Abstract
Transportation is widely present in human activities and supports many economic activities. Using phones, reading mails, traveling, and flying involve the routing of messages, people, and goods. One of the present aims of research is to fill the gap between academic research and practical applications. Our aim is to present a simple and flexible heuristic for solving the capacitated vehicle routing problem and heterogeneous fleet vehicle routing problems, and discuss its advantages compared to other well-known heuristics. The flexibility of our approach comes from the simplicity of the solution procedure and is especially important when the algorithm is going to be applied to solving real-life problems.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Altinel, I.K., & Öncan, T. (2005). A new enhancement of the Clarke and Wright savings heuristic for the capacitated vehicle routing problem. Journal of the Operational Research Society, 56(8), 954–961. doi: 10.1057/palgrave.jors.2601916.
Augerat, P., Belenguer, J.M., Benavent, E., Corberán, A., Naddef, D., & Rinaldi, G. (1995). Computational Results with a Branch and Cut Code for the Capacitated Vehicle Routing Problem. Research Report 949-M, Universite Joseph Fourier, Grenoble, France.
Baldacci, R., Battara, M., & Vigo, D. (2008). Routing a heterogeneous fleet of vehicles, in: B. Golden, S. Raghavan, and E. Wasil (eds), The Vehicle Routing Problem — Latest Advanced and New Challenges, Springer, 3–28.
Baldacci, R., & Mingozzi, A. (2009) A unified exact method for solving different classes of vehicle routing problems, Mathematical Programming, 120(2), 347–380. doi: 10.1007/s10107-008-0218-9.
Balinski, M., & Quandt, R. (1964). On an integer program for a delivery problem, Operations Research, 12, 300–304.
Battara, M., Benedettini, S., & Roli, A. (2011). Leveraging saving-based algorithms by master-slave genetic algorithms, Engineering Applications of Artificial Intelligence, 24(4), 555–566. doi: 10.1016/j.engappai.2011.01.007.
Bramel, J., & Simchi-Levi, D. (2002). Set-covering-based algorithms for the capacitated VRP, in: P. Toth and D. Vigo (eds), The Vehicle routing, SIAM Publishing: Bologna, 85–108.
Brandao, J. (2011). A tabu search algorithm for the heterogeneous fixed fleet vehicle routing problem, Computers & Operations Research, 38, 140–151. doi: 10.1016/j.cor.2010.04.008.
Cocan, M., Florea, I., & Pop (married Stanojević), B. (2008), Models for Combinatorial Optimization and Methaheuristics in Operations Research (in Romanian: Modele si metode de optimizare combinatoriala si metaeuristica in cercetari operationale), Editura Universitatii Transilvania, Brasov, ISBN 978–973–598–188–4.
Charon, I., & Hudry, O. (2001), The noising methods: a generalization of some metaheuristics, European Journal of Operational research, 135(1), 86–101. doi: 10.1016/S0377-2217(00)00305-2.
Choi, E., & Tcha, D.-W. (2007). A column generation approach to the heterogeneous fleet vehicle routing problem. Computers and Operatins Research, 34, 2080–2095. doi: 10.1016/j.cor.2005.08.002.
Clarke, G., & Wright, J.V. (1964). Scheduling of vehicles from a central depot to a number of delivery points. Operations Research, 12, 568–581.
Corominas, A., Garcia-Villoria, A., & Pastor, R. (2010). Fine-tuning a parametric Clarke and Wright heuristic by means of EAGH (empirically adjusted greedy heuristics). Journal of Operational Researches Society, 61, 1309–1314. doi: 10.1057/jors.2009.89.
Christofides, N., & Eilon, S. (1969). An algorithm for the vehicle dispatching problem. Operations Research Quarterly, 20, 309–318.
Christofides, N., Mingozzi, A., & Toth, P. (1979). The vehicle routing problem, in: N. Christofides, A. Mingozzi, P. Toth, & L. Sandi (eds). Combinatorial Optimization, Wiley, Chichester, 315–338.
Dantzig, G.B. & Ramser, J.H. (1959). The truck dispatching problem. Management Science, 6(1), 80–91.
Duhamel, C., Lacomme, P., & Prodhon, C. (2012). A hybrid evolutionary local search with depth first search split procedure for the heterogeneous vehicle routing problems. Engineering Applications of Artificial Intelligence, 25, 345–358. doi: 10.1016/j.engappai.2011.10.002.
Fulga, C., &@@@@ Pop (married Stanojević), B. (2007). Portfolio selection with transaction costs, Bulletin Mathematique de la Societe des Sciences Mathematiques de Roumanie, 50(4), 317–330, WOS:000255161800004.
Golden, B., Assad, A., Levy, L., & Gheysens, F. (1984). The fleet size and mix vehicle routing problem, Computers & Operations Research, 11(1), 49–66. doi: 10.1016/0305-0548(84)90007-8.
Groer, C. (2012). VRPH. Retrieved from http://www.coin-or.org/projects/VRPH.xml.
Laporte, G., & Semet, F. (2002). Classical heuristics for the capacitated VRP, in: P. Toth and D. Vigo (e ds), The Vehicle routing problem. SIAM Monographs on Discrete Mathematics and Applications, SIAM Publishing: Bologna, 109–128.
Li, F., Golden, B. & Wasil, E. (2007). A record-to-record travel algorithm for solving the heterogeneous fleet vehicle routing problem, Computers & Operations Research, 34, 2734–2742. doi: 10.1016/j.cor.2005.10.015.
Penna, P.H.V., Subramanian, A., Ochi, L.S. (2013). An iterated local search heuristic for the heterogeneous fleet vehicle routing problem, Journal of Heuristics, 19, 201–232. doi: 10.1007/s10732-011-9186-y.
Pop (married Stanojević), @@@@B., & Dzit¸ac, I. (2007). Mixed variables fuzzy programming algorithms, Studies in Informatics and Control, 16(2), 411–416.
Pop (married Stanojević), B., & Dzit¸ac, I. (2006). On a fuzzy approach to solving multiple criteria fractional programming problem, International Journal of Computers, Communications and Control, 1, 381–385. WOS: 000203014800064.
Pop (married Stanojević), B., & Stancu-Minasian, I.M. (2008). A method of solving fully fuzzified linear fractional programming problems, Journal of Applied Mathematics and Computing, 27(1–2), 227–242. doi: 10.1007/s12190-008-0052-5.
Pop, P., & Pop Sitar, C. (2011). A new efficient transformation of the generalized vehicle routing problem into the classical vehicle routing problem, Yugoslav Journal of Operations Research, 21(2), 187–198. doi: 10.2298/YJOR1102187P.
Prins, C. (2009). Two memetic algorithms for heterogeonous fleet vehicle routing problems, Engineering Applications of Artificial Intelligence, 22, 916–928. doi: 10.1016/j.engappai.2008.10.006.
Stanojević, B., & Stancu-Minasian, I.M. (2012). Evaluating fuzzy inequalities and solving fully fuzzified linear fractional programs, Yugoslav Journal of Operations Research, 22(1), 41–50. doi: 10.2298/YJOR110522001S.
Stanojević, B., & Stanojević, M. (2013a), Solving method for linear fractional optimization problem with fuzzy coefficients in the objective function, International Journal of Computers, Communications and Control, 8(1), 146–152. WOS: 000312043600016.
Stanojević, B., & Stanojević, M. (2013b). On the efficiency test in multi-objective linear fractional programming problems by Lotfi et al. 2010, accepted for publication in: Applied Mathematical Modelling, doi: 10.1016/j.apm.2013.01.041.
Stanojević, M., Stanojević, B., & Vujošević, M. (2013a). Enhanced savings calculation and its applications for solving capacitated vehicle routing problem. Applied Mathematics and Computation (accepted for publication) doi: 10.1016/j.amc.2013.04.002.
Stanojević, M., Vujošević, M., & Stanojević, B. (2013b). On the cardinality of the non-dominated set of multi-objective combinatorial optimization problems, Operations Research Letters, 41(2), 197–200, doi: 10.1016/j.orl.2013.01.006.
Stanojević, M., Stanojević, B., & Vujošević, M. (2009, September). A new savings algorithm for the vehicle routing problem. Paper presented at the 9th Balkan Conference on Operational Research.
Stanojević, M., Vujošević, M., & Stanojević, B. (2008a). Computation results of finding all efficient points in multiobjective combinatorial optimization, International Journal of Computers, Communications and Control, 3(4), 374–383. WOS:000260214800006.
Stanojević, M., Vujošević, M., & Stanojević, B. (2008b). Number of efficient points in some multiobjective combinatorial optimization problems, International Journal of Computers, Communications and Control, 3(Supplementary Issue), 497–502. WOS:000257497600082.
Stanojević, M., & Vujošević, M. (2006). An exact algorithm for Steiner tree problem on graphs, International Journal of Computers, Communications and Control, 1(1), 41–46.
Taillard, E.D. (1999). A heuristic column generation method for the heterogeneous fleet VRP, RAIRO Operations Research, 33(1), 1–14. doi: 10.1051/ro:1999101.
Vujošević, M., Stanojević, M., & Mladenović, N., (1996). Optimization methods — networks, location and multiple criteria models (in Serbian, Metode Optimizacie — Mrezni, lokacijski, visecriteriumski modeli), DOPIS Beograd.
Editor information
Editors and Affiliations
Copyright information
© 2014 Milan Stanojević and Bogdana Stanojević
About this chapter
Cite this chapter
Stanojević, M., Stanojević, B. (2014). Set-Covering-Based Approximate Algorithm Using Enhanced Savings for Solving Vehicle Routing Problem. In: Jakšić, M.L., Rakočević, S.B., Martić, M. (eds) Innovative Management and Firm Performance. Palgrave Macmillan, London. https://doi.org/10.1057/9781137402226_22
Download citation
DOI: https://doi.org/10.1057/9781137402226_22
Publisher Name: Palgrave Macmillan, London
Print ISBN: 978-1-349-48666-3
Online ISBN: 978-1-137-40222-6
eBook Packages: Palgrave Business & Management CollectionBusiness and Management (R0)