Project Scheduling ARCH 738: REAL ESTATE PROJECT MANAGEMENT Morgan State University Jason E. Charalambides, PhD, M.ASCE, AIA, ENV_SP (This material has been prepared for educational purposes) Introduction 2
Introduction! There is a timing factor that relates the series of activities to the cost and to the execution of a Construction Project.! Scheduling can be considered as the process of designing the interrelationships of activities and timing from the beginning to the conclusion of a Project.! For the generation of a Construction Schedule the following need to be organized: " Fragmentation of project into activities " Designing relationships between activities " Construction of diagrams indicating activities and durations " Determining a Critical Path 3 Introduction! Some Fundamental Definitions: " Activity: Work with estimated timing that will yield a defined outcome. An activity would have an estimated cost and an expected amount of man-hours " Man-hour: An hour of work for a worker (depends on type of activity and skill level) " Float/Slack: The number of days within which an activity can start and finish. An activity may be possible to start early and finish early, or start late and finish late without impacting the total project time. " Critical Path: The set of activities that have no float and determine the total duration of the project. Any modification to the Critical Path will impact the duration of the project 4
Introduction! There are three basic methods of representation of a project schedule that we shall address in this course: " Bar/Gantt Charts " Network Analysis / CPM & " PERT 5 Introduction! Steps to be Taken " Define the activities " Sequence them " Estimate time for each activity " Develop the schedule! Techniques " Gantt Chart " CPM " PERT " Computer software hybrid methods 6
!!!! Activity Duration 7 Activity Duration! An Activity has to be defined! The quantity of work per activity is calculated " Measure from plans and specifications! Available resources should be identified and quantified! Labor and Equipment productivity should be determined! Activity durations are calculated by division of Quantity of work by Work Labor and/or Equipment Productivity Quantity of Work T = Productivity! Productivity Rates can be obtained from: " RS Means " Other published records (if available) " Company's historical records " Or through Project Manager's and site Foremen's experience and expertise. 8
Activity Duration! Example: " Measure the time it takes for a 4,000 cubic yards of loose soil to be removed. " Production per hour:! If the excavator can operate about 0.75 yd 3 per minute on that type of soil... 3 3 Productivity= 0.75yd = 45yd 1 min 1 hour " Therefore, it can be estimated that the total amount of time necessary for one operator with an excavator will take... 3 Time= 4000yd 45 yd 3 hour 89 hour " Note that the above estimation does not account for contingencies such as meal breaks etc. 9 Bar/Gantt Charts 10
! Example of a Bar Chart generated on MS. Project 11 Bar Charts! What are they? " Gantt charts are set on two axes. The Abscissa is dedicated to time reference, and the Ordinates indicate a series of activities. " It is visually simple method that allows users to illustrate the start and finish dates of the activities. " Gantt charts generated by contemporary software such as MS Project, or the more advanced Primavera) also show the dependencies and the relationships between activities, as well as current schedule status using percent-complete shadings and a vertical "TODAY" line. 12
Bar Charts! Example " A very simple Bar Chart 13! Example Bar Charts " Gannt Chart with dependencies,! Note the numbers that refer to the week of beginning of an activity and the week of ending of an activity.! Arrows indicate the dependency of an activity upon the completion of another activity " Source: Woodgate, 1967 14
Bar Charts Vs Networks! Transition " As seen here, the qualities and characteristics of one method can be infused in another. " On top we see a typical Gannt chart that includes the critical path of the project, and on the bottom a network with Activity on Axis that also indicates the critical path 15! Use Gantt / Bar Charts " There is a lot of software that is available at this time that can perform a vey sophisticated set of tasks that will lay out a schedule in Bar Charts. " Primavera happens to be a very advanced program but it is also a very complicated software where professionals with many years of experience end up not knowing many of the hidden treasures it carries. " Microsoft project is a much more affordable type of software that can be learnt within a few hours of simple experimentation, and would be more than adequate for smaller to medium size projects. " The method indicates milestones/events/activities in a time order. 16
CPM / PERT 17! Example of Network with Critical Path Method 18
Critical Path Method! Main Points " Created by DuPont & Remington Rand (1956). " Deterministic task times " Activity on Node Construction " Also known as the Cost/Time Trade-off analysis method 19! Example of Activity on Arrow PERT network 20
Project Evaluation and Review Technique! Main Points " Developed by the US Navy, Booz & Hamilton, and Lockheed Co " Multiple task time estimates " Was specifically designed for the Polaris Missile " Activity on Arrow network construction " Probabilistic method - Uses probability theory and applies three time estimates 21 CPM / PERT Networks! Activity on Node " Nodes represent activities, and arrows show precedence relationships! Activity on Arrow " Arrows represent activities and nodes are events for points of time! Event " Completion or beginning of an activity in a project 22
CPM / PERT Networks! Some Standard Procedures: 23 CPM / PERT Networks! Some Standard Procedures: 24
CPM / PERT Networks! Activity on Axis " The activity is indicated on the axis together with the duration (e.g. days) allowing the user to calculate the total time for the project, " But this is not as flexible as the AON. 25 CPM / PERT Networks! What if we have concurrent activities in AOΑ? Incorrect Precedence Relationship Correct Precedence Relationship " Two nodes can never be connected through two activities. For concurrent activities, a third node and a dummy activity may be used instead 26
CPM / PERT Networks! Determining the Critical Path in a schedule " Consider that on each node the upper number is the activity, and the lower number is the duration (e.g days) and try all scenarios:! 1-2-4-7 yields 10 days! 1-2-5-6-7 yields 9 days! 1-3-5-6-7 yields 8 days! 1-3-4-7 yields 9 days 27 CPM / PERT Networks! Determining the Critical Path in a schedule " The longest of the paths is the critical path, in this case the path 1-2-4-7.! Critical is the longest! That path determines the minimum amount of time (average) that the project will take 28
CPM / PERT Networks! Slack or Float " Slack or Float refers to the amount of time can be delayed without disturbing the finish time of the project! That means that the Critical Path is undisturbed.! No activity on the Critical Path has Slack " There are two types of Slack: " Total Slack TS! That is the difference between ES and LS times, or equivalently, LF and LS times. " Free Slack FS! That is the difference between the EF time and the earliest of the ES times of all its immediate predecessors. 29 CPM / PERT Networks! Forward Pass " Having a number of days within which an activity can take place is what we call a slack or float. " Given this "float" time, the manager can determine the early start and early finish dates for all of the uncompleted segments of work for all network activities. " Calculation of the early start date and early finish date accommodates the manager in deciding the earliest possible allocation of the resources that may be needed for completion of the project and the activities contained within, such as the expenditure of the resources and expenditures of man hours. 30
CPM / PERT Networks! Backward Pass " Similar in concept (and opposite in direction) is the backward pass in the area of project management. " It is the calculation of late finish dates and late start dates for the portions of schedule activities that have not been completed and it is determined by starting at the project s scheduled end date and working backwards through the schedule network logic. " The end date may be set by the assigning party, or it may be determined through use of a forward pass. " To accommodate an easier visual aid to forward and backward pass, another method of graphing the AON is indicated in the next slide 31 CPM / PERT Networks! Mode Configuration for Activity on Node 32
CPM / PERT Networks! Conducting a Forward and a Backward Pass " Using the node design that accommodates the information for early start & finish, and late start & finish, applied on the diagrammed schedule below, a Forward Pass and a Backward Pass will be conducted: 33 CPM / PERT Networks! Conducting a Forward Pass " Using the following diagrammed schedule, a Forward Pass will be executed:! Start at the beginning of the CPM/PERT network to determine the earliest activity times! Earliest Start Time (ES) " Earliest time an activity can start " ES=Maximum EF of immediate predecessors! Earliest Finish Time (EF) " Earliest time an activity can finish " Earliest start time plus activity time EF =ES +t 34
CPM / PERT Networks! Conducting a Forward Pass " By following this process, a network indicating the Earliest Activity Start and Finish Times can be constructed: 35 CPM / PERT Networks! Conducting a Forward Pass " One more view with arrows explaining the way time is added: " " " " " " " " " " " So here we see how activity 1 ends on the 3 rd month and activity 7 ends on the 10 th month. 36
CPM / PERT Networks! Conducting a Backward Pass " Using the same diagrammed schedule, a Backward Pass will be executed to determine the latest activity times :! Start at the end of the CPM/PERT network to determine the earliest activity times! Latest Start Time (LS) " Latest time an activity can start without extending the critical path.! Latest Finish Time (LF) LS= LF t " Latest time an activity can be completed without delaying the project (extending the critical path) " LF=minimum LS of immediate predecessors 37 CPM / PERT Networks! Conducting a Backward Pass " Similarly, the process can be applied to indicate the Latest Activity Start and Finish Times. 38
Crashing/Expediting 39 Crashing/Expediting! The ultimate goals when it comes to timing are Quality and Profit. " Finishing a project on time is a goal that is based on the schedule of operations. " Alteration of the project schedule's delivery date may have an impact on the operations which can entitle the owner to impose penalty if that goal is not met. " Early delivery may be profitable and an owner may provide an incentive to the PM to finish earlier, but not always:! A tollway can produce more revenue earlier,! A summer resort beach hotel delivered in Winter will have maintenance costs for very little gain if any! " Sacrificing quality for time will likely lead to several problems both in short and long run, and it can become a very complicated matter. 40
Crashing/Expediting! Crashing an activity or the schedule may require more human resources, more equipment, or likely both. " It can be anticipated that minimizing the time necessary for an activity to be completed, will come at a cost. " That cost may be higher or even much higher than simple addition of resources, because of several factors such as risk, sense of urgency that allows operators to use cost leverage, limitations in resources, etc. " Therefore, crashing a project schedule or an activity, should take place after considering the cost/benefit ratio.! Incentives need to be clearly set! Risks of any failure should be measured! Monetary benefits should be compared to the costs 41 Crashing/Expediting! A simple method to apply Crashing for a Project: " Draw an AOA, show the Critical Path along with normal ES, EF, LS and LF for each activity " Using the most economical method crash the project one day at a time until the targeted or closest to targeted project duration is met. List the added costs for the project on a daily basis. " Graph the project time vs direct costs.! If there are indirect costs identify and add them. " List the total project cost for each day of the project duration between normal and crash times. " Plot the total and the indirect cost curves on the graph. " Determine the most economically feasible duration for the project (when you should not crash any further). 42
Probabilistic Time Estimation 43 Probabilistic Time Estimation! Quoting: That path determines the minimum amount of time (average) that the project will take " The term average is key in this situation. " Average means that on an average basis each activity takes a certain amount of time. " So each activity can take more or it can take less time,... " Average means that it the activity, or the schedule altogether, has a 50% possibility to be completed at that estimated amount of time, and that is based on data that give the average time that each activity is anticipated to take! " So this is not a guarantee that the activity will be completed by that average estimated time! 44
Probabilistic Time Estimation! How do we calculate a duration that would be more likely than average? " It is optional for each and every activity that is on the critical path to be given an average duration, together with an optimistic and a pessimistic duration " That will allow a cumulative calculation of project durations that will give a fairly precise number that will correspond to possibilities of project completion. " Complicated methods of calculating probabilities through the use of probability tree or Monte-Carlo simulation may yield results with relatively high precision " In PERT, use of Z-Score (a statistical measurement of a score's relationship to the mean in a group of scores) can be just as effective and much more efficient. 45 Probabilistic Time Estimation! PERT makes provisions for Uncertainties: " TM Most probable activity duration! Most likely Best Guess. " TP Pessimistic activity duration! If everything goes wrong excluding highly unusual catastrophes as force majeur. " TO Optimistic activity duration! If everything goes right! " For standard straight activities with well known historic data the above should not vary much. " The greater the risk or uncertainty, the greater the variance. 46
Probabilistic Time Estimation! PERT Calculation of Expected time of an activity duration as the weighted average of three time estimates: " T O & T P likely to occur: " T M is 4 times more likely to occur: T E = T O+4T M +T P 6 " Activity time durations have been traditionally following a beta distribution (unimodal with single peak value) " The distribution has finite and positive end points, i.e. no negative durations can occur! " It is not necessarily symmetrical Note: A normal distribution does not satisfy the last two criteria 47 Probabilistic Time Estimation! PERT Figure: Determination of activity durations: 48
Probabilistic Time Estimation! Example determining the Estimated Time: " Given that TO=5, TM=9, and TP=20, determine the value of TE: T E = T O+4T M +T P 6 = 5+4 9+19 =10 6 49 Probabilistic Time Estimation! Variability of Activity durations: " It is necessary to examine the reliability of the expected time. If the time is highly variable, i.e. the range of the estimates is very large, that generates less managerial confidence.! e.g. a situation of {5,9,19} vs {8,9,10} " A means of measuring the variability of an activity's duration is needed. " This measure is given by the Standard Deviation Δσ of the activity's probability distribution. " PERT simplifies the calculation of the Δσ because the distribution consists of only three values. 50
Probabilistic Time Estimation! Variance and Standard Deviation: " Δσ is the square root of Variance Δσ=[ T P T O 6 ] V =[ T P T O 6 " A high Δσ represents high level of uncertainty in this case. " In case more than one critical path exists (rare but possible to have two paths with same length), the one with the highest variance is chosen to determine the variance and the standard deviation. " Paths that are close to the critical path's duration, but with higher variances should be carefully addressed as becoming the critical path. ]2 51! Variance : Probabilistic Time Estimation " Consider the two following scenarios! A : " T O =4 " T M =6 " T P =8! B : " T O =4 " T M =5.5 " T P =10 T E (A) = 4+4 6+8 6 =6 T E (B) = 4+4 5.5+10 =6 6 52
! Variance : Probabilistic Time Estimation " Although the expected durations are identical, the variances differ substantially. That causes great difference in the risk profile of each scenario: V A = (8 4)2 6 2 =0.44 V B = (10 4)2 6 2 =1 V B V A =2.27 " A factor of risk difference of the scale of 2.27 occurs between the two projects. Project B is substantially more risky. 53 Probabilistic Time Estimation! Using Z scores: " A table of values of Z scores can be used to determine the risk factor or the probability of something. " In this case it can be applied to the schedule to determine the chances of a schedule being completed in any time other than the average anticipated: Z = D T E Δ σ " Where D is the goal duration 54
Probabilistic Time Estimation! Using Z scores: " e.g. What is the likelihood that a project with an expected time T E of 20 days will be completed within 23 days, given that the standard deviation of the critical path is 3 days? Z = 23 20 =1 3 " From Z Tables: Source for table: http://figures.boundless.com/18108/full/normal01.jpeg 55 Probabilistic Time Estimation! Using Z scores with formula: " Tables are convenient if they are available at any given time. " Sometimes a formula (especially if registered in a calculator) may be much quicker to use. " The probability of a Z score can be returned by the following formula: 1 Prob= 1+e (0.07056 Z 3 +1.5976 Z )! Where e is Euler's constant 56
Probabilistic Time Estimation! Example using Z values: " Using an estimated value for optimistic duration, pessimistic duration, and most probable duration for each of the activities, determine the probability of finishing the following project at 95% of the average time (Critical Path is shown on continuous lines): " Note: The shown schedule is simplified for the purposes of this exercise. 57 Probabilistic Time Estimation! Example using Z values: " Setting values in a table (highlighted variance is on Critical Path): 58
Probabilistic Time Estimation! Example using Z values: Z = 807 849 15.51 = 2.708 1 Prob= 1+(2.7183) =0.0032 (0.07056 ( 2.708)3 +1.5976 ( 2.708)) " Δσ = 15.51, TE = 849 days. " D = 95% of TE = 807 days. " Therefore, the chances of finishing this 849 days work in 807 days are 0.3%, which can be considered an impossibility! " Let's try 870 days: Z = 870 849 15.51 =1.354 1 Prob= 1+(2.7183) 0.912 (0.07056 (1.354)3 +1.5976 (1.354)) " At 91.2% it can be considered close to certainty! 59 Probabilistic Time Estimation! How can this be used? " A PM can determine what would potentially be a timing for guaranteed completion of a project and use that information accordingly before bidding the project. " Risk of bidding a project on shorter schedule may be a gamble that a PM would have to take provided the incentive is worth the risk. " At any rate, there is no guarantee on scheduling, but a well structured schedule with sound estimations for activities and relations of each activity is the best a PM can do. 60
Summary & Conclusion 61 Summary & Conclusion! Timing and duration of a project is dependent upon a series of sequential activities that need to take place for the completion of the project.! The series of activities that are sequential, each one being dependent on preceding activities and upon which subsequent activities are dependent, is the Critical Path.! The Critical Path determines the total duration of a project.! Activities on the CP have no float (slack)! Schedules can be represented through the use of Bar Charts, or Networks with Activities on Arrow, or Activities on Node " Contemporary software performs most custom functions and usually represent schedules on Bar Charts! Forward Pass and Backward Pass are methods to determine the Earliest Start/Finish and Latest Start/Finish.! Probabilistic Time Estimation with PERT allows managers to determine optimum project duration for bidding or Risk Management 62