Abstract
An important aspect of infrastructure management is the scheduling of maintenance tasks, which implies the allocation of tasks to different crews or machines and the determination of an execution order. To this end, different aspects have to be considered. On the one hand, the maintenance operator is interested in reducing direct maintenance costs, e.g. travel costs. On the other hand, priorities must be considered by scheduling maintenance tasks. Often, this is done by urgency rules, an inflexible method that resolves prioritised tasks first. In this paper, another approach is discussed. Instead of urgency rules, the maintenance tasks are afflicted with penalty costs that have to be paid for every day until the task is resolved. Then, the later the execution time of such a job, the higher are the penalty costs. By minimising the sum of penalty costs and travel costs, a solution with small overall costs can be found. The resulting scheduling problem is a multi-depot vehicle routing problem with travel and customer costs. For this extension of a vehicle routing problem, different formulations as mixed-integer linear program are developed. For small instances, these formulations are compared with respect to their computation time in a solution method that uses a commercial solver.
Similar content being viewed by others
References
Albrecht AR, Panton DM, Lee DH (2013) Rescheduling rail networks with maintenance disruptions using problem space search. Comput Oper Res 40(3):703–712
Budai-Balke G (2009) Operations Research Models for Scheduling Railway Infrastructure Maintenance. No. 456. Rozenberg Publishers
Clarke G, Wright JW (1964) Scheduling of vehicles from a central depot to a number of delivery points. Oper Res 12(4):568–581
Dantzig GB, Fulkerson DR, Johnson SM (1959) Solution of a large-scale traveling-salesman problem. J Oper Res Soc Am 2(4):393–410
Desrochers M, Laporte G (1991) Improvements and extensions to the Miller-Tucker-Zemlin subtour elimination constraints. Oper Res Lett 10(1):27–36
Baldacci R, Christofides N, Mingozzi A (2007) An exact algorithm for the vehicle routing problem based on the set partitioning formulation with additional cuts. Math Program 115(2):351–385
Eksioglu B, Vural AV, Reisman A (2009) The vehicle routing problem: a taxonomic review. Comput Ind Eng 57(4):1472–1483
Fu L, Trudel M, Kim V (2009) Optimizing winter road maintenance operations under real-time information. Eur J Oper Res 196(1):332–341
Gillett BE, Miller LR (1974) A heuristic algorithm for the vehicle-dispatch problem. Oper Res 22(2):340–349
Gorman MF, Kanet JJ (2010) Formulation and solution approaches to the rail maintenance production gang scheduling problem. J Transp Eng 136(8):701–708
Heinicke F, Simroth A (2013) Application of Simulated Annealing to Railway Routine Maintenance Scheduling. In: Proceedings of the 14th International Conference on Civil, Structure and Environmental Engineering Computers, Civil-Comp Press, Stirlingshire, UK, Paper 27. doi:10.4203/ccp.102.27
Heinicke F, Simroth A, Tadei R, Baldi MM (2013) Job order assignment at optimal costs in railway maintenance. In: Proceedings of the 2nd International Conference on Operations Res and Enterpr Syst (ICORES2013), pp 304–309, SciTePress
Kumar SN, Panneerselvam R (2012) A survey on the vehicle routing problem and its variants. Intell Inf Manag 4(3):66–74
Laporte G (2007) What you should know about the vehicle routing problem. Naval Res Logist 54(8):811–819
Macedo R, Alves C, Clautiaux F, Hanafi S (2011) Solving the vehicle routing problem with time windows and multiple routes exactly using a pseudo-polynomial model. Eur J Oper Res 214(3):536–545
Miller CE, Tucker AW, Zemlin RA (1960) Integer programming formulation of traveling salesman problems. J ACM 7(4):326–329
Miwa M (2002) Mathematical programming model analysis for the optimal track maintenance schedule. Q Rep RTRI 43(3):131–136
Morcous G, Lounis Z (2005) Maintenance optimization of infrastructure networks using genetic algorithms. Autom Constr 14(1):129–142
Nemhauser GL, Wolsey LA (1988) Integer and combinatorial optimization. Wiley, New York
Oyama T, Miwa M (2006) Mathematical modeling analyses for obtaining an optimal railway track maintenance schedule. Jpn J Ind Appl Math 23(2):207–224
Pataki G (2003) Teaching integer programming formulations using the traveling salesman problem. SIAM Rev 45(1):116–123
Peng F, Kang S, Li X, Ouyang Y, Somani K, Acharya D (2011) A heuristic approach to the railroad track maintenance scheduling problem. Comput Aided Civ Infrastruct Eng 26(2):129–145
Podofillini L, Zio E, Vatn J (2006) Risk-informed optimisation of railway tracks inspection and maintenance procedures. Reliab Eng Syst Saf 91(1):20–35
Quiroga LM, Schnieder E (2010) A heuristic approach to railway track maintenance scheduling. In: Proceedings of 12th International Conference on Computer System Design and Operation in Railw and Other Transit Systems, pp 687–699, WIT Press. doi:10.2495/CR100631
Scholten, BP (2006) Guidelines for sustainable partnerships in railway maintenance. Final Report TREN-ECON2-012, ECORYS Nederland BV
Tan KC, Lee LH, Zhu QL, Ou K (2001) Heuristic methods for vehicle routing problem with time windows. Artif Intell Eng 15(3):281–295
Vale C, Ribeiro I, Calçada R (2012) Integer programming to optimize tamping in railway tracks as preventive maintenance. J Transp Eng 138(1):123–131
Van Eijl CA (1995) A polyhedral approach to the delivery man problem. Technical Report 95–19, Department of Mathematics and Computing Science, Eindhoven University of Technology
Van Zante-de Fokkert JI, den Hertog D, van den Berg FJ, Verhoeven JHM (2007) The Netherlands schedules track maintenance to improve track workers’ safety. Interfaces 37(2):133–142
Acknowledgments
We would like to thank the two anonymous reviewers for the helpful comments.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Heinicke, F., Simroth, A., Scheithauer, G. et al. A railway maintenance scheduling problem with customer costs. EURO J Transp Logist 4, 113–137 (2015). https://doi.org/10.1007/s13676-014-0071-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13676-014-0071-3