MILP formulations of cumulative constraints for railway scheduling - A comparative study

This paper introduces two Mixed Integer Linear Programming (MILP) models for railway traffic planning using a cumulative scheduling constraint and associated pre-processing filters. We compare standard solver performance for these models on three sets of problems from the railway domain and for two of them, where tasks have unitary resource consumption, we also compare them with two more conventional models. In the experiments, the solver performance of one of the cumulative models is clearly the best and is also shown to scale very well for a large scale practical railway scheduling problem

Evaluation of planning policies for marshalling track allocation using simulation

Planning the operational procedures in a railway marshalling yard is a complex problem. When a train arrives at a marshalling yard, it is uncoupled on an arrival yard and then its cars are rolled to a classification yard. All cars should eventually be rolled to the classification track that has been assigned to the train they’re supposed to depart with. However, there is normally not enough capacity to compound all trains at once. In Sweden, cars arriving before a track has been assigned to their train can be stored on separate tracks called mixing tracks. All cars on mixing tracks will be pulled back to the arrival yard, and then rolled to the classification yard again to allow for reclassification. Today all procedures are planned by experienced dispatchers, but there are no documented strategies or guidelines for efficient manual planning. The aim of this paper is to examine operational planning strategies that could help dispatchers find a feasible marshalling schedule that minimizes unnecessary mixing. In order to achieve this goal, two different online planning strategies have been tested using deterministic and stochastic simulation. The Hallsberg marshalling yard was used as a case study, and was simulated for the time period between December 2010 and May 2011. The first tested strategy simply assigns tracks to trains on a first come-first served basis, while the second strategy uses time limits to determine when tracks should be assigned to departing trains. The online planning algorithms have been compared with an offline optimized track allocation. The results from both the deterministic and the stochastic simulation show that the optimized allocation is better than all online strategies and that the second strategy with a time limit of 32 hours is the best online method

The opportunistic replacement and inspection problem for components with a stochastic life time

The problem of finding efficient maintenance and inspection schemes in the case of components with a stochastic life time is studied and a mixed integer programming solution is proposed. The problem is compared with the two simpler problems of which the studied problem is a generalisation: The opportunistic replacement problem, assuming components with a deterministic life time and The opportunistic replacement problem for components with a stochastic life time, for maintenance schemes without inspections

Mixed integer-linear formulations of cumulative scheduling constraints - A comparative study

This paper introduces two MILP models for the cumulative scheduling constraint and associated pre-processing filters. We compare standard solver performance for these models on three sets of problems and for two of them, where tasks have unitary resource consumption, we also compare them with two models based on a geometric placement constraint. In the experiments, the solver performance of one of the cumulative models, is clearly the best and is also shown to scale very well for a large scale industrial transportation scheduling problem

Optimisation of simultaneous train formation and car sorting at marshalling yards

Efficient and correct freight train marshalling is vital for high quality carload freight transportations. During marshalling, it is desirable that cars are sorted according to their individual drop-off locations in the outbound freight trains. Furthermore, practical limitations such as non-uniform and limited track lengths and the arrival and departure times of trains need to be considered. This paper presents a novel optimisation method for freight marshalling scheduling under these circumstances. The method is based on an integer programming formulation that is solved using column generation and branch and price. The approach minimises the number of extra shunting operations that have to be performed, and is evaluated on real-world data from the Hallsberg marshalling yard in Sweden

Hump Yard Track Allocation with Temporary Car Storage

In rail freight operation, freight cars need to be separated and reformed into new trains at hump yards. The classification procedure is complex and hump yards constitute bottlenecks in the rail freight network, often causing outbound trains to be delayed. One of the problems is that planning for the allocation of tracks at hump yards is difficult, given that the planner has limited resources (tracks, shunting engines, etc.) and needs to foresee the future capacity requirements when planning for the current inbound trains. In this paper, we consider the problem of allocating classification tracks in a rail freight hump yard for arriving and departing trains with predetermined arrival and departure times. The core problem can be formulated as a special list coloring problem. We focus on an extension where individual cars can temporarily be stored on a special subset of the tracks. An extension where individual cars can temporarily be stored on a special subset of the tracks is also considered. We model the problem using mixed integer programming, and also propose several heuristics that can quickly give feasible track allocations. As a case study, we consider a real-world problem instance from the Hallsberg Rangerbangård hump yard in Sweden. Planning over horizons over two to four days, we obtain feasible solutions from both the exact and heuristic approaches that allow all outgoing trains to leave on time

Track Allocation in Freight-Train Classification with Mixed Tracks

We consider the process of forming outbound trains from cars of inbound trains at rail-freight hump yards. Given the arrival and departure times as well as the composition of the trains, we study the problem of allocating classification tracks to outbound trains such that every outbound train can be built on a separate classification track. We observe that the core problem can be formulated as a special list coloring problem in interval graphs, which is known to be NP-complete. We focus on an extension where individual cars of different trains can temporarily be stored on a special subset of the tracks. This problem induces several new variants of the list-coloring problem, in which the given intervals can be shortened by cutting off a prefix of the interval. We show that in case of uniform and sufficient track lengths, the corresponding coloring problem can be solved in polynomial time, if the goal is to minimize the total cost associated with cutting off prefixes of the intervals. Based on these results, we devise two heuristics as well as an integer program to tackle the problem. As a case study, we consider a real-world problem instance from the Hallsberg Rangerbangård hump yard in Sweden. Planning over horizons of seven days, we obtain feasible solutions from the integer program in all scenarios, and from the heuristics in most scenarios

Optimerad rangering: slutsatser och resultat från projektet RANPLAN

Sammanfattning Rapporten innehåller kortfattade slutsatser och resultat från en studie genomförd i projektet RANPLAN, som har utförts av SICS Swedish ICT AB på uppdrag av Trafikverket under åren 2010-2013. Fokus är på Hallsbergs rangerbangård, men resultaten är tillämpbara även på andra rangerbangårdar med vall. Datorkörningar visar att blanddragen kan öka kapaciteten på rangerbangårdar väsentligt, mätt i antalet samtidiga tåg som kan hanteras, till en kostnad av en ökad mängd vagnsrörelser. I en jämförande datorstudie av simulering och optimering framgick också att de optimala planerna var betydligt effektivare, mätt i antalet vagnsrörelser, än de simulerade planerna. Resultaten pekar tydligt på att datorstödd optimering av planeringsprocessen för rangerbangårdar både är praktiskt möjligt och kan ge stora effektivitetsvinster

Optimized shunting with mixed-usage tracks

We consider the planning of railway freight classification at hump yards, where the problem involves the formation of departing freight train blocks from arriving trains subject to scheduling and capacity constraints. The hump yard layout considered consists of arrival tracks of sufficient length at an arrival yard, a hump, classification tracks of non-uniform and possibly non-sufficient length at a classification yard, and departure tracks of sufficient length. To increase yard capacity, freight cars arriving early can be stored temporarily on specific mixed-usage tracks. The entire hump yard planning process is covered in this paper, and heuristics for arrival and departure track assignment, as well as hump scheduling, have been included to provide the neccessary input data. However, the central problem considered is the classification track allocation problem. This problem has previously been modeled using direct mixed integer programming models, but this approach did not yield lower bounds of sufficient quality to prove optimality. Later attempts focused on a column generation approach based on branch-and-price that could solve problem instances of industrial size. Building upon the column generation approach we introduce a direct arc-based integer programming model, where the arcs are precedence relations between blocks on the same classification track. Further, the most promising models are adapted for rolling-horizon planning. We evaluate the methods on historical data from the Hallsberg shunting yard in Sweden. The results show that the new arc-based model performs as well as the column generation approach. It returns an optimal schedule within the execution time limit for all instances but from one, and executes as fast as the column generation approach. Further, the short execution times of the column generation approach and the arc-indexed model make them suitable for rolling-horizon planning, while the direct mixed integer program proved to be too slow for this. Extended analysis of the results shows that mixing was only required if the maximum number of concurrent trains on the classification yard exceeds 29 (there are 32 available tracks), and that after this point the number of extra car roll-ins increases heavily

Track Allocation in Freight-Train Classification with Mixed Tracks

We consider the process of forming outbound trains from cars of inbound trains at rail-freight hump yards. Given the arrival and departure times as well as the composition of the trains, we study the problem of allocating classification tracks to outbound trains such that every outbound train can be built on a separate classification track. We observe that the core problem can be formulated as a special list coloring problem in interval graphs, which is known to be NP-complete. We focus on an extension where individual cars of different trains can temporarily be stored on a special subset of the tracks. This problem induces several new variants of the list-coloring problem, in which the given intervals can be shortened by cutting off a prefix of the interval. We show that in case of uniform and sufficient track lengths, the corresponding coloring problem can be solved in polynomial time, if the goal is to minimize the total cost associated with cutting off prefixes of the intervals. Based on these results, we devise two heuristics as well as an integer program to tackle the problem. As a case study, we consider a real-world problem instance from the Hallsberg Rangerbangard hump yard in Sweden. Planning over horizons of seven days, we obtain feasible solutions from the integer program in all scenarios, and from the heuristics in most scenarios