Competitive Production Routing Problem: Modeling, Solving and Valid Inequalities

Document Type : Original Article

Abstract

Transportation is an important factor in the economic, production and service systems and it has allocated a significant portion of the gross domestic product (GDP) of any country. Production routing problem is development of the traveling salesman and vehicle routing problems in which scheduling and production planning are considered too. Generally, in the above problems it is assumed that there is a monopoly and the impact of competitors has not been considered. In this paper, for creating competitive condition, it is assumed that the earliest and latest time of competitor arrival is known. After modeling problem as mixed intger programming, valid inequalities are proposed, and their effects on the model have been investigated by the CPLEX software. These inequalities are provided for production routing problem with homogeneous and heterogeneous vehicles, separately. To evaluate the performance of the proposed valid inequalities, the results of them have been compared.

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References

[1]      Adulyasak, Y., Jean-François, C., and Raf, J. "The production routing problem: A review of formulations and solution algorithms." Computers & Operations Research, 55, 2015, 141-152.
[2]      Adulyasak, Y., Jean-François, C., and Raf J. "Benders decomposition for production routing under demand uncertainty." Operations Research, 63, 2015, 851-867.
[3]      Tavakkoli-Moghaddam, R., Gazanfari, M., Alinaghian, M., Salamatbakhsh, A., and Norouzi, N. "A new mathematical model for a competitive vehicle routing problem with time windows solved by simulated annealing." Journal of Manufacturing Systems, 30, 2011, 83-92.
[4]      Norouzi, N., Tavakkoli-Moghaddam, R., Ghazanfari, M., Alinaghian, M., and Salamatbakhsh, A. "A new multi-objective competitive open vehicle routing problem solved by particle swarm optimization." Networks and Spatial Economics, 12, 2012, 609-633.
[5]      Díaz-Madroñero, M., David, P., and Josefa, M. "Integrated production and routing planning decisions under uncertainty: a case study." 9th Conference of the European Society for Fuzzy Logic and Technology, 2015.
[6]      Senoussi, A., Nadia Kinza, M., Bernard, P., Nadjib, B., and Stéphane, D."Modeling and solving a one-supplier multi-vehicle production-inventory-distribution problem with clustered retailers." The International Journal of Advanced Manufacturing Technology, 85, 2016, 971-989.
[7]      Adulyasak, Y., Jean-François, C., and Raf, J. "Formulations and branch-and-cut algorithms for multivehicle production and inventory routing problems." INFORMS Journal on Computing, 26, 2013, 103-120.
[8]      Ghorbani, Z., Tavakkoli-Moghaddam, R., Vahdani, B., Minaee, M., and Mousavi, S. "Solving an Analysis Network Process Model for Selection of the Dispatching Rules by an Interval-valued Intuitionistic Fuzzy Set." The Modares Journal of Management Research in Iran, 18, 2014, 195-214.
[9]      Akbari, M. "a model for production and inventory control in crisis condition". The Modares Journal of Management Research in Iran, 19, 2016, 45-70.
[10]   Mansoori, F., Abbasnejad, T., and Askarpour, H. “Designing an agile supply chain network in terms of demand dependence on price.” Modern Research in Decision Making, 2, 2017, 179-206.
[11]   Bard, J.F., and Nananukul, N. "A branch-and-price algorithm for an integrated production and inventory routing problem." Computers & Operations Research, 37, 2010, 2202-2217.
[12]   Montoya-Torres, J.R., Franco, J.L., Isaza, S.N., Jiménez, H.F., and Herazo-Padilla, N. "A literature review on the vehicle routing problem with multiple depots." Computers & Industrial Engineering, 79, 2015, 115-129.
[13]   Kulkarni, R. V., and Bhave, P. R. "Integer programming formulations of vehicle routing problems." European Journal of Operational Research, 20, 1985, 58-67.
[14]   Pochet, Y., and Wolsey. L.A. "Polyhedra for lot-sizing with Wagner—Whitin costs." Mathematical Programming, 67, 1994, 297-323.

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