Possession assessment and capacity evaluation of the Central Queensland Coal Network

Transcription

1 EURO J Transp Logist (2015) 4: DOI /s RESEARCH PAPER Possession assessment and capacity evaluation of the Central Queensland Coal Network Martin Savelsbergh Hamish Waterer Matthew Dall Chad Moffiet Received: 23 January 2014 / Accepted: 17 October 2014 / Published online: 14 November 2014 Ó Springer-Verlag Berlin Heidelberg and EURO - The Association of European Operational Research Societies 2014 Abstract This paper presents PACE, an optimisation-based Possession Assessment and Capacity Evaluation decision support tool that efficiently and effectively evaluates schedules of planned maintenance and renewal work for rail infrastructure, allowing users to quickly and comprehensively assess the work schedules against the competing objectives of asset reliability, resource requirements, and contract compliance. The development of PACE was commissioned by Aurizon; the owner, manager, and maintainer, of the Central Queensland Coal Network, the largest export coal rail network in Australia, to help address the challenges foreseen in managing this critical piece of infrastructure. In this paper, we describe the multicommodity network flow hierarchical optimisation model underlying PACE and discuss how the tool facilitates the construction of innovative, end-to-end asset management strategies that safely deliver reliability and capacity at least cost. Keywords Rail infrastructure Maintenance scheduling Capacity evaluation Multi-commodity network flow M. Savelsbergh H. Waterer (&) School of Mathematical and Physical Sciences, Centre for Optimal Planning and Operations, The University of Newcastle, Callaghan, NSW 2308, Australia hamish.waterer@newcastle.edu.au M. Savelsbergh martin.savelsbergh@newcastle.edu.au M. Dall C. Moffiet Aurizon Network Pty Ltd, Brisbane, QLD 4000, Australia matthew.dall@aurizon.com.au C. Moffiet chad.moffiet@aurizon.com.au

2 140 M. Savelsbergh et al. 1 Introduction Mining is a key part of Australia s economy. Mineral export earnings in were AUD107.9 billion. The vast majority of these export earnings was contributed by coal and iron ore which together accounted for AUD95.8 billion (Bureau of Resources and Energy Economics 2013). Coal and iron ore export supply chains critically depend on the transport capacity provided by Australia s rail infrastructure and these supply chains are literally getting longer: mineral bodies closer to ports which were exploited first are becoming exhausted, and so supply chains are stretching further to reach resources that are more difficult to access. Combined with increasing export volumes, this makes intelligent, efficient, and effective management of this critical piece of infrastructure vitally important. Maintenance and renewal work plays a crucial role in the management of rail infrastructure as it ensures that infrastructure assets, e.g., track, signals, and rail crossings, are in a condition that allows safe, reliable, and efficient transport. However, the planning of such work is complex, because there is a need to balance three competing objectives: maximising the capacity that can be provided to infrastructure users, ensuring the reliability of the infrastructure assets, and minimising the costs associated with maintenance and renewal activities. The maintenance and renewal of infrastructure assets requires resources, i.e., equipment and personnel, which implies an expense to the infrastructure provider. At the same time, this work temporarily reduces capacity, which may result in a loss of revenue for the infrastructure provider. Moreover, the cost and impact depends on the location and the timing of the work, because infrastructure usage varies over time and the repositioning of personnel and equipment costs money. Also, the location and timing of the work needs to be balanced with the frequency of those activities. Shorter than necessary times between consecutive maintenance work on an asset, for example, results in either reduced productivity or an increase in costs. As export volumes grow, balancing the need (or desire) to accommodate more traffic with the need (or obligation) to perform maintenance and renewal work to ensure safe, reliable, and efficient transport gets progressively more important and more challenging. In this paper, we discuss an optimisation-based decision support tool named PACE which enables the quick assessment of schedules of planned maintenance and renewal work against the aforementioned three criteria. The development of PACE is a key initiative of Aurizon Network Pty Ltd (Aurizon Network Pty Ltd 2013a), the division of Aurizon Holdings Ltd that owns, manages, and maintains, Australia s largest export coal rail network, the Central Queensland Coal Network (CQCN). Aurizon is the world s largest rail transporter of coal from mine to port for export markets. They haul more than 500 kt of coal per day, bound for markets in Japan, China, South Korea, India and Taiwan. The CQCN consists of 2,670 km of track spread over four major coal systems: Moura, Blackwater, Goonyella, and Newlands.

3 Possession assessment and capacity evaluation 141 Fig. 1 Goonyella System in the Central Queensland Coal Network, Queensland, Australia. Source These systems had a combined annualised throughput of 210 Mtpa in the first quarter of the financial year (Aurizon Network Pty Ltd 2013b). Approximately 60 % of the coal carried on the CQCN is coking coal and the remaining 40 % is thermal coal. At current prices 1 this coal is valued at approximately AUD25 billion per annum. To provide a better feel for the size and complexity of the CQCN, we examine the Goonyella System, depicted in Fig. 1, in more detail. It is comprised of approximately 924 km of electrified track which services the 30 mines located in the Bowen Basin coal region. The coal from these mines is loaded onto trains at a load point and hauled over distances of up 320 km, taking in excess of 5 h, to two coal export terminals in the Port of Hay Point located adjacent to the Great Barrier Reef World Heritage Area. Approximately 20,000 train trips from a terminal at the port to a load point at a mine and back (so-called train jobs) are executed per year (Aurizon Network Pty Ltd 2013b). The main rail corridor extends between Coppabella and the Dalrymple Bay and Hay Point coal terminals and consists of 136 km of bi-directional duplicated track. Due to the terrain, the maximum number of train paths, that is, sequences of track sections reserved for use by a particular train job, along the main rail corridor is 72 per day. The Goonyella System infrastructure is comprised of over 100 different types of maintainable item: approximately 4,560 items that can be counted, and approximately 5,900 km of items that are measured by length. 1 The Australian Financial Review, sourced 19 November 2013.

4 142 M. Savelsbergh et al. At a terminal, the coal is received at a rail receival station, or unloader, where it is then transported by conveyor belt to a stacking unit, or stacker. The stackers assemble stockpiles of blended coal in the terminal stockyard. The stockpiles are retrieved by a reclaiming unit, or reclaimer, and transported by conveyor belt to a ship loader which loads the coal into the hold of an awaiting vessel. The combined throughput of both terminals was 96.5 Mt in the financial year (North Queensland Bulk Ports Corporation 2013). Also of note in Fig. 1 is that a new terminal and several new mines are proposed and may start operations in the near future. One of Aurizon s six strategic initiatives is to build more comprehensive asset management and operating system plans. This is motivated, in part, by the need to deliver the increasing forecast volumes of coal. The goal is to provide a network capacity of 310 Mtpa by 2015 (QR National Limited 2012). Accomplishing this will be challenging: a higher throughput requires more maintenance and renewal work, and all the while the coal chain must become more efficient. Future schedules of planned maintenance and renewal work will need to incorporate innovative, end-to-end asset management strategies that safely deliver reliability and capacity at least cost, which will require a better understanding of the trade-offs between capacity, reliability, and cost. This will likely require a more sophisticated approach to that which is employed at present. If the coal chain is to become more efficient, then the frequency, duration, and distribution of track work across the network, needs to be reassessed so that infrastructure expansions, renewals, and maintenance happen at the right place at the right time. It will be essential that an appropriate schedule of planned work is both developed and executed so that every minute on track is utilised in the best possible way. However, the development of such a schedule is complicated and an appropriate suite of optimisation-based decision support tools is required. This paper focuses on PACE, one decision support tool in the suite, namely one that efficiently and effectively evaluates work schedules, and allows users to quickly and comprehensively assess the potential benefits of changing the current structure of work schedules. The main contribution of this paper is the development of an optimisation-based decision support tool that enables the efficient and effective evaluation of schedules of planned maintenance and renewal work for rail infrastructure at a scale and level of detail never carried out before, at least as far as the authors are aware. The mathematical modelling underlying the tool is innovative and includes: multicommodity flows over time, fleet capacities, the fair distribution of unmet contracted demand across multiple contracts, and a post-processing phase that selects a solution with preferable characteristics from among the alternate optima to the problem. Following the evaluation, users of the tool are able to quickly and comprehensively assess the quality and performance of a work schedule against competing objectives using a number of carefully selected indicators. The visualisation of these indicators facilitates a comprehensive understanding and analysis of each work schedule. The tool has been validated by Aurizon and is intended to be used to construct and analyse high quality prospective work schedules for the Goonyella System for the financial year.

5 Possession assessment and capacity evaluation 143 Despite its importance, optimisation models and algorithms for coal and iron ore rail infrastructure maintenance and renewal work are virtually nonexistent. The industry has focused on developing optimisation models and algorithms for scheduling rolling stock, because hauling coal and iron ore generates the revenues. Rail infrastructure maintenance and renewal work has been viewed, mostly, as a necessary requirement for doing business. These attitudes are also reflected in the scientific literature, with many more articles dedicated to train scheduling, see, for example, the early survey of Cordeau et al. (1998) and the real-life case in point described by Ireland et al. (2004). The industry realises that the time is right to put the scheduling of this work on an equal footing; optimally maintaining the infrastructure is as important as optimally using the infrastructure. This broader perspective has most likely been prompted by increasing labour costs, decreasing unutilised capacity due to the postponement of investment in new or renewed infrastructure, and aging infrastructure requiring increased maintenance. Again, these attitudes are reflected in the scientific literature where the scheduling of rail infrastructure maintenance is receiving increased attention. The early literature focused on single links in the rail network (Higgins 1998; Higgins et al. 1999; Budai et al. 2006), however, more recently, the problem is being considered at the network level. See Budai-Balke (2009) and Soh et al. (2012) for overviews of the developing techniques for scheduling rail infrastructure maintenance. Rail infrastructure maintenance ranges from (long) capital track work, such as major track upgrades and renewals, to the just as important (short) routine track maintenance, which includes ballast cleaning, resurfacing, and grinding. Among the more recent articles in the literature, there are those that focus on the scheduling of long work (see, for example, Gorman and Kanet 2010 and Peng and Ouyang 2012, 2013), and those that focus on the scheduling of a specific type of short work (see, for example, Vale et al and Zhang et al. 2013). More challenging is the consideration of both long and short work (see, for example, Nemani et al. 2010, Pouryousef et al. 2010, Bog et al. 2011, Peng et al. 2011, and Borraz-Sánchez and Klabjan 2012). Finally, we note the articles by Boland et al. (2013a) and Boland et al. (2013b) on the scheduling of preventive maintenance in the Hunter Valley Coal Chain which is located in New South Wales, Australia. Importantly, they not only consider the rail infrastructure, but also the load point infrastructure at mine sites and the terminal infrastructure at the port, all of which impact the performance of the coal chain as a whole. In this paper we consider schedules of planned maintenance and renewal work which may include both long and short work. Presently, these schedules are still developed manually by Aurizon personnel. The purpose of the PACE decision support tool is to efficiently and effectively evaluate these work schedules so that the user can quickly and comprehensively assess them against the competing objectives of asset reliability, resource requirements, and contract compliance. The use of model-driven decision support systems (DSSs) is becoming increasingly common (Power and Sharda 2007) as it is recognised that they can help managers make better decisions, and that better decisions require understanding the relationship between management practises and performance (Sharahi and

6 144 M. Savelsbergh et al. Abedian 2009). Eom and Lee (1990), Eom et al. (1998), and Eom and Kim (2006) provide surveys of DSS applications from Many of the DSSs surveyed, like ours, embed quantitative models such as linear programming or network models. The remainder of the paper is organised as follows. In Sect. 2, we describe Aurizon s current practice for constructing schedules of maintenance and renewal work together with its advantages and disadvantages. In Sect. 3, we discuss PACE, a Possession Assessment and Capacity Evaluation tool designed to facilitate the development of schedules of maintenance and renewal work. In Sects. 4 and 5, we discuss in more detail the capacity evaluation and possession assessment modules of PACE. In Sect. 6, we discuss the visualisation of the data used and produced by PACE to facilitate a comprehensive understanding and analysis of a schedule of maintenance and renewal work. While the current implementation of PACE offers a significant improvement over current practice, a number of extensions that will enhance the realism of PACE are planned. These are discussed in Sect. 7, where we also provide a brief overview of the next phase of work in which PACE will be expanded from a work schedule evaluator to a work schedule optimiser, thus facilitating the efficient automated construction and analysis of high quality schedules of maintenance and renewal work. This work is to commence later in Scheduling of maintenance and renewal work By its very nature, maintenance and renewal work is either moving or stationary, referring to the relative speed with which the physical location of the work being performed moves with time. An example of moving work is the rail grinding of a section of track. This work requires a rail grinding machine which moves at speed along the track while the work is being performed. Formation repair of the same section of track is an example of stationary work. While this work is incrementally performed along the length of the track section, the speed with which this work progresses is negligible relative to moving work. Moving work has a smaller impact on network capacity, in terms of train paths lost, compared to stationary work of the same duration. At present, Aurizon emphasises the use of system-wide shutdowns for stationary maintenance and renewal work: traffic on the entire rail network is stopped, allowing uninterrupted access to the track for the duration of the shutdown. Moving work is scheduled to occur outside of these shutdowns. A calendar year typically consists of a mixture of fortnightly 12 h shutdowns and monthly 36 h shutdowns, with one longer 60 h shutdown in July so that work requiring longer durations, such as infrastructure expansion, can be performed. The scheduling of shutdowns is largely performed without consideration for the state of the assets, i.e., how much work needs be performed where and at what time, or whether the work can be resourced; it is simply assumed that the system shutdowns are necessary and sufficient to perform the required stationary maintenance and renewal work.

7 Possession assessment and capacity evaluation 145 A twelve month rolling schedule of shutdowns is developed and maintained. A tentative schedule of the specific stationary maintenance and renewal work to be performed during a given shutdown is prepared and published three weeks prior to the shutdown. The schedule is finalised two weeks prior to the shutdown. While the system-wide shutdown approach simplifies the planning process, having all of the stationary work concentrated in these shutdowns makes it challenging, and often impossible, to ensure that the necessary resources are available at the required times. Consequently, in practice, some of the stationary work is scheduled outside of the shutdowns, between train jobs, in an ad hoc and opportunistic way. Consequently, much of the stationary maintenance work is either performed too early or too late, both of which can have costly consequences. For example, if speed restrictions for trains are imposed on track sections requiring maintenance, then this may affect throughput or the efficiency of above-rail operations. The system shutdowns scheduled in the Goonyella System during the period October 2012 September 2013 as well as the realised schedule of stationary maintenance and renewal work for this period (aggregate work at the line section level) is depicted in Fig. 2. We observe that, with respect to time, 54 % of the work is performed outside of a shutdown. An additional 9.2 % of the available rail network capacity would be released if all maintenance and renewal work was performed within the system shutdowns, but this would, however, require seven times as many resources as the realised schedule. (These statistics are easily produced using PACE, but are difficult and time-consuming to generate without PACE). To better understand the impact of track work on rail network capacity and to start exploring whether there are opportunities for alternate work strategies, we show in Fig. 3 a daily breakdown of the total rail network capacity, measured in terms of train paths, in the Goonyella System for the period October 2012 September The thin blue lines indicate the number of available train paths each day (taking track work into account) and the think red line indicates the number of train jobs each day. This utilised capacity is limited on the one hand by the demand for coal (contracted demand), the number of trains (fleet capacity), and the throughput of the terminals (terminal capacity). The system shutdowns are clearly noticeable, as is the unutilised capacity outside of the shutdowns. An aggregated view of rail network capacity for the same period shows that track work results in a loss of 23 % of the total rail network capacity and that much of this work is not being performed during the system shutdowns. Despite that, 25 % of the total rail network capacity remains unutilised. Thus, there is an opportunity to do more work outside of system shutdowns without impacting the contracted demand, which may reduce the resource requirements and may allow better alignment of maintenance and renewal work needs and execution. Figure 4 shows a proposed alternate schedule of localised shutdowns in the Goonyella System for the period October 2012 September 2013 showing the aggregate work at the line section level. This schedule was developed retrospectively using PACE. All stationary maintenance and renewal work can be scheduled within these shutdowns with the same resource requirements as that of the realised

8 146 M. Savelsbergh et al. Fig. 2 System shutdowns scheduled during the period October 2012 September 2013 as well as the realised schedule of stationary maintenance and renewal work in the Goonyella System for that period (aggregate work at the line section level) schedule shown in Fig. 2. An additional 8.1 % of the available rail network capacity would be released if this schedule were used. 3 PACE, a Possession Assessment and Capacity Evaluation tool PACE, an acronym for Possession Assessment and Capacity Evaluation, is an optimisation-based decision support tool commissioned by Aurizon to facilitate the development, evaluation, and assessment, of schedules of maintenance and renewal work. Figure 5 shows a schematic overview of PACE, more details about which are provided below. The two main components comprising PACE are the capacity evaluation module and the possession assessment module. The capacity evaluation module solves a hierarchical optimisation model, the details of which can be found in Sect. 4. The possession assessment module takes the output of the capacity

9 Possession assessment and capacity evaluation 147 Fig. 3 Daily breakdown of the total rail network capacity in the Goonyella System for the period October 2012 September The vertical axis measures the number of train paths with 72 being the maximum number of train paths per day along the main rail corridor between Coppabella and the terminals. The blue lines indicate the number of available train paths each day after track work and the red line indicates the number of train jobs each day evaluation module and performs a detailed wear and repair analysis of network assets and a detailed evaluation of required resources, the details of which can be found in Sect Asset register, maintenance policy, renewals and expansions The asset register consists of a list of assets in the system that require maintaining. Each asset has a preventive maintenance policy that specifies the work that should be performed on the maintainable items of the asset so that the asset remains in good working order. The work required to maintain each item is specified as a set of work products to be performed. Each work product is uniquely defined by the type of asset being maintained, the type of preventive repair required, and the type of resource the repair requires. Asset maintenance policies largely specify cyclic maintenance work which must be broken up into work parcels satisfying minimum and maximum requirements. This work can be either continuous or discrete in nature. An example of a continuous work product is the formation repair of a section of track by a track construction gang. For a generic 20 km section of track, the maintenance policy might require 100 m of formation repair to be performed for every million tonnes of coal hauled over that section. An example of a discrete work product is minor maintenance of turnouts by mechanical trade. For a section of track containing five short turnouts, the maintenance policy might require minor maintenance be performed for each turnout, for every 200 kt of coal hauled over that section. In both of these examples, the work requirements are specified in terms of track usage. Maintenance work schedules are constructed using an estimate of track usage based on contracted demand, but the actual work performed may be adjusted based on

10 148 M. Savelsbergh et al. Fig. 4 Proposed alternate schedule of localised shutdowns in the Goonyella System for the period October 2012 September 2013 showing the aggregate work at the line section level. This schedule was developed retrospectively using PACE more up to date information of actual track usage. In addition to the cyclic work there may also be aperiodic work such as renewals, that is, replacing existing assets, and infrastructure expansion, for example, track duplication or adding additional signals. 3.2 Work scenarios A work scenario for a given planning horizon is specified by a work schedule, a shutdown schedule, the rail and terminal networks infrastructure, and the contracted demands. A work schedule is a schedule of maintenance and renewal work to be performed on the assets in the system. The schedule consists of a list of work events for the work products associated with each asset. Each work event is specified by a start and end time, the quantity of work to be performed, the quantity of resource that will be made available for the work, and the percentage reduction in the

11 Possession assessment and capacity evaluation 149 Maintenance Policy Asset Register Repair Requirements Resource Requirements Renewals and Expansions Work Scenario Work Schedule Shutdown Schedule Network Infrastructure Contracted Capacity Capacity Evaluation Stockyard Statistics Throughput Statistics Possession Assessment Asset Reliability Resource Utilisation Contract Compliance Performance Criteria Fig. 5 Schematic overview of PACE capacity of the asset during the work event. The interval of time spanned by concurrent work events on a given asset when that asset is not operating at its nominal capacity is often referred to as a possession of, or as an outage on, that asset. A shutdown schedule consists of a list of system shutdowns. Each shutdown is specified by a start and end time. The rail network infrastructure consists of lists of assets, specifically, load points, junctions, and line sections, each specifying their nominal capacity, and how they are related to the other rail network assets. Similarly, the terminal network infrastructure consists of lists of assets, specifically, unloaders, stackers, reclaimers, ship loaders, and berths. Contracted demand is a list of contracts that producers have with the different terminals as to the volume of coal from each load point that will be exported via each terminal. A contract specifies, for a load point and terminal combination, a period of time and an amount of coal that needs to be sent during that period. 3.3 Capacity evaluation The capacity evaluation module in PACE takes as input a given work scenario and evaluates the maximum throughput of the system over the planning horizon. This is done by solving a side-constrained multi-commodity maximum flow problem that is formulated as a linear programming problem. More details of the model are given in Sect. 4. Outputs of this module include various throughput statistics, such as the

12 150 M. Savelsbergh et al. tonnes hauled for each contract over time, the tonnes passing through each terminal over time, the tonnes hauled over each line section over time and between successive possessions, and stockyard statistics for the terminals, such as daily pad levels. 3.4 Possession assessment The possession assessment module in PACE takes as input the work schedule and contracted demands from a given work scenario, and the corresponding throughput statistics output by the capacity evaluation module. The work scenario is then assessed against three performance criteria: asset reliability, resource requirements, and contract compliance. The asset reliability criterion assesses the performance of the work scenario by relating the amount of repair work performed on each asset in the work schedule to the amount of wear incurred over the planning horizon, and whether the work performed is consistent with the maintenance policy. Asset reliability is discussed in more detail in Sect. 5. The resource requirements criterion assesses the number of resources of each type required to implement the work scenario. The contract compliance criterion assesses whether each contract can be satisfied under this work scenario, that is, the required volume of coal can be hauled from the load point to the terminal in the specified period. 4 Capacity evaluation It is natural to model the movement of coal in loaded trains from a mine s load point to an unloader at a terminal as a flow over time in a network (i.e., a dynamic network flow problem). Boland et al. (2013a) and Boland et al. (2013b) show that the movement of coal within a terminal, from an unloader to a berth by way of conveyors, and the stacking and reclaiming of coal to and from stockyard pads, can also be modelled as a flow over time in a network. Moreover, it is shown that depending on the structure of the (complete) network, it may be possible to reduce the dynamic network flow problem to a standard network flow problem. As the Goonyella network satisfies the conditions on the network structure, our starting point for evaluating the throughput of a given maintenance and renewal schedule for the Goonyella system is a standard network flow problem. (Details of the transformation from a dynamic flow problem to a standard network flow problem are given below). An important aspect of system throughput evaluation is the modelling of the capacities of the assets (rail and terminal infrastructure assets) and the modelling of the fleet capacity (trains). But because the true goal is to determine the maximum possible utilised capacity of the system for a given maintenance and renewal schedule, it is also necessary to model the contracted demand for coal (which imposes limits on the movement of coal in space and time) and to model how maintenance and renewal work is performed (since work performed during system shutdowns affects throughput differently than maintenance and renewal work performed in the form of individual events).

13 Possession assessment and capacity evaluation 151 Finally, it is critical to recognize the importance of the terminals in the coal chain, the stockyard in particular as it provides a buffer against variations in capacity in different parts of the network (because inventory of coal can be built up and drawn down at the stockyards). In the remainder of this section, we discuss these and other notable features of the capacity evaluation model in more detail. The complete mathematical formulation can be found in the Appendix along with computational results evaluating the available rail network capacity for three work scenarios consisting of data from the Goonyella System during the period October 2012 September Time slices, travel times, and system time A work schedule is a planned schedule of maintenance and renewal work events that are to be performed on various assets in the system during specified intervals of time within the planning horizon. During a work event the associated assets experience either a partial, or a complete, reduction in throughput capacity. A time slice corresponds to a maximal interval of time during which the throughput capacity in the system is constant. At the start and end of each work event the capacity of each asset associated with the event changes, and so the capacity of the system changes. Consequently, the set of all start and end times of work events defines a set of time points at which the capacity in the system changes, while between two consecutive time points the capacity of the system remains constant. Thus, two consecutive time points define a time slice. Capacity evaluation is based on the following ideas. Given that throughput capacity in the system during a time slice is constant, the maximum volume of coal that can be sent through the system during each time slice in the planning horizon can be determined by solving a maximum flow problem. The throughput over the planning horizon is then the sum of the maximum flows in each of the time slices of the planning horizon. This approach, however, does not account for the time taken for coal to travel in the network, which is not negligible. The time for a loaded train to travel from a load point at a mine to an unloader at a terminal can be in excess of 5 h. Consequently, the problem that needs to be solved is a maximum dynamic network flow problem (see, for example, Skutella 2009). However, as we explain below, this dynamic network flow problem can be transformed to a standard maximum flow problem by exploiting the structure of the network. A dynamic network flow problem can be transformed to a standard one, if there is a node in the network that is common to all flow paths in the network. (This result follows from the theory presented in Koch et al. (2011)) The Goonyella rail network exhibits such structure as the train paths between any load point and terminal pair traverse the main rail corridor. The underlying mathematical network is a tree in which every leaf node is either a source or a sink. We refer to such a common node as the reference location and to the local time at the reference location as the system time. The dynamic network flow problem can now be transformed to a standard one, by measuring flow at every node in the network in system time.

14 152 M. Savelsbergh et al. Example 1 Figure 6 shows a small network with associated arc travel times and capacities and lists a set of arc outages with durations both in local time and in system time. Figure 7 shows a graph of the flow into the sink at each point in system time with and without time offsets. The example illustrates the transformation of local times into system times as well as the necessity of doing so, because we see that without the time offsets the total flow into the sink over the planning horizon is less than the actual total flow into the sink over the planning horizon. (Of course the opposite effect may occur in other examples). The dynamic flow problem on the rail network can thus be transformed easily to a standard flow problem. The terminal networks are not trees, but because the travel times in these networks are assumed to be zero, the flow problem on the terminal networks is already a standard flow problem. More specifically, to account for travel time in the system, all assets in the system are assigned a time offset that captures the time taken for coal to travel from that asset to the reference location (for assets that are upstream of the reference location) or the time taken for coal to travel from the reference location to the asset (for assets that are downstream of the reference location). Thus, these time offsets measure the difference between time local to the various assets in the system and system time. The start and end times of work events on these assets are shifted by these offsets so that the time slices are measured in system time. This standardisation of time in the system using a reference location results in travel times being implicitly incorporated into the network. Consequently, the maximum volume of coal that can be sent through the system during the planning horizon is the sum of the maximum static flows in each of the time slices of the planning horizon. 3,5 A 1,5 3,5 B 2,10 5,5 System time 4,5 C 100% Local System time outages time Head Tail A [4,6] [10,12] [13,15] B [9,11] [11,13] [14,16] C [2,4] [9,11] [13,15] Fig. 6 Example network and associated arc outages. Arc labels indicate (travel time, capacity)

15 Possession assessment and capacity evaluation 153 Flow into sink 10 5 Without offsets System time Flow into sink 10 5 With offsets System time Fig. 7 Flow into the sink of the example network, with and without time offsets 4.2 Modelling asset capacities In the absence of any work event, the capacity of an arc representing an asset in the network is the nominal throughput rate (measured in tonnes per day) of the corresponding section of track in the case of the rail subnetwork, or machine in the case of the terminal subnetwork, prorated by the length of the time slice. The nominal throughput rate of a section of track is taken to be the product of the weighted average of the capacity of the trains that utilise that section and the nominal number of train paths, or slots, that can be utilised per day. If the corresponding section of track is a balloon loop serving either a load point or an unloader, then the number of slots available per day is known and is derived from either the upstream or downstream infrastructure respectively. If the corresponding section of track is not a balloon loop, then the number of slots available per day is determined by the headway, that is, the minimum time between successive trains. For example, consider an arc a corresponding to a section of track that is not a balloon loop. Then the number of length of a day slots per day a ¼ headway a and the throughput a ¼ weighted average train capacity slots per day a : The capacity of the arc a in time slice i is then capacity ai ¼ throughput a duration of time slice i :

16 154 M. Savelsbergh et al. 4.3 Modelling fleet capacity The capacities, which restrict the volume of coal that can be sent through the system, that have been discussed thus far, are due to the nominal throughput rates of the various assets. Another form of capacity that must be considered is the availability of trains to transport the coal from the load point of each mine to the unloader at a terminal. In the model, it is assumed that the fleet of trains is homogeneous, and that each train has a nominal payload equal to the weighted average of the nominal payloads of the available trains. The capacity of the fleet, specifically, the capacity of the fleet in a given interval of time, is measured in tonne hours (th). The available fleet capacity in each time slice is given by the product of the number of trains in the fleet, the weighted average nominal payload in tonnes, and the length of the time slice in hours. For a given load point and terminal pair, the time it takes a train to travel empty from that terminal to the load point, be loaded with coal, travel loaded from the load point to an unloader at the terminal, and unload the coal, is known as the cycle time. The required fleet capacity for each load point and terminal pair in each time slice is the product of the cycle time for that pair and the volume of coal destined for that terminal that flows through the load point in that time slice. Thus the required fleet capacity for the system is the sum of the required fleet capacities for all load point and terminal pairs, and this cannot exceed the available fleet capacity in any time slice. In our arc based model the fleet capacity constraints are approximated in the following way. Consider an arc a corresponding to a section of track in the rail network. Let the cycle time of that track section be denoted by cycle time a. The cycle time of a section of track in the rail network is the sum of the time it takes a train to traverse the track section empty plus the time it takes a train to traverse it loaded. That is, cycle time a ¼ empty travel time a þ loaded travel time a : If the section of track is a balloon loop of a load point j then the loading time needs to be taken into consideration. That is, cycle time a ¼ empty travel time a þ loading time j þ loaded travel time a : Similarly, the unloading time needs to be considered if the section of track is a balloon loop of a terminal k. That is, cycle time a ¼ loaded travel time a þ unloading time k þ empty travel time a : If the flow on arc a in time slice i is denoted by flow ai, and the available fleet capacity in time slice i is denoted by fleet capacity i, then the fleet capacity constraint in each time slice is written as

17 Possession assessment and capacity evaluation 155 cycle time a flow ai fleet capacity i : rail arcs 4.4 Modelling maintenance and renewal impact One management strategy for performing planned maintenance and renewal work is to shutdown the network. That is, all trains in the network are parked wherever they are presently located, thus reducing the available fleet capacity to zero for the duration of the shutdown. Since it takes time to park the train fleet leading up to a shutdown the available fleet capacity does not suddenly drop to zero, but rather there is a ramping down as the available capacity gradually decreases to zero. Similarly, at the conclusion of the shutdown there is a gradual ramping up of the available capacity as the fleet starts moving and comes up to speed. To model the ramping down of available fleet capacity immediately before a shutdown and the ramping up immediately after, additional time points are introduced and the change in the available fleet capacity is approximated by piecewise constant functions. The idea is illustrated in Fig. 8, where the solid line represents actual available fleet capacity measured in tonne hours and the dashed lines indicate the piecewise constant approximation. Each piece in the piecewise constant function introduces a new time point and thus two new time slices. An alternative is to model individual maintenance and renewal work events. During a work event, the capacity of an arc is reduced by a certain percentage that depends on the work being performed. If multiple work events are being performed on the asset simultaneously, then the maximum percentage reduction in capacity is applied. Thus, if reduction ai is the maximum percentage reduction in capacity of the asset associated with arc a in time slice i, then capacity ai ¼ throughput a duration of time slice i reduction ai : Modelling stockpiling of coal at the terminals Although we focus on the flow of coal through the rail network, we cannot ignore the flow of coal through the terminals. One aspect of the modelling of a terminal is Ramp-down Shutdown Ramp-up Fig. 8 Modelling the ramping down and ramping up of available fleet capacity. The solid line represents available fleet capacity measured in tonne hours and the dashed lines indicate a piecewise constant approximation using four time points to represent each of the ramp-down and the ramp-up periods

18 156 M. Savelsbergh et al. especially important. Treating time slices independently ignores any interaction between them which may result in an underestimate of the throughput that can be achieved over the planning horizon. Consecutive time slices do interact due to the stockpiling of coal on pads at the terminals. The stockyard acts as a buffer and links the inbound and the outbound flows of coal at a terminal. Consequently, the outbound capacity of a terminal may be achieved even if the inbound capacity of a terminal is reduced by track work when sufficient stockpiles of coal have been built up previously. Similarly, inbound capacity of a terminal may be achieved even if the outbound capacity of a terminal is reduced due to work being performed on equipment when stockyard capacity is available to build additional stockpiles of coal. The stockpiled coal on each pad in the stockyard at each terminal is conserved from one time slice to the next. That is, the stockpiled coal at the end of one time slice is available at the beginning of the next time slice. However, each pad in the stockyard has limited capacity and thus the opportunity to provide a buffer during periods when the inbound and outbound capacities of the terminal differ because of maintenance and renewal work is also limited. This aspect is captured by providing an upper bound on the volume of coal that can be stockpiled on each pad at each terminal. The volume of coal on each pad at the start and end of the planning horizon are required to be equal. That is, the coal that is on a pad at the end of the last time slice is available at the beginning of the first time slice, and the inventory level is no prescribed but rather determined by the model. Wrapping the end of the planning horizon back to the beginning of the planning horizon attempts to emulate a steady state condition and avoids end effects that the model may exploit. 4.6 Modelling contracted demand Producers have contracts with the different terminals as to the volume of coal from each load point that will be exported via each terminal. A contract specifies, for a load point and terminal combination, a period of time and an amount of coal that needs to be sent during that period. The start and end times of these periods introduce new time points and new time slices. The maximum flow model maximises the utilised capacity of the system subject to these contracted demands, that is, more coal will never be sent from a load point to a terminal than is contracted. Consider a contract between a load point j and a terminal k over a given period. Let the flow of coal through load point j in time slice i that is destined for terminal k be denoted by flow jik. Then the contracted demand constraint that restricts the total flow that can be sent from load point j to terminal k during this period is written as flow jik contracted demand jk : time slices Producers have contracts with the different terminals as to the volume of coal from each load point that will be exported via each terminal. Consequently load point demand profiles can be refined by terminal. That is, the coal from each load point

19 Possession assessment and capacity evaluation 157 can be separated into commodities that are distinguishable by the terminal exporting it. Thus there will be as many commodities flowing through the network as there are terminals, and each commodity can only be exported by a unique terminal. The problem is now a multi-commodity network flow problem in which the sum of the commodities flowing is to be maximised subject to the sum of the commodities flowing on each arc not exceeding the capacity of the arc. The objective function is max flow jik contracts time slices and for each arc a and time slice i, we have the capacity constraint flow aik capacity ai : terminals If contracted demand exceeds utilised capacity then there is unmet demand. In this case, the unmet demand is fairly distributed across all contracts without reducing the utilised capacity. This is done by making the relative unmet demand of each contract as close as possible to the relative unmet demand of the system, more specifically, we find a solution which minimises the sum over all contracts of the squared difference between the relative unmet demand of a contract and the relative unmet demand of the system. Note that utilised capacity is not changed, it is simply redistributed over the contracts in a fair way. Consider a contract c between a load point and terminal pair over a given period. Let the relative unmet demand for this contract be denoted by relative unmet demand c ¼ contracted demand c utilised capacity c : contracted demand c Then the total utilised capacity ¼ utilised capacity c ; the and the total contracted demand ¼ contracts contracts contracted demand c ; total contracted demand total utilised capacity relative total unmet demand ¼ : total contracted demand To distribute the unmet demand fairly across all contracts a solution that minimises ðrelative total unmet demand relative unmet demand c Þ 2 contracts is sought. Table 1 gives an example involving two contracts in which the unmet demand has been allocated fairly using the above approach.

20 158 M. Savelsbergh et al. Table 1 Fairly distributing unmet contracted demand Contract Contracted Utilised Unmet Relative unmet demand capacity demand demand (%) Total Contract Contract All coal is not considered equal. If there is insufficient utilised capacity in the system to satisfy the contracted demand, then preference is given to contracts where the distance the coal has to be hauled is greatest, that is, the load point and terminal are the farthest apart. Thus, rather than maximising the volume of coal in tonnes, a solution that maximises the volume of coal weighted by the distance it has been hauled, measured in tonne kilometres (tkm), is sought. (One tonne of coal hauled one kilometre equates to one tonne kilometre as the name suggests.) This solution maximises the velocity of the system over the planning horizon, measured in kilometres per hour (km/h). The system velocity is defined to be the total volume of coal throughput over the planning horizon weighted by the distance it has been hauled (tkm), divided by the capacity of the fleet over the planning horizon (th), the latter of which is constant. 4.7 Modelling infrastructure changes Another feature of the model is that a time interval is associated with a capacity of an asset, indicating the period in time for which this particular capacity is in effect. In this way, the model can accommodate the specification and handling of changes to the infrastructure over time, for example, increases in the capacity of a load point, or the addition of new track in the rail network at some future date. The start and end times of these intervals introduce time points at which the capacity of the system changes. (It is implicitly assumed that the intervals for a specific asset do not overlap and do not introduce gaps, i.e., the intervals form a partition of a larger interval). 4.8 Solution filtering The existence of multiple optima is to be expected when solving maximum flow problems. However, the situation is greatly exacerbated in this context by the temporal aspect of the problem. Moreover, the nature of the solution algorithms produce extreme solutions in which flows are either at capacity or take value zero. Not surprisingly this leads to solutions that would not be considered desirable in practice. For example, load point flows and terminal outbound flows alternate between zero and maximum capacity in successive time slices. To address this, a post-processing phase is employed to select a solution with preferable characteristics from among the alternate optima. At present, this functionality is limited to selecting a solution with smooth utilised capacity at the

21 Possession assessment and capacity evaluation 159 load points at the weekly level. This filtering occurs after unmet contracted demand has been redistributed and is achieved by penalising the deviation of cumulative flow from a cumulative target without reducing the utilised capacity and without changing the unmet contracted demand distribution (if there is any unmet demand). Consider a contract c for a load point and terminal pair over a given period. Let the weekly target tonnage be denoted by capacity of contract c target c ¼ weeks in contract c and the capacity utilised in week w of contract c be denoted by utilised cw. The weekly cumulative targets are given by: target c1 ¼ target c target c2 ¼ 2 target c.. target cw ¼ w target c The weekly cumulative realisations are given by: utilised c1 ¼ utilised c1 utilised c2 ¼ utilised c1 þ utilised c2.. utilised cw ¼ utilised c1 þþutilised cw To smooth the utilised capacity an alternate optima is selected that minimises target cw utilised 2 cw : target contracts weeks cw This approach to smoothing has been previously used by Boland et al. (2013b, 2015). 5 Possession assessment The possession assessment module in PACE assesses a work scenario against three performance criteria, namely, asset reliability, resource requirements, and contract compliance. The asset reliability criterion is discussed in detail below. The resource requirements criterion assesses the number of resources of each type, required each day, to implement the work scenario, and reports this as a percentage of the number of resources of each type specified in the work schedule each day. The contract compliance criterion assesses whether each contract can be satisfied under this work scenario, that is, the required volume of coal can be hauled from the load point to the terminal in the specified period.

22 160 M. Savelsbergh et al. The purpose of reliability assessment is to ensure that the quantity of maintenance work scheduled for each work product of each maintainable item of an asset, and the frequency with which this work is completed, is consistent with the maintenance policy of that item. The maintenance policy defines the wear rate of a maintainable item for a given work product, as either a quantity of (repair) work required per unit of time, or as a quantity of (repair) work required per tonne hauled over the asset. Consequently, for a given work product, the amount of wear that the corresponding maintainable item is subject to in a given period is either the length of that period, or the number of tonnes hauled over the asset during that period, multiplied by the wear rate. Consider a work event e for a work product p of a maintainable item. Let t denote the end of work event e. If the frequency of work of work product p on the item is specified in terms of time, then the cumulative wear of work product p at time t is wear pt ¼ wear rate p t: Let a denote the arc corresponding to the asset of the maintainable item. Again, let t denote the end of work event e. If the frequency of the work on the item is specified in terms of the number of tonnes hauled over the asset, and the flow on arc a in a time slice i is denoted by flow ai, then the cumulative wear at time t is wear pt ¼ wear rate p flow ai : time slices prior to t The repair rate for each work product is the quantity of work that can be performed on the corresponding maintainable item during a work event, per unit time. The spark time of a work event is the duration of the event less the setup and cleanup times for the corresponding work product. For a given work schedule, the maximum amount of repair of a given work product that can be performed on the corresponding item in a given period is the sum of the spark times of the corresponding work events in the period, multiplied by the repair rate. However, the amount of repair can never exceed the amount of wear. Thus, the realised amount of repair is limited by the realised amount of wear incurred by the work product, at all times. Consider a work event e for a work product p of a maintainable item. Let t denote the completion time of work event e. If spark e denotes the spark time of work event e for work product p, then the cumulative repair of work product p at time t is repair pt ¼ min wear pt ; repair p;prevðtþ þ repair rate p spark e where prevðtþ denotes the completion time of the work event for work product p immediately preceding event e. The wear index measures the difference between the amount of wear and the amount of repair over time as a percentage of the total cumulative wear of the work product. For work product p at time t, the wear index is

23 Possession assessment and capacity evaluation 161 wear index pt ¼ 100 wear pt repair pt wear pt where wear pt is the total cumulative wear of work product p which occurs at the end of the planning horizon at time T. Since the amount of repair can never exceed the amount of wear, it may be the case that the maximum amount of repair of a given work product that can be performed in a work event may be greater than the realised amount of repair. This is referred to as repair slack. Let t denote the completion time of work event e. The repair slack for work product p at time t is slack pt ¼ max repair p;prevðtþ þ repair rate p spark e wear pt ; 0 : The slack index measures the repair slack at the completion of each work event as a percentage of the total maximum amount of repair that has been scheduled for the work product. The slack index for work product p at time t is slack pt slack index pt ¼ 100 repair rate p total spark p where total spark p ¼ spark e : work events 6 Visualisation An important component of PACE is the visualisation of data which facilitates a comprehensive understanding and analysis of a work scenario, the schedule of maintenance and renewal work in particular. Figure 2 shows a visualisation of the schedule of stationary maintenance and renewal work in the Goonyella system for the period October 2012 September The plot shows the aggregate work at the line section level and highlights the temporal aspects of the work schedules as well as the percentage reduction in the capacity of an asset during each work event. The figures below provide further insight into this schedule. Due to the data being incomplete at the level of detail required by PACE, the possession assessment has only been performed for a limited number of work products. (In practice there are at least 70 work products, across 25 asset types, 65 repair types, and 35 resource types). Figure 9 shows the system throughput over time in tonnes at the weekly level. The target tonnage depicts what could be achieved if the realised capacity of each contract was supplied at a constant rate in the absence of any work being performed in the system. The deviations from this target are due to work events reducing track capacity and system shutdowns reducing fleet capacity.

24 162 M. Savelsbergh et al. Fig. 9 Profile of the weekly system throughput over time corresponding to the realised work schedule for the Goonyella system for the period October 2012 September 2013 depicted in Fig. 2 (as evaluated by PACE) Figure 10 shows the daily resource requirements for each resource type as a percentage of the quantity of resources available. In this case, only a single resource was assumed available, since the actual quantity of resource available in practice was not always known. Consequently, the plot indicates the quantity of resource that has been used each day. We observe that certain resource types, e.g., Rail Grinding Turnout and Schwartz Undercutter, are used only a few times during the year, whereas others, i.e., High Production Resurfacing Machine, is used frequently (although the utilisation is relatively low in most cases). Track construction gangs are use throughout the year, but the number of gangs varies widely (40 gangs during one short period in December). In general, the resource requirements profile is used to identify the times when the quantity of resources specified as available in the work schedule is not consistent with the quantity required. Additional resources of a given type will be required at those times when the requirements exceed 100 %. Conversely, the quantity of resources of a given type specified in the work schedule can be reduced at times when the requirements drop below 100 %. Figures 11 and 12 show two different visualisations of the wear index described in Sect. 5. The plots show the aggregate work index at the line section level, for the associated repair types in the work schedule. The wear index heat map plots the maximum value of the aggregate wear index over time, and so provides a high level overview of the worst case wear for the given work schedule. For example, we see that for work product 16-Track Resurfacing, the wear index reaches a very high value during the considered period for line section GA441, but never reaches a high level for line section NP768. This is not necessarily surprising, since line section