in the cost management process (CROW, 2010). The outcome of this analysis is used to determine the appropriate budget for contingency cost. However, A separate probabilistic analysis on event uncertainty can be executed in more large-scale infrastructure projects in the risk management process. These analysis only determine the budget for event uncertainty. Risk and opportunity events that have an impact on the project schedule, cannot be added afterwards due to the arrangement of activities in the network structure (Covert, 2013). Hence, the identified event uncertainty serves always as extra input for probabilistic scheduling. It requires risk management to be continuously linked and interdependent on time management. Time related risks and opportunities can have an impact on activities in the original schedule, or bring possible changes to the schedule network defined as branching (Primaned, 2013). Probabilistic branching inserts a series of activities in the schedule network with a set of enabling switches, based on the probability of occurrence of these additional or repeated activities (e.g. failed test) (Covert, 2013). Conditional branching changes values in existing activities (e.g. resources), if certain events occur in the project. 30 Theoretical framework

32 Risk Management Risk management is defined as a generic process that coordinates activities to manage and control a project related to risks and opportunities (ISO31000, 2009). The purpose of risk management is to identify, analyze, treat and monitor the risk and opportunity events continuously throughout the system life cycle and to communicate the risk assessment of event uncertainty to relevant stakeholders (ISO15288, 2008). It includes minimizing the unwanted results of risks and maximizing the wanted results of opportunities. The goal of risk management of an infrastructural project before contract award is twofold (Berkelaar, 2014). Firstly, risk management contributes to the Economically Most Advantageous Solution (EMAS) products such as the traffic hindrance plan and the development of the risk mitigation plan. Secondly, project buffers are estimated as part of risk management to reserve time and budget for the occurrence of risk events and other forms of scheduling and costing uncertainty. The integration of the probabilistic analysis with the central risk register is an essential item, in order to formulate a sharp but realistic bid in cost and time (Berkelaar, 2014) Process In order to manage and formulate risk and opportunity events explicitly, contractors have tailored the risk management process to fit their projects. The risk management process consists of seven generic steps (Figure 10), based on the Dutch RISMAN method (van Well-Stam D. et al., 2003). 1. Set up RM RMP Risk register 2. Identify / Update 3. Allocate 4. Quantify Risk register 5. Determine mitigating measures 6. Evaluate effect of mitigating measures 7. Analyze and report Analyzes and reports Figure 10 Risk management process (Berkelaar, 2014) The first step in this process is the set-up of the Risk Management Plan (RMP). This document sets out the strategic requirements for the risk management process. The main issues in the RMP focus on the project-specific approach, including applied resources and techniques, to ensure all aspects of the project are examined for event uncertainty. The RMP sets out the type, content, and frequency of reports, and describes the roles of the risk owners (Lester, 2014). 31 Theoretical framework

33 The set-up of the risk register involves the formulation of project-specific risk categories (e.g. discipline, phase or geographic location), criteria (e.g. cost, time, probability, safety, environment and quality) and threshold levels. If these issues are clearly defined, the risk register will act as a repository for all identified risks and opportunities. The second step entails the application of risk identification techniques, in order to examine each element of the project. This examination can be done according to the WBS. Each work package is examined for event uncertainty from seven RISMAN-brillen (van Well-Stam D. et al., 2003) (technical, legal, organization, political, financial, spatial and social), such that a complete risk identification is executed. The consideration of multiple risk views aims to optimize efficiency through all project disciplines. The identified risk and opportunities are formulated as an event with cause and consequence in the register, as illustrated in Table 4. This is done according to the SMART criteria (Project Management Institute, 2008). Table 4 SMART example risk identification in risk register ID Risk Cause Consequence R022 Assumption to leave out object 17 from tender scope is wrong. Client cannot be persuaded to skip object 17 before May 12th Extra cost ( ) due to realization of object 17. Delay of 4 weeks on critical path. The third step in the risk management process focuses on the allocation of risks, which is done to the party that is best suited to bear the risks and/or execute the mitigating measures. Internal allocation refers to responsibilities in the contractor s organization. External allocation is done in accordance with the client. The allocation of responsibilities in the project helps to create a pro-active attitude in risk control. The fourth step involves the quantification of event uncertainty. It is an essential part for risk prioritizing and serves as input for the probabilistic analysis. Three approaches can be applied to quantify the events: qualitative, semi-quantitative (S-Q) and fully quantitative (Full-Q). The application of the approaches is dependent on project phase and complexity. The qualitative approach only ranks events in order of importance, while the semi-quantitative approach uses project-specific scoring classes to determine probabilities and consequences. The full quantitative approach determines a set of values for probability (%), direct cost ( ), and time (working days). These values are documented in the risk register and serve as input for probabilistic costing and scheduling. A lack of knowledge about the exact consequence values expresses the inherent variability in risk management. The consequence value is illustrated in Table 5 by the L, T U values. In most cases the triangular distribution is applied for the estimate of event consequence (CROW, 2010; Primaned, 2013). Table 5 example risk quantification in risk register ID Full-Q R022 (%) Direct cost ( ) Time (work days) P L T U L T U Theoretical framework

34 The fifth and sixth step of the process describe the preventive and corrective mitigating measures and risk response strategies (Figure 11). Preventive measures reduce the probability and/or consequence before the risk occurs, whereas corrective measures deals with the effect of the consequence after the risk occurred. Likewise, similar measures exist to exploit opportunities. The effects of mitigating measures are assessed with an initial (score before implementing preventive measures) and residual (score assuming preventive measures are executed and effective) quantification. Preventive measures form part of the bid and are scope for the contract phase. Corrective measures are estimated on basis of the residual risk profile with aid of the probabilistic analysis and thus form the project buffers. In time this risk profile will change and updates in the risk register are required. Hence, risk management is not a one-time exercise but a cyclic process. Figure 11 Risk response strategy (Berkelaar, 2014) The seventh step provides insight in the top risks and opportunities. At this point, the risk register is coupled to the costing and scheduling process for the probabilistic assessments Linkage of risk register The integration of the full quantitative risk register with costing and scheduling is an essential part, in order to execute the probabilistic analysis and optimize the project. Linking the risks and opportunities to their appropriate activities in the schedule provides insight into the potential impact on the critical path and the required risk action. Less important risks can then be accepted, others insured or mitigated in preventive or corrective manners. Active risk control may save costs, but requires a pro-active approach of the risk management process. It is possible that the occurrence of events in risk management are subjected to systemic uncertainty, expressed as statistical dependence. An example of this type of uncertainty is the dependence between the occurrence of extreme wind and wave heights in the planning of offshore installations (Wolfert, 2014). The SSK-2010 advises not to apply statistical dependence in risk management, if not investigated properly (CROW, 2010). The effect of this uncertainty is explained in the next section. 33 Theoretical framework

35 4.1.3 Systemic uncertainty Systemic uncertainty exists in the cost, time and risk management process and is concerned with understanding and managing causes and effects. It is proposed for this research to divide systemic uncertainty in statistical and functional dependence (Figure 12). The difference between these two types of dependence is that functional dependence absolutely determines a relationship between variables (Gradel & Väänänen, 2011), whereas statistical dependence implies that the distribution function of a variable is influenced by another random variable (Dekking et al., 2005). The focus in this report is on statistical dependences existing in the management processes and functional dependences, as the cost-schedule relationship, between these processes. The examination of statistical dependence is further decomposed into dependent Bernoulli distributions in risk management, and Continuous and Discrete distributions in cost and time management (Figure 12). This distinction is concerned with the limitation of the Pearson correlation coefficient to simulate dependent Bernoulli random variables in a MC simulation (Madsen & Birkes, 2013). Systemic uncertainty Statistical Functional Bernoulli Continuous Discrete Figure 12 Systemic uncertainty decomposed Statistical dependence Statistical dependence involves uncertainty about statistical relationships between random variables or events in the project. In probability theory, dependence refers to any situation in which random variables or events do not fulfil mathematical conditions of statistical independence (Dekking et al., 2005). Statistical independence between two events, e.g. in risk management, means that the occurrence of one event does not affect the probability of the other event (8). Likewise, two random variables in cost or time management are statistical independent, if the realization of one variable doesn t consistently affect the probability distribution of the other (9). In statistical independent cases, the conditional probability functions are exactly the same as the marginal probability functions (Dekking et al., 2005). (8) (9) 34 Theoretical framework

36 In the infrastructure industry the assumption of independence is usually adopted, according to cost experts of DACE meeting 4, because of the difficulty of modelling statistical dependence. This assumption is inconsistent with reality, since statistical dependence is common in infrastructure projects that are decomposed into smaller work packages (Arizaga, 2007). In general, the more work packages are distinguished, the greater the likelihood that statistical dependence between variables to a great or lesser extent exists (Chau, 1995). Suppose a road project is decomposed into four subsystems in an object tree (Figure 13), which during project planning are further specified to a lower level of detail. In this case, it is very likely that statistical dependence exists between cost items due to the application of steel or concrete elements in at least three subsystems. Road Tunnel Viaduct Figure 13 Object tree of example infrastructure project Wildlife tunnel Markings The usual approach to deal with statistical dependence between random variables, with exception of Bernoulli random variables, is the Pearson correlation coefficient (ρ) (Vrijling & van Gelder, 2009). This correlation coefficient is a measure for the linear dependence of two random variables and indicates how strongly these variables change with each other. The Pearson correlation coefficient (10) is derived from the mixed central moments or covariance ( ) and variances ( ) (Dekking et al., 2005). A calculation of the Pearson correlation coefficient between two cost items is performed in appendix B. In which: (10) An approach to deal with statistical dependence in a project that is decomposed in work packages is the development of a correlation matrix (Arizaga, 2007). If historical project data is available, statistical dependence between these work packages can objectively be analyzed. The problem arising, when calculating the correlation coefficient with this approach, is that the statistically analyzed coefficients grows rapidly with the amount of work packages in the project. A matrix with 100 variables requires to estimate 4,950 correlation coefficients in the project (Arizaga, 2007). In addition, historical project data about activity duration, units and prices is scarce in the infrastructure industry (Gelder, 1999). Therefore, subjective judgment is often included in the estimate of the Pearson correlation coefficients. The SSK-2010 present a practical methodology to allow subjective judgment in the probabilistic cost analysis. 4 Meeting about the added value of probabilistic costing, organized by SIG PRA of DACE on 5 th of June 2014, with participants from the public and private sector in the Dutch construction industry. 35 Theoretical framework

37 Continuous and Discrete distributed random variables The application of statistical dependence in the cost and time management process entails the identification of relationships between continuous and discrete distributed random variables. These variables, subjected to inherent variability in costing and scheduling, are activity durations, units and prices. A straightforward example of a statistical strong dependence in the probabilistic costing exist between the cost items excavation and transport of sand. The amount of sand can be modelled as a triangular distribution with the 3-point estimate, in which the most likely amount of sand is based on technical drawings. The upper and lower quantity values are based on geotechnical variability and experience. Now suppose that a low amount of sand is encountered in the project. Consequently, the estimated quantities of excavation and transport in the assessment should both corresponds to the optimistic tail values. A low quantity in one correlated cost item, reinforces low quantities of other items. This is defined as a positive correlation. A weaker cost dependence between material prices of sheet piles and structural steel is caused by the common price fluctuation of raw steel in the world marketplace. The most likely prices of these materials are based on current market conditions, while the width of the spread is determined by market expectations. Figure 14 illustrates the dependence structure, in which the nodes represent price information variables and links represent dependences. It shows that when the sample value from the price of structural steel is large, the sample value from the price of sheet piles is also likely to be large. Therefore, there is a higher chance of obtaining a large sum of both cost items compared to the independent value. The presence of non-common production factors potentially reduces the strength of the statistical dependence. These factors influence the inherent variability on one specific price item. Raw steel Production factor Sheet piles Structural steel Production factor Figure 14 Dependence structure of cost items with common cause Similar statistical dependences between the duration of activities are modelled with the Pearson correlation coefficient in time management. These dependences are often caused by common causes such as weather and site conditions Bernoulli distributed random variables The application of systemic uncertainty in the risk management process is related to the statistical dependence of risks and opportunities. In probability theory, these events are referred to as dependent Bernoulli distributed variables. The correlation structure for these variables cannot be described with the traditional Pearson correlation coefficient (10). Normally, the planning of an infrastructural project doesn t include statistical dependence between risk and opportunity events. This is caused by a lack of historical data about the mutual occurrence of 36 Theoretical framework

38 events in projects, and the constraint of planning and budgeting software 5 to support other correlation structures besides the Pearson correlation coefficient (Madsen & Birkes, 2013). The limited literature available (Vrijling & van Gelder, 2009) does propose an analytical solution for an alternative correlation structure. This structure only restrict itself to two statistical dependent Bernoulli distributed variables ( and ), in which four degrees of dependence between events are identified. and are uncorrelated. and are 100% positively correlated. and are 100% negatively correlated. and are partially correlated (most general situation). It is derived from literature review that the correlation structure between two Bernoulli distributed events can only be described when certain boundary conditions are met (Vrijling & van Gelder, 2009). Risk registers often contain a large amount of risks and opportunities. Further research is required to analyze available project data and identify statistical dependent events in infrastructure projects. Especially if such dependences exist, the impact of correlation in the risk register should be examined to enhance future control and controlled results of projects SSK-2010 principles In the SSK-2010 guideline (CROW, 2010) a standard is described about the employment of probabilistic costing in the planning of infrastructure projects. This guideline prescribes the use of a triangular distribution to assess inherent variability. Event uncertainty should be quantified as probability times consequence, with the associated consequence estimated with the triangular distribution. In order to assess statistical dependence, the SSK-2010 proposes to include subjective judgment in the cost estimate. It is prescribed to fully correlate all quantities and all prices with the Pearson coefficient to each other. This principle prevents the specification of a large amount of correlation coefficients. Hence, two probabilistic cost estimates are simulated: 1. Statistical independent analysis with iterations. a. No correlation between events in risk management. b. No correlation between units and prices in cost management. 2. Statistical dependent analysis with iterations. a. No correlation between events in risk management. b. Full correlation (ρ=1) between all quantities in cost management. c. Full correlation (ρ=1) between all prices in cost management. The results of the statistical independent analysis will be used to compare the relative importance of the forms of uncertainty, with respect to their contribution to the project cost variance. The statistical dependent analysis allows management to analyze probabilities of exceeding cost targets. The P70 level of risk acceptance is used to derive the required contingency cost. 5 Primavera Risk Analysis and typically make use of the Pearson correlation coefficient. 37 Theoretical framework

39 Sum of cost items The effect of Pearson correlation When considering systemic uncertainty it is important to recognize the significant role that Pearson correlation coefficients have on project schedules and budgets. Positive statistical dependence is the most common kind of systemic uncertainty and substantially increases variability, while negative statistical dependence reduces variability (Chapman & Ward, 2011). However, the latter is only applied for cases with two random variables. This is because if variable X 2 and X 3 are both negatively dependent on X 1, then it is very likely that positive dependence exists between X 2 and X 3. This positive dependence will contribute to an increase in variance in the summation of these variables (Chau, 1995). Figure 15 illustrates an example with on the Y-axis the sum of possible costs for structural steel and sheet piles, and on the X-axis the Pearson correlation coefficient between the prices of both cost items. The quantities of both items are considered statistical independent. This example is elaborated in part two of appendix B ,5 0 0,5 1 Pearson correlation coefficient between cost items (ρ) Figure 15 Sum of two cost items subjected to statistical dependence +1 St. dev. +2 St. dev. -1 St. dev. -2 St. dev. Mean Mode It can be concluded from this example that failing to account for the Pearson correlation coefficient (ρ=0), underestimates the variance of the sum of project cost items when positive statistical dependence exists (ρ>0). Especially, Pearson correlated distributions with a large bandwidth can exert a large influence on the project (Hulett, 2011) Functional dependence The interconnection between project cost and time, such as the cost-resource loaded schedule in the IPA method, is defined as a type of functional dependence (Shr & Chen, 2006). This type of dependence strictly defines the relationship between variables, in which one variable uniquely determines another. The formulation of these relationships is typically done once the project is decomposed into work packages, and TD and TI costs are identified. The main benefit of the inclusion of the functional cost-schedule relationship in the statistical analysis of uncertainty is to probabilistic cost estimate. The integrated costs and resources in the schedule of the IPA method, do not have an impact on the time results. Therefore, there exists no difference in probabilistic schedule results between the SPA and IPA methods (AACE, 2011). The costschedule functional dependence only works one way. The next chapter will explicitly define the costschedule relationships in the IPA method. 38 Theoretical framework

40 3.2 Methods Project uncertainty, as defined in the first part of this chapter, is quantified in order to perform a probabilistic analysis. The second part of this chapter describes the process of the IPA and SPA method. The DA method doesn t define project-specific uncertainty, but instead applies an acrossthe-board percentage based on historical data and gut feeling. This method is described in this part Probabilistic analysis The most popular technique to execute a probabilistic analysis is the MC simulation (AACE, 2011; Covert, 2013). Statistical analysis, based on analytic techniques of applied probability and statistics, is also used to analyze probabilities of exceeding schedule and budget targets. The application of the MC simulation is preferred in project planning due to its time-efficiency and flexibility. Moreover, it is relatively easy to add large numbers of probability distributions and their associated dependences together into a single operation (AACE, 2011; Hulett, 2011) MOM The analytical technique applied for statistical analysis in this report is the Method of Moments (MOM). The MOM relies on exact statistical calculation of moments, in order to derive project cost and duration estimates. Moments provide a source of information about the shape of a probability distribution and are classified in raw, central and standardized moments (Covert, 2013). The first raw moment is the mean (µ). Central moments measure the dispersion around the mean, such as the variance ( ). A standardized moment is skewness, which is defined in chapter 3.3. Analytical expressions are derived quite easily, but are more difficult to generalize to complex situations such as dependent schedule data and non-identically mixed distributions (Gelder, 1999). It is suitable for simple probabilistic cost estimates, in order to derive the variance of systems in the project MC simulation The MC simulation translates the specified project uncertainty into their potential impact on project objectives. The MC method computes a project model many times, typically iterations for costing (CROW, 2010) and iterations for scheduling (Primaned, 2013), with input values from the cost, time and risk management processes. These values are chosen at random for each iteration from the probability distribution of these values. A MC-simulation is carried out with the aid of computer software. It is a particularly useful tool, when complex relationships are involved like multiple paths and branching in the schedule network (Chapter ). The introduction of advanced computer software in recent years (e.g. Primavera and Polaris) enables the integration of probabilistic costing and scheduling into a single MC-analysis. The recommended practice about the IPA method (AACE, 2011) describes an improvement in the cost management process over the SPA method, which estimates project cost without explicit reference to schedule uncertainty. Both the IPA and SPA methods are applied in the infrastructure industry and enable management with a basis for decision-making under uncertainty about (Chapman & Ward, 2011; Hulett, 2011): The likelihood of completing the project on budget and on end-delivery date. The required contingency needed to provide the desired amount of certainty. The most important sources of uncertainty so that a contingency plan can be developed. 39 Theoretical framework

41 3.2.2 SPA method The separated probabilistic assessment (SPA) method (Figure 16) analyses project uncertainty isolated in the cost, time and risk management process. Hence, the MC simulation can only analyse either the probability of exceeding schedule or budget targets separately. This method is currently applied in large-scale D&C and DBFM tenders in the Netherlands. Systems Engineering Deterministic scheduling Input Discipline Input Discipline Input Discipline Input Discipline Deterministic costing Risk Management Variability on D 1 RISMAN Variability on Q, P 1 MC simulation on schedule Events on Time 2 Quantitative Risk Register Events on Cost 2 MC simulation on cost Probabilistic scheduling 4 Probabilistic costing Statistical dependence Figure 16 SPA method process (Modified) (Berkelaar, 2014) 3 3 Statistical dependence The SPA method starts with decomposing of the project into manageable work packages according to SE. These work packages contain all project information and establish the baseline for deterministic costing and scheduling, and risk management. Subsequently, project uncertainty is applied in the following order: 1. The specification of inherent variability in the project is dependent foremost on the experience of the person estimating schedules and costs. The probability density functions on activity durations (D) are applied in the scheduling process, whereas the distribution on quantities (Q) and prices (P) is evaluated in the costing process. 2. Event uncertainty is evaluated in the risk register by the responsible risk manager in the project. In this document a strict distinction is made between risks and opportunities on cost and/or time. Time related events are assigned to the activities in the deterministic schedule and serve as input for the MC simulation on time. Likewise, cost related events are integrated in the cost estimate. Events that have an impact on time and also have impact on TD direct costs are coupled via the risk register. These events serve as input for both MC simulations on costs and schedule. The input of inherent variability and event uncertainty enables the computer software to run two statistical independent MC simulations on cost and time. 40 Theoretical framework

42 i. An example of a coupled cost-schedule event is risk R022 in Table 4. This event causes a delay of 4 weeks, in which object 17 has to be realized. The realization of object 17 involves a TI material cost item and a TD labour cost item. The labour cost item is functionally dependent on the estimated 4 weeks delay. 3. Statistical dependence measured with the Pearson correlation coefficient between activity durations in probabilistic scheduling, and between quantities and prices in probabilistic costing is quantified, in order to run two statistical dependent MC simulations. 4. The functional dependence between costing and scheduling is taken into account on a rudimentary level for the estimate of TD indirect cost. This step in the SPA method process has no scientific base, but is executed based on common sense. i. Firstly, the output of probabilistic scheduling is analyzed in order to derive the probability of exceeding the contractual end-delivery milestone by for example a month. Suppose, this month delay has a probability of 10%. ii. Secondly, a new identified risk on cost is quantified in the risk register with the derived probability value from probabilistic scheduling. The risk consequence is then equal to the TD indirect cost of a month. Interest and maintenance cost items make up the bulk of these costs in a DBFM tender. Suppose, an interest rate of 3% over 140 Million is applied and the TD indirect costs are estimated at 345,000 per month. iii. Thirdly, a final MC simulation on cost is executed to account for the indirect cost effect of schedule uncertainty on a rudimentary base. This simulation will then include a risk with a probability of 10% with an impact of 345,000. The outcome of the SPA method (Figure 17) provides two reliability intervals on cost and schedule, that predict the end-delivery date or budget (X-axis) within a certain probability value (Y-axis). The marginal probability of completing the project within target point (c) is illustrated in Figure 17 with the grey area and is defined as. 41 Theoretical framework Figure 17 The outcome of the SPA method (Modified) (Covert, 2013) IPA method The integrated cost-schedule probabilistic assessment (IPA) method (Figure 18) analyses project uncertainty in the cost, time and risk management simultaneously in a cost-resource loaded schedule. It enables management to execute a single MC simulation on the joint probability of exceeding schedule and budget targets.

43 The IPA method adopts the WBS as a common basis for the integrated probabilistic approach and links the cost, schedule and risk information to work packages. Project uncertainty is applied in the IPA method, after the cost-resource loaded schedule is developed. Systems Engineering Deterministic costing Deterministic scheduling Input Discipline Input Discipline Input Discipline Risk Management Identify TD and TI cost items 1 Assign to activities in schedule RISMAN Variability on D, Q, P 2 MC simulation on cost-loaded schedule Integrated probabilistic analysis Events on Time and Cost 3 Quantitative risk register Figure 18 IPA method process Statistical dependence 4 1. The development of the cost-resource loaded schedule is initiated by the identification of TD and TI cost items in the project. These cost items have to be assigned to their associated activities with a common daily time unit in the deterministic schedule. This places cost items correctly in time, so the functional cost-schedule dependence is completely evaluated. i. Direct cost items ( ) that vary with the duration of an activity (e.g. labour, equipment) and direct cost items ( ) not related to schedule duration (e.g. material, subcontractor) are linked to activities in the schedule, in order to estimate the cost of an activity (A) (equation 11). This equation defines the functional dependence between cost and schedule on work package level. The summation of all activity costs is then equal to the project direct costs. ii. Indirect cost items which are decomposed in TI ( ) (e.g. site establishment, insurance) and TD ( ) (e.g. project management, interest) costs are linked to hammock activities in the schedule, in order to estimate the cost of a hammock activity (H) (equation 12). The summation of all hammock activities is equal to the project indirect cost. A hammock activity is defined as the summary of a group of activities hanging between project start and end date (Primaned, 2013). Therefore, TD indirect cost are functional dependent on the duration of a group of activities. 2. The inherent variability on activity durations (D), quantities (Q) and prices (P) of TI and TD cost items is then simultaneously applied in the integrated schedule. 42 Theoretical framework

44 3. Event uncertainty as quantified in the risk register on time and cost is implemented in the cost-resource loaded schedule, in order to evaluate the impact of risks and opportunities. In contrast with the SPA method, no more coupling of time and TD direct cost in the risk register is required. This is taken into account by the defined functional dependences (equation 11 and 12) in the cost-resource loaded schedule. A single MC simulation is executed to evaluate the statistical independent results of the combined effect of cost and schedule uncertainty. 4. Statistical dependence expressed with the Pearson correlation coefficient on activity durations, quantities and prices is applied in the integrated schedule to perform a single statistical dependent MC simulation. (11) In which: (12) The outcome of the IPA method (Figure 19) is a joint probability distribution, which predicts the project budget (X-axis) and end-delivery date (Y-axis) within a certain probability value (Z-axis). The conditional probability of completing the project within both cost (x) and schedule (y) objectives is defined as. If the conditional probability functions are equal to the marginal probability functions, then cost and schedule are probabilistic independent (equation 8) (Dekking et al., 2005). These statistical conditions are demonstrated for the example case with the Bayes Theorem in the chapter Figure 19 The outcome of the IPA method (modified) (Covert, 2013) 43 Theoretical framework

45 Development of cost-resource loaded schedule Two important issues must be addressed with respect to the development of a cost-resource loaded schedule in the planning of an infrastructure project. These two issues are related to the linkage of cost items with activities in the deterministic schedule, which is illustrated by the dotted lines in Figure 18. The first issue focuses on the distinction between TD and TI cost items. This distinction is only employed in the IPA method and requires a different level of thinking about cost items than the SPA method. The SPA method only makes distinction between direct and indirect cost items, whereas the IPA method makes an extra distinction between TD and TI cost items. Therefore, cost items in the IPA method are arranged in four groups. Especially, understanding about TD direct cost items in the Dutch infrastructure industry should be increased 6. The second issue focuses on the difference in cost and schedule structures. These structures often become disjoint in the planning of an infrastructure project (Hulett & Campell, 2002). Project schedules are continuously updated, whereas cost expert will have lots of work in the final stage of project planning. Therefore, serious effort is required to coordinate the level of detail in costing and schedule on each other in project planning. This effort is required to enable the linkage of cost items to activities, in order to develop the cost-resource loaded schedule. These two issues, related to the development of the cost-resource loaded schedule, demonstrate that the IPA method requires a relatively higher level of effort to perform cost and schedule estimates in the planning of an infrastructure project than the SPA method DA method Project estimates of durations, units and prices are often based on most likely values (DACE, 2007). The DA method considers project uncertainty by relying on predetermined or mandated percentage of the most likely base estimate (Burroughs & Juntima, 2004). These percentages determine the project cost and schedule contingency level. The advantages of this method are its simple application and consistency. The DA method is utilized most in the project planning of traditional and specified contracts, in which a fixed contingency percentage is used (CROW, 2010). The disadvantage of this method is the fact that it removes specificity of the forms of uncertainty from the costing and scheduling process, making it inflexible to more complex and poorly defined projects. A more flexible variant is consulting a skilled estimator to use his expertise to assign the contingency levels. The experts typically considers a range of across-the-board percentages for contingency cost, from which the experts will select a specific level (Burroughs & Juntima, 2004). This selection is based on the project contract, context, complexity and turnaround time. If this flexible variant becomes more structured and project uncertainty is further defined, then the estimate tends to move towards probabilistic costing and scheduling. The ranges of percentages applied in this report are shown in Table 6 7. These percentages are used as reference values, in order to specify a realistic amount of project uncertainty in the simulation 6 This observation is derived from conversations with experts, which all have a different perception of TD direct cost items in the infrastructure industry. 7 These figures are typical for construction projects, in which VolkerInfra is involved (Schenk, 2014). 44 Theoretical framework

46 experiments. A typical percentage for contingency time in the early stages of project planning is set at 5% of the deterministic schedule 8. Table 6 Deterministic cost percentages Type of uncertainty Across-the-board cost percentages Inherent variability 1% - 3% Event uncertainty 2% - 5% (occasional up to 10%) Pearson correlation Unknown The range in Table 6 for inherent variability and event uncertainty are determined based on subsequent costing of reference projects. Statistical dependence expressed with the Pearson correlation coefficient in cost and time management is not applied by VolkerInfra. As a result, there is no data available about the potential impact on budget. In principle, subsequent costing of the DA method demonstrates a black box principle. Experience and common sense prove that cost contingency must be added to cover project uncertainty, however no specific insight is obtained in the contingency cost structure by the DA method (DACE, 2007). This is lack of insight is described by the management information concept Management information The estimate of contingency levels with the probabilistic methods is based on statistical analysis of the identified project uncertainty. In contrast, the deterministic method applies a range of predetermined percentages over the base estimate to estimate the contingency levels. It is good to be aware of the fact that not all project uncertainty will be identified or quantified correctly in project planning. Hence, a probabilistic analysis is dependent on input variables (Trash in, Trash out) and only statistically analyzes identified forms of uncertainty. The deterministic method does take the unidentified forms of uncertainty in project planning into account in the contingency estimate (DACE, 2007). Therefore, a combination of the deterministic and probabilistic methods provides management with an overview of information related to project uncertainty. This management information is defined as the amount of statistically analyzed project uncertainty in relation to the predetermined percentage of the base estimate (DACE, 2007). The management information of contingency cost is indicated with orange boxes in Figure 20. The IPA method provides the most management information, because it also includes the combined effects of schedule and cost uncertainty (functional dependence). Furthermore, information is obtained in the IPA and SPA method about inherent variability, event uncertainty and statistical dependence. Management information enables decision-making about project uncertainty and works as an incentive for progressive optimization of schedule, cost and resource requirements (Project Management Institute, 2008). 8 Typical percentage applied by consultant project control from Primaned Projectadvies bv. 45 Theoretical framework

47 Profit General overhead Contingency Unidentified Functional Statistical Event Variability IPA Unidentified Statistical Event Variability SPA Unidentified DA Cost Direct Indirect Further detailing Figure 20 Management information in price of bid (Modified) (DACE, 2007) With respect to the comparison of methods, the probabilistic methods provide extra insight compared to the deterministic method in the following issues (DACE, 2007): Information about the contribution of forms of uncertainty to the total project variance. Information about the effectiveness and efficiency of possible mitigation measures. Project control in order to steer on the required probabilities of achieving objectives. 46 Theoretical framework

48 3.3 Mechanism The last part of this chapter explores an initial comparison between the IPA and SPA method, based on a simplified project. The purpose of this comparison is to gain first insight into the mechanism behind both methods. In particular, the forms of uncertainty that tend to increase the cost effect of schedule uncertainty are examined. This effect is only fully evaluated with the IPA method (Hulett, 2011). The MOM and the MC simulation are employed to statistically analyze project uncertainty in the initial comparison. The MOM calculations are presented in Appendix C. It is expected that different confidence intervals are estimated by the IPA and SPA method in cost management. These intervals are compared on basis of the derived contingency cost and the probabilities of exceeding the most likely cost value. There exist no difference in probabilistic scheduling between the methods (chapter ) Set-up case The project uncertainty applied in the initial comparison is shown in Table 7. The parameters and distribution types are based on the presented theory in chapter 3.1 and the SSK-2010 principles described in chapter Normal distributions are applied in this analysis because the raw, central and standardized moments are relatively easy to derive from this type of distribution. There is no risk on cost added in the analysis, because this form of uncertainty will bring no difference in cost result between the IPA and SPA methods. Table 7 Forms of uncertainty with distribution types and randomly chosen parameters Uncertainty Costing process Scheduling process Inherent variability Normal distributions Normal distributions on all quantities (Q) on all activity Durations (D) on all prices (P) Event uncertainty - A single risk event 100 days delay 40% probability of occurrence Statistical dependence SSK principle (Q, P) Subjective judgment on D ρ=1 ρ=1 The deterministic network schedule (Figure 21) has a primary and secondary path of activities. The four activities reflect a simplistic variant of multiple paths in a project. Still, it ensures that not every form of schedule uncertainty is part of the critical path. A hammock activity is employed from project start (PS) to project finish (PF), in order to assign the indirect cost item in the schedule. The deterministic project turnaround time is 270 days. PS A 100 B 80 C 120 D 50 PF Hammock Figure 21 Node diagram of schedule network 47 Theoretical framework

49 The deterministic cost estimate is shown in Table 8 and contains TI and TD cost items. These cost items are stretch out over the four activities, in which the TD cost items will tend to vary with the duration of activities and project. The relations between activities and costs are elaborated in detail in appendix C. The first three items are direct cost, while the fourth item is an indirect cost item. The deterministic project cost estimate is 1,736,000. Table 8 Deterministic cost estimate Item Description Quantity Unit Price ( ) Cost ( 1,000) 1 Labour 14,720 mh TD Material 5000 m3 TI Subcontractor 1 ls TI 600, Site overhead 6,480 mh TD Total 1,736 The computation of costing and scheduling with the IPA and SPA method is further worked out in the appendix C, in which each form of uncertainty is added separately in the estimate. This is done according to the processes described in Figure 16 and Figure 18, with the exception of SE. The marginal impact of a form of uncertainty is captured after each process step and is used to make the comparison between methods. The fourth step of the SPA method process (Figure 16) is ignored in the estimate. This subjective step has no scientific base and can be interpreted in several ways Probabilistic results The cost results of the IPA and SPA methods are presented as mean value, standard deviation and contingency cost in Table 9. These results obtained from the MC simulation compare well, as expected, with the results obtained through the MOM calculations in appendix C. There exist only an average error of 0.16%. It is assumed that this error originates from the large-tailed distribution of labour cost items, which is the result of the product of activity duration, quantity and price (11). It is found that often MC simulation do not provide a stable answer for such multiplication cases (Covert, 2013). Table 9 IPA and SPA method simulation results initial comparison Cost estimate IPA method SPA method ( 1,000) Mean (µ) St. dev. (σ) P70 Budget Mean (µ) St. dev. (σ) P70 budget Variability 1, ,792 1, ,780 + Event 1, ,936 1, ,883 + Correlation 1, ,965 1, ,910 The relative difference between the IPA and SPA methods in cost values increases, each time a form of uncertainty is added to the analysis. Especially, the estimated cost variance (σ 2 ) of the IPA method is larger than the SPA method. This difference originates from the statistical analyzed cost effect of schedule uncertainty in the IPA method. A significant change in mean values exist, when the risk event on time is assessed. The discrepancy between methods is then caused by the difference in expected indirect costs. The project budgets of the IPA and SPA methods in Table 9 are based on the P70 level of certainty. The probabilities of completing the project within the deterministic budget in Table 10 are almost equal for the IPA and SPA methods. 48 Theoretical framework

50 Probabilitiy density (%) Table 10 Contingency cost percentage and likelihood of completing within most likely budget IPA method SPA method Contingency cost percentage over deterministic budget 13% 16% Probability of achieving deterministic budget 36% 37% A simplified plot of the reliability intervals for the cost estimate of both methods is illustrated in Figure 22. The Y-axis defines the probability density (%) and the X-axis defines the project cost range in millions ( ). Figure 22 clearly shows that the IPA method estimates a larger range of possible cost values than the SPA method. Thus, the IPA method statistically analyzes a larger amount of uncertainty defined as management information. Less visible in the figure is the minor difference in expected project cost (µ) between the IPA and SPA method, that is caused by the estimate of the indirect cost item. The IPA method effectively integrates this TD cost item in the schedule, making it functionally dependent on the total project duration. Consequently, the risk on the critical path causes the expected indirect cost to increase. This combined effect of cost and schedule uncertainty is not evaluated by the SPA method. The green line represent the deterministic total project cost of 1.7 million. 3,0E-06 2,5E-06 2,0E-06 1,5E-06 1,0E-06 5,0E-07 0,0E+00-5,0E ,5 1 1,5 2 2,5 3 Project cost ( Million) IPA SPA Deterministic Figure 22 Cost reliability intervals of the IPA and SPA methods in initial comparison case The limitations of the initial comparison case are the limited amount of activities, cost items, and risks in the schedule. Moreover, no branch specific figures are applied and the contingency costs in Table 10. Therefore, an unrealistic high amount of contingency costs is estimated in this project Probabilistic assumptions The initial comparison case demonstrates that probabilistic costing and scheduling are interrelated by the functional cost-schedule dependence applied in the IPA method. The obtained insight about the mechanism behind both methods is described in the following sections Assumption of dependence The dependence between cost and schedule results is mathematically explained with the scatter plot in Figure 23. This scatter plot includes the statistically analyzed results of inherent variability and event uncertainty from Table 7. Statistical dependence between activity durations, units and prices is not taken into account in this plot. Figure 23 is only used to underpin the assumption of conditional 49 Theoretical framework

51 dependence. This cost-schedule scatter plot is developed after each MC simulation of the IPA method software. Figure 23 Scatter plot result initial comparison case of IPA method The scatter plot provides the joint probability of completing the project within budget and enddelivery date. Suppose that the contractual date is set at 13 November and the budget is fix at 2,035,075. Event A is then defined as completing the project within budget and event B is defined as completing the project on time. These marginal probabilities are illustrated with the dotted line in Figure 23, which are respectively and. The Bayes Theorem is applied (equation 13), in order to derive the conditional probabilities of event A and B (Dekking et al., 2005). (13) The joint probability of event A and B [ ] is indicated with green dots in Figure 23. The conditional probabilities based on equation 13 are presented below. These conditional probabilities significantly diverge from the marginal probabilities. This contradicts with the assumption of independence (chapter ) between probabilistic costing and scheduling in the SPA method. The conditional probability of event A, given that event B is true, is. This means that the probability of completing the project within budget is 80%, when it is known that the project will finish before 13 November. The conditional probability of event B, given that event A is true, is. This means that the probability of completing the project before the contractual date is 97%, when it is know that the project is completed within budget. Its indicates that there is limited amount of uncertainty originating from TI costs in the project. This uncertainty is the inherent variability on material cost. 50 Theoretical framework

52 Figure 23 demonstrates that a P70 value on costing and P85 value on scheduling in the initial comparison case does provide a more optimistic joint level of certainty (68%), than one would expect in the assumption of independence (70% x 85% = 59,5%). A joint cost-schedule level of certainty is currently not applied in management and control of infrastructure projects. The NASA handles the cost-schedule scatter plot in the development of projects, with an estimated life-cycle cost greater than $250 million, based on a 70% joint cost-schedule confidence level (JCL) (Nair, 2013). This case demonstrates that a JCL provides a more optimistic figure about the probabilities of achieving project cost and schedule objectives together Insight in mechanism The mechanism that causes these conditional probabilities to diverge from their marginal ones is illustrated in Figure 24. This mechanism is defined as the cost effect of schedule uncertainty, in which schedule uncertainty tends to affect the estimate of TD direct and indirect cost items differently. Effect on TD direct cost Effect on TD indirect cost Schedule uncertainty Activity duration Critical path Secondary paths Project duration Figure 24 Effect of schedule uncertainty on TD direct and indirect costs items in this thesis Three forms of schedule uncertainty are applied throughout this report: inherent variability and event uncertainty on activity duration, and Pearson correlation between activity durations. The cost effect is decomposed in two consequences. TD direct cost items tend to vary, when schedule uncertainty occurs in their respective activities. TD indirect cost items will vary, when schedule uncertainty occurs on the critical path (Figure 24). In the infrastructure industry, TD indirect cost items can also be assigned to hammock activities in secondary paths such as the duration of a construction site. In this thesis, the assumption is made that TD indirect cost items are only functionally dependent on project duration. Hence, no TD indirect cost items are linked to hammock activities in secondary paths. The cost effect of schedule uncertainty is fully evaluated in the IPA method (chapter 3.2.3), whereas the SPA method (chapter 3.2.2) only captures the TD direct cost effect of schedule risks and opportunities via the risk register (example R022). It is considered that the modified cost-schedule risk in the SPA method (step 4 in Figure 16) is a pragmatic approach to include the TD indirect cost effect of schedule uncertainty into the analysis. However, it requires expert judgement about the length of delay and corresponding TD consequence cost. 51 Theoretical framework

53 Table 11 illustrates what cost effects of schedule uncertainty are evaluated by the IPA and SPA methods. It demonstrates that the SPA method cannot statistically analyze the cost effect of TD indirect cost items, as opposed to the IPA method. Moreover, the impact of inherent variability and Pearson correlation on activity durations are not taken into account in the estimate of TD direct cost items by the SPA method. Table 11 Cost effect of schedule uncertainty evaluated by the IPA and SPA methods Linkage mechanism TD direct cost TD indirect cost Inherent variability on time IPA IPA Event uncertainty on time IPA + SPA IPA Pearson correlation on time IPA IPA Schedule-Cost drivers In order to demonstrate the added value of the IPA method in the infrastructure industry, a quantitative comparison between the amount of management information obtained from the IPA and SPA method is executed in the next chapter. Therefore, assumptions are formulated about dominant uncertainty parameters that tend to increase the numerical difference in analyzed information Direct cost items The first schedule-cost driver is the measure of asymmetry of the probability distribution on activity duration. This measure is defined as skewness, which is classified as a standardized moment. The derivatives of raw and central moments (i.e. mode (T), mean (µ) and standard deviation (σ)) are used, in order measure the Pearson mode skewness ( ) (14) (Covert, 2013). (14) The Pearson mode skewness is also suitable for other types of probability distributions than the triangular type in Figure 25. The deterministic top values on time are applied in the direct cost estimate of the SPA method, while the IPA method considers the probability distribution on activity duration in the estimate of direct costs. Figure 25 Triangular distributions with positive skewness (left) and zero skewness (right) 52 Theoretical framework

54 It can be concluded that a Pearson mode skewness of zero, in which the mean and top value coincide (right Figure 25), will estimate similar expected cost values for the IPA and SPA method. However, the IPA method will estimate a larger spread on direct cost items. This conclusion can be verified from the MOM figures in Table C 5 in appendix C. The initial case only applies normal distributions on activity duration, which have a Pearson mode skewness of zero. Therefore, the methods have identical mean values and vary in cost variation for TD direct cost items. It is expected that probability distributions with positive (left Figure 25) and negative Pearson mode skewness on time will cause a relative larger difference in direct cost figures. In addition to the spread, also the mean cost values are assumed to diverge between the IPA and SPA method. Therefore, the Pearson mode skewness of inherent variability is considered to be a dominant uncertainty parameter that causes a significant difference in the direct cost figures between methods Indirect cost items The second schedule-cost driver is the amount of project uncertainty on the critical path of the schedule. Especially when complex and extensive schedules exist, the impact of schedule uncertainty on the project turnaround time is difficult to analyze. This information is required for the estimate of TD indirect cost items in this thesis. Event uncertainty is often the dominant form of uncertainty in project scheduling (Chapman & Ward, 2011; Mubarak, 2010). It is considered that the amount of schedule risks and opportunities on the critical path and the complexity of the schedule network are dominant uncertainty parameters, that cause a difference in cost figures between the IPA and SPA methods. The dynamics of the Pearson mode skewness and the amount of event uncertainty on time in a projects are both applied in the development of cases in the next chapter. These cases are statistically analyzed, in order to determine the possible quantitative difference in contingency cost between methods. 53 Theoretical framework

55 4. Simulation experiment 54 Simulation experiment

56 The theoretical framework has resulted in the formulation of several assumptions about the mechanism behind the IPA and SPA method. These assumptions are verified in the simulation experiments, in order to demonstrate the added value of the IPA method in quantitative terms. These quantitative terms are defined in the first part of this chapter. Moreover, the cases studies in the cost, time and risk management process are described. Reversed engineering, that is based on branch specific figures, is applied to specify uncertainty. The second part of this chapter presents the cost results from the IPA and SPA methods. These results are used to develop a cost diversion diagram. This diagram is involves the comparison between the cost reliability intervals of both methods. Finally, these cost diversion models are evaluated and conclusions are formulated about the mechanism behind each method. Figure 26 illustrates the structure of the simulation experiment chapter. Cases Diversion diagrams Evaluation 4.1 Set-up cases Figure 26 Structure of simulation experiment The fictive project applied in this chapter represents an infrastructure project decomposed into 4 work packages on an abstract level. This amount of work packages is sufficient to compare the IPA and SPA methods. Moreover, extra work packages do not contribute to the results of the simulation experiments. The work packages applied entail information about cost items, activities and forms of uncertainty. Information about linked physical elements from the object tree and required functions in the work packages is ignored in the analysis. These sources of information are not relevant for the quantitative comparison of the IPA and SPA method. The 4 work packages are identical, which enables the design of schedule variants with multiple critical paths. The simulations are executed according to the described processes in Figure 16 and Figure 18 in chapter 3.2. The dynamics in cost, time and risk management are taken into consideration by establishing a set of schedule variants, cost ratios and uncertainty scenarios. In total, this set consist of 90 simulation experiments. Project WP1 WP2 WP3 WP4 Cost items Activities Uncertainty Figure 27 Work packages (WP) in WBS of project applied in the simulation experiments 55 Simulation experiment

57 4.1.1 Deterministic scheduling The dynamics of deterministic scheduling are taken into account by 3 variants of the network diagram (Figure 28). These variants illustrate flexibility in the project schedule. The most rigid schedule is a network diagram, involving only work packages in serial sequence. Flexibility in time management increases as work packages are scheduled more in parallel sequence (AACE, 2011; Pekelharing, 2014b). The parallel sequence potentially mitigates possible activity overruns on the critical path, by enabling overruns in secondary paths. The hammock activity hangs between project start and finish, which illustrates the total project duration. Figure 28 Three variants of a network diagram in deterministic scheduling A single work package consist of: A cluster of 5 activities in serial sequence. Activities with each a duration equal to 50 calendar days. The project includes a total of 20 activities equally divided over 4 work packages. Adding more activities in the schedule, does not provide any relevant information in the comparison of methods. The deterministic end-delivery milestones for the schedule variants are presented in Table 12. With respect to this study, the choice for the deterministic duration of activities is also not relevant. The focus of the simulation experiments is on the amount of schedule uncertainty. The Serial schedule variant is further elaborated in the main report. The results of the Semi- and Parallel schedule variants are elaborated in appendix D. Table 12 Deterministic construction time in the schedule variants Schedule variant project duration (days) Serial 1000 Semi- 500 Parallel Deterministic costing The dynamics of deterministic costing are taken into account by the application of 2 different cost ratios for TD and TI cost items. The Low ratio consist of a low amount of TD cost items and the High ratio consist of a high amount of TD cost items in the infrastructure industry. 56 Simulation experiment

58 The project applied in the simulation experiments involves TD and TI cost items in direct and indirect cost components. The percentages for TD and TI cost items in the Serial schedule variant are illustrated in Table 13. These percentages are based on the figures presented in chapter Table 13 Cost ratios Serial schedule variant based on the percentages presented in chapter TD/TI Ratio Low ratio High ratio Direct cost (%) TD cost items TI cost items Indirect cost (%) TD cost items TI cost items Cost ratio (%) TD cost items TI cost items The linkage between deterministic costing and scheduling is defined in Figure 29. A single work package defines the relationships between activities and direct cost items as: A cluster of 5 TD direct cost items evenly assigned to the 5 activities. A single TI direct cost item assigned to 1 activity. Figure 29 Linkage of direct and indirect cost items to activities The project includes a total of 20 TD and 4 TI direct cost items equally divided over 4 work packages. There exists only 1 TD and 1 TI indirect cost item, which are linked to the hammock activity in the IPA method. This amount of cost items is chosen due to practical software limitations. The time to run the MC simulation increases significantly, when statistical dependence between all quantities or prices is considered. The deterministic project budget of the Serial schedule variant is estimated at 6 Million. The deterministic cost structures in the Serial schedule variant are illustrated in Figure 30. The cost structures applied in the Semi- and Parallel schedule variants are slightly different, as a result of the shorter deterministic project duration and the fixed unit rate per day on indirect cost items. This causes the deterministic indirect costs to vary between schedule variants. 57 Simulation experiment

59 Budget 6 M Budget 6 M Direct Indirect Direct Indirect 4.8 M 1.2 M 5.36M 0.64 M TD TI TD TI TD TI TD TI 0.96 M 3.84 M 1.02 M 0.18 M M M M M Figure 30 Deterministic cost structure High ratio (left) and Low ratio (right) of 'Serial schedule variant Project uncertainty The dynamics of the forms of uncertainty in an infrastructure project are taken into account by simulating 5 uncertainty scenarios. The scenarios involve different parameters for inherent variability, event uncertainty and statistical dependence on time. These parameters are already introduced in chapter The functional cost-schedule dependence is only taken into account by the IPA method, in order to analyze the cost effect of schedule uncertainty. The amount of specified uncertainty is determined, based on reversed engineering of the presented percentages in Table 6. The information about project uncertainty in the work packages establishes the basis for each uncertainty scenario. The same computation principle as the initial case in chapter 3.3 is applied, in which the classified forms of uncertainty are added separately to the analysis. Hence, the marginal impact of each form of uncertainty in the scenarios is captured and analyzed Inherent variability Inherent variability in the project is assessed with the triangular distribution. This assessment is based on the practical guideline SSK-2010 that is described in chapter The triangular distributions are applied in a single work package on: Quantities of TD (5x) and TI (1x) direct cost items. Prices of TD (5x) and TI (1x) direct cost items. Duration of Activities (5x). The project indirect costs are estimated by the means of triangular distributions on: Quantities of TD (1x) and TI (1x) indirect cost items. Prices of TD (1x) and TI (1x) indirect cost items. All variables (72x) in the project are subjected to inherent variability. Only the L and U input values for the duration of activities vary in the scenarios, while the spread on duration is kept constant. The changes in the distribution on activity durations are measured with the Pearson mode skewness. Inherent variability is applied in scenario A, B and C in Table Simulation experiment

60 Event uncertainty Event uncertainty in the project is assessed with the Bernoulli distribution. In all 4 work packages, an event is quantified in the risk register as: A risk with a direct cost impact of 200,000 with a probability of occurrence of 20%. In addition to the 4 risks on cost, the risk register in the scenarios also involves quantified events on time. A set of risks (delay in schedule) or opportunities (advances in schedule) are used to further develop the scenarios. These events on time are equally distributed over the work packages. Probabilistic branching is not assessed in this project. Event uncertainty is applied in scenario B and C in Table Statistical dependence Statistical dependence in the project is assessed with the Pearson correlation coefficient, according to the practical guideline of the SSK-2010 in chapter Therefore, a statistical dependent analysis is simulated with full correlation between all quantities (ρ=1) and all prices (ρ=1). Likewise, the 5 uncertainty scenarios assess full Pearson correlation (ρ=1) between all activity durations in the project. The Pearson correlations on quantities, prices and activity durations are only applied in scenario C. The remaining scenarios A and B do not include statistical dependence in the analysis Scenarios The uncertainty scenarios are presented in Table 14. These scenarios are designed with the described parameters, which are all related to schedule uncertainty. This enables to evaluate the sensitivity of schedule uncertainty with respect to the contribution to the cost effect through the IPA method. Scenario 0 is designed as benchmark, in which the mean of the project schedule is expected to coincide with the most likely end-delivery date. The uncertainty parameters of scenario -2 and -1 are fixed in a way, that the probabilistic schedule is likely to finish before the most likely estimate. In contrast, the schedule uncertainty in scenario 4 and 5 will cause the project to finish after the deterministic completion date. Skewness (A), Events (B) and Pearson correlation (C) in the schedule are added one at the time in the cumulative analysis, in order to evaluate the marginal impact of each form of uncertainty on contingency costs. Scenario C contains all specified forms of uncertainty in the uncertainty assessment. Table 14 Uncertainty scenarios with parameters related to schedule uncertainty Scenario Skewness on time ( ) +Events on Time +Correlation on time (ρ) -2 A B +8 Opportunities C 1-1 A B +4 Opportunities C 1 0 A 0 B 0 C 1 1 A 0.32 B +4 Risks C 1 2 A 0.64 B +8 Risks C 1 59 Simulation experiment

61 4.1.4 Quantitative comparison measures In order to demonstrate the added value in quantitative terms of the IPA method, a similar analysis is executed as the initial comparison case in chapter 3.3. Any combination of schedule variants, cost ratios and uncertainty scenarios are statistically analyzed with the IPA and SPA methods. In the SPA method, the fourth step in Figure 16 is ignored. The cost results of both methods are compared on the marginal impact of the specified forms of uncertainty. Figure 31 illustrates the reliability intervals on costs for the Serial schedule variant with High cost ratio in uncertainty scenario 2A. This figure only involves the marginal impact of inherent variability. The Y-axis defines the cumulative probability (%) and the X-axis defines the project budget in Millions ( ). I. The first measure to compare the methods is the contingency cost ( ). The contingency cost level is set here at the P70 level of certainty. It is estimated that with this cost target, the project will have a probability of 70% to complete within budget. In the infrastructure industry, it should be considered that unidentified forms of uncertainty might occur in the project (chapter 3.2.5). The difference in P70 budget between the IPA method ( 6,169,264) and the SPA method ( 6,116,426) is presented in Figure 31. II. The second measure to compare the methods is the likelihood of achieving the most likely cost estimate (%). The difference in the probability of achieving the deterministic budget between the IPA method (21%) and SPA method (34%) is presented in Figure 31. Figure 31 Cost reliability intervals with quantitative comparison measures in uncertainty scenario 2A 60 Simulation experiment