Abstract
Despite the vast body of literature on vehicle routing problems, little attention has been paid to multi-compartment vehicle routing problems that investigate transportation of different commodities on the same vehicle, but in different compartments. In this project, we present two strategically different versions of the MCVRP in general settings. In the first version, different commodities may be delivered to the customer by different vehicles, but the full amount of each product must be delivered by a single vehicle. In the second version, each customer may only be serviced by a single vehicle, which must deliver the full amount of all commodities demanded by that customer. We present a Branch-and-Price algorithm for solving the two versions of the problem to optimality and we analyze the effect of the strategic decision of whether or not to allow multiple visits to the same customer by comparing the optimal costs of the two versions. Computational results are presented for instances with up to 100 customers and the algorithm can solve instances with up to 50 customers and 4 commodities to optimality.
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References
Archetti C, Bianchessi N, Speranza MG (2015) A branch-price-and-cut algorithm for the commodity constrained split delivery vehicle routing problem. Comput Oper Res 64:1–10
Archetti C, Campbell AM, Speranza MG (2014) Multicommodity vs. single-commodity routing. Transp Sci 50(2):461–472
Avella P, Boccia M, Sforza A (2004) Solving a fuel delivery problem by heuristic and exact approaches. Eur J Oper Res 152(1):170–179
Ben Abdelaziz F, Roucairol C, Bacha C (2002) Deliveries of liquid fuels to sndp gas stations using vehicles with multiple compartments. In: 2002 IEEE International Conference on Systems, Man and Cybernetics , vol 1, pp 478–483
Boland N, Dethridge J, Dumitrescu I (2006) Accelerated label setting algorithms for the elementary resource constrained shortest path problem. Oper Res Lett 34(1):58–68
Brown GG, Ellis CJ, Graves GW, Ronen D (1987) Real-time, wide area dispatch of mobil tank trucks. Interfaces 17(1):107–120
Brown GG, Graves GW (1981) Real-time dispatch of petroleum tank trucks. Manage Sci 27(1):19–32
Chajakis ED, Guignard M (2003) Scheduling deliveries in vehicles with multiple compartments. J Global Optim 26:43–78
Coelho LC, Laporte G (2015) Classification, models and exact algorithms for multi-compartment delivery problems. Eur J Oper Res 242(3):854–864
Cornillier F, Boctor FF, Laporte G, Renaud J (2008) An exact algorithm for the petrol station replenishment problem. J Oper Res Soc 59(5):607–615
Cornillier F, Boctor FF, Laporte G, Renaud J (2008) A heuristic for the multi-period petrol station replenishment problem. Eur J Oper Res 191(2):295–305
Dantzig GB, Wolfe P (1960) Decomposition principle for linear programs. Oper Res 8(1):101–111
Dantzig GB, Wolfe P (1961) The decomposition algorithm for linear programs. Econometrica 29(4):767–778
Derigs U, Gottlieb J, Kalkoff J, Piesche M, Rothlauf F, Vogel U (2011) Vehicle routing with compartments: applications, modelling and heuristics. OR Spectr 33(4):885–914
Desaulniers G, Desrosiers J, Solomon M (eds.) Column generation. Springer (2005)
El Fallahi A, Prins C, Calvo RW (2008) A memetic algorithm and a tabu search for the multi-compartment vehicle routing problem. Comput Oper Res 35(5):1725–1741
Henke T, Speranza MG, Wäscher G (2015) The multi-compartment vehicle routing problem with flexible compartment sizes. Eur J Oper Res 246(3):730–743
Irnich S, Desaulniers G (2005) Shortest path problems with resource constraints. In: Desaulniers G, Desrosiers J, Solomon M (eds.) Column generation. Springer, pp 33–65
Lahyani R, Coelho LC, Khemakhem M, Laporte G, Semet F (2015) A multi-compartment vehicle routing problem arising in the collection of olive oil in Tunisia. Omega 51:1–10
Laporte G, Gendreau M, Potvin JY, Semet F (2000) Classical and modern heuristics for the vehicle routing problem. Int Trans Oper Res 7(4–5):285–300
Muyldermans L, Pang G (2010) On the benefits of co-collection: experiments with a multi-compartment vehicle routing algorithm. Eur J Oper Res 206(1):93–103
Reed M, Yiannakou A, Evering R (2014) An ant colony algorithm for the multi-compartment vehicle routing problem. Appl Soft Comput 15:169–176
Repoussis PP, Tarantilis CD, Ioannou G (2007) A hybrid metaheuristic for a real life vehicle routing problem. In: Numerical Methods and Applications. Springer, pp 247–254
Ryan DM, Foster BA (1981) An integer programming approach to scheduling. In: Wren A (ed) Computer scheduling of public transport urban passenger vehicle and crew scheduling. North-Holland, Amsterdam, pp 269–280
Toth P, Vigo D (2014) Vehicle routing: problems, methods, and applications. MOS-SIAM Series on optimization
Vanderbeck F (2000) On Dantzig–Wolfe decomposition in integer programming and ways to perform branching in a branch-and-price algorithm. Oper Res 48(1):111–128
Van der Bruggen L, Gruson R, Salomon M (1995) Reconsidering the distribution structure of gasoline products for a large oil company. Eur J Oper Res 81(3):460–473
Wang Q, Ji Q, Chiu CH (2014) Optimal routing for heterogeneous fixed fleets of multicompartment vehicles. Math Probl Eng
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Mirzaei, S., Wøhlk, S. A Branch-and-Price algorithm for two multi-compartment vehicle routing problems. EURO J Transp Logist 8, 1–33 (2019). https://doi.org/10.1007/s13676-016-0096-x
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DOI: https://doi.org/10.1007/s13676-016-0096-x