A comparative study of the capability of alternative mixed integer programming formulations
Abstract
In selecting the best mixed integer linear programming (MILP) formulation the important issue is to figure out how to evaluate the performance of each candidate formulation in terms of selected criteria. The main objective of this study is to propose a systematic approach to guide the selection of the best MILP formulation among the alternatives according to the needs of the decision maker. For this reason we consider the problem of “selecting the most appropriate MILP formulation for a certain type of decision maker” as a multi-criteria decision making problem and present an integrated AHP-TOPSIS decision making methodology to select the most appropriate formulation. As an example the proposed decision making methodology is implemented on the selection of the MILP formulations of the Capacitated Vehicle Routing Problem (CVRP). A numerical example is provided for illustrative purposes. As a result, the proposed decision model can be a tool for the decision makers (here they are the scientists, engineers and practitioners) who intend to choose the appropriate mathematical model(s) among the alternatives according to their needs on their studies. The integrated AHP-TOPSIS approach can simply be incorporated into a computer-based decision support system since it has simplicity in both computation and application.
First published online: 09 May 2017
Keyword : capacitated vehicle routing problem, AHP, TOPSIS, multi-criteria analysis, optimization, operations research, mathematical model
How to Cite
Kececi, B., Derya, T., Dinler, E., & Ic, Y. T. (2018). A comparative study of the capability of alternative mixed integer programming formulations. Technological and Economic Development of Economy, 24(2), 561–584. https://doi.org/10.3846/20294913.2016.1213202
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
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Eksioglu, B.; Vural, A. V.; Reisman, A. 2009. The vehicle routing problem: a taxonomic review, Computers and Industrial Engineering 57(4): 1472–1483. https://doi.org/10.1016/j.cie.2009.05.009
Expósito-Izquierdo, C.; Rossi, A.; Sevaux, M. 2016. A two-level solution approach to solve the clustered capacitated vehicle routing problem, Computers and Industrial Engineering 91: 274–289. https://doi.org/10.1016/j.cie.2015.11.022
Ezzatneshan, A. 2010. A algorithm for the vehicle problem, International Journal of Advanced Robotic Systems 7(2): 125–132. https://doi.org/10.5772/9698
Faulin, J.; Juan, A. A. 2008. The ALGACEA-1 method for the capacitated vehicle routing problem, International Transactions in Operational Research 15(5): 599–621. https://doi.org/10.1111/j.1475-3995.2008.00640.x
Gendreau, M.; Laporte, G.; Potvin, J.-Y. 2002. Metaheuristics for the Capacitated VRP, in P. Toth, D. Vigo (Eds.). SIAM monographs on discrete mathematics and applications. Philadelphia: SIAM, 129–154. https://doi.org/10.1137/1.9780898718515.ch6
Gouveia, L.; VoB, S. 1995. A classification of formulations for the (time-dependent) traveling salesman problem, European Journal of Operational Research 83(1): 69–82. https://doi.org/10.1016/0377-2217(93)E0238-S
Hacioglu, U.; Dincer, H. 2015. A comparative performance evaluation on bipolar risks in emerging capital markets using fuzzy AHP-TOPSIS and VIKOR approaches, Inzinerine Ekonomika-Engineering Economics 26(2): 118–129. https://doi.org/10.5755/j01.ee.26.2.3591
Haimovich, M.; Kan, A. H. G. R.; Stougie, L. 1988. Vehicle routing, methods and studies. Analysis of Heuristics for Vehicle Routing Problems, 47–61.
Ivlev, I.; Kneppo, P.; Bartak, M. 2014. Multicriteria decision analysis: a multifaceted approach to medical equipment management, Technological and Economic Development of Economy 20(3): 576–589. https://doi.org/10.3846/20294913.2014.943333
Ji, P.; Chen, K. 2007. The vehicle routing problem: the case of the Hong Kong postal service, Transportation Planning and Technology 30(2–3): 167–182. https://doi.org/10.1080/03081060701390841
Kabak, M.; Dağdeviren, M. 2014. A hybrid MCDM approach to assess the sustainability of students’ preferences for university selection, Technological and Economic Development of Economy 20(3): 391–418. https://doi.org/10.3846/20294913.2014.883340
Kara, I.; Bektas, T. 2005. Minimal load constrained vehicle routing problems, in V. S. Sunderam, G. D. van Albada, P. M. A. Sloot, J. J. Dongarra (Eds.). Computational Science – ICCS 2005. ICCS 2005. Lecture Notes in Computer Science. Vol 3514. Berlin Heidelberg: Springer-Verlag, 188–195. https://doi.org/10.1007/11428831_24
Kara, I.; Derya, T. 2011. Polynomial size formulations for the distance and capacity constrained vehicle routing problem, in Numerical Analysis and Applied Mathematics ICNAAM 2011 AIP Conference Proceedings 1389, 19–25 September 2011, Halkidiki, Greece, 1713–1718.
Khandekar, A.; Antuchevičienė, V. J.; Chakraborty, S. 2015. Small hydro-power plant project selection using fuzzy axiomatic design principles, Technological and Economic Development of Economy 21(5): 756–772. https://doi.org/10.3846/20294913.2015.1056282
Kou, G.; Peng, Y.; Lu, C. 2014. MCDM approach to evaluating bank loan default models, Technological and Economic Development of Economy 20(2): 292–311. https://doi.org/10.3846/20294913.2014.913275
Kulkarni, R. V.; Bhave, P. R. 1985. Integer programming formulations of vehicle routing problems, European Journal of Operational Research 20(1): 58–67. https://doi.org/10.1016/0377-2217(85)90284-X
Laporte, G.; Nobert, Y. 1987. Exact algorithms for the vehicle routing problem, Annals of Discrete Mathematics 31: 147–184. https://doi.org/10.1016/s0304-0208(08)73235-3
Laporte, G.; Semet, F. 2002. Classical Heuristics for the Capacitated VRP, in P. Toth, D. Vigo (Eds.). SIAM monographs on discrete mathematics and applications. Vol. 9. The vehicle routing problem. Philadelphia: SIAM, 109–128.
Liu, P. 2009. Multi‐attribute decision‐making method research based on interval vague set and TOPSIS method, Technological and Economic Development of Economy 15(3): 453–463. https://doi.org/10.3846/1392-8619.2009.15.453-463
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