Abstract
Multi-compartment vehicle routing problems arise in a variety of problem settings in which different product types have to be transported separated from each other. In this paper, a problem variant which occurs in the context of glass waste recycling is considered. In this problem, a set of locations exists, each of which offering a number of containers for the collection of different types of glass waste (e.g. colorless, green, brown glass). In order to pick up the contents from the containers, a fleet of homogeneous disposal vehicles is available. Individually for each disposal vehicle, the capacity can be discretely separated into a limited number of compartments to which different glass waste types are assigned. The objective of the problem is to minimize the total distance to be travelled by the disposal vehicles. For solving this problem to optimality, a branch-and-cut algorithm has been developed and implemented. Extensive numerical experiments have been conducted in order to evaluate the algorithm and to gain insights into the problem structure. The corresponding results show that the algorithm is able to solve instances with up to 50 locations to optimality and that it reduces the computing time by 87% compared to instances from the literature. Additional experiments give managerial insights into the use of different variants of compartments with flexible sizes.
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Abdulkader, M. M. S., Gajpal, Y., & El Mekkawy, T. Y. (2015). Hybridized ant colony algorithm for the multi compartment vehicle routing problem. Applied Soft Computing, 37, 196–203.
Archetti, C., Campbell, A., & Speranza, M. G. (2016). Multi-commodity versus single-commodity routing. Transportation Science, 50, 461–472.
Avella, P., Boccia, M., & Sforza, A. (2004). Solving a fuel delivery problem by heuristic and exact approaches. European Journal of Operational Research, 152, 170–179.
Brown, G. G., & Graves, G. W. (1981). Real-time dispatch of petroleum tank trucks. Management Science, 27, 19–32.
Caramia, M., & Guerriero, F. (2010). A milk collection problem with incompatibility constraints. Interfaces, 40, 130–143.
Chajakis, E. D., & Guignard, M. (2003). Scheduling deliveries in vehicles with multiple compartments. Journal of Global Optimization, 26, 43–78.
Coelho, L. C., & Laporte, G. (2015). Classification, models and exact algorithms for multi-compartment delivery problems. European Journal of Operational Research, 242, 854–864.
Cornillier, F., Boctor, F. F., Laporte, G., & Renaud, J. (2008). A heuristic for the multi-period petrol station replenishment problem. European Journal of Operational Research, 191, 295–305.
Cornuejols, G., & Harche, F. (1993). Polyhedral study of the capacitated vehicle routing problem. Mathematical Programming, 60, 21–52.
Derigs, U., Gottlieb, J., Kalkoff, J., Piesche, M., Rothlauf, F., & Vogel, U. (2011). Vehicle routing with compartments: Applications, modelling and heuristics. OR Spectrum, 33, 885–914.
El Fallahi, A., Prins, C., & Wolfer Calvo, R. (2008). A memetic algorithm and a tabu search for the multi-compartment vehicle routing problem. Computers & Operations Research, 35, 1725–1741.
Elbek, M., & Wøhlk, S. (2016). A variable neighborhood search for the multi-period collection of recyclable materials. European Journal of Operational Research, 249, 540–550.
Fagerholt, K., & Christiansen, M. (2000). A combined ship scheduling and allocation problem. Journal of the Operational Research Society, 51, 834–842.
Golden, B. L., Raghavan, S., & Wasil, E. A. (2008). The vehicle routing problem: Latest advances and new challenges. New York: Springer.
Goodson, J. C. (2015). A priori policy evaluation and cyclic-order-based simulated annealing for the multi-compartment vehicle routing problem with stochastic demands. European Journal of Operational Research, 241, 361–369.
Henke, T., Speranza, M. G., & Wäscher, G. (2015). The multi-compartment vehicle routing problem with flexible compartment sizes. European Journal of Operational Research, 246, 730–746.
Koch, H., Henke, T., Wäscher, G. (2016): A genetic algorithm for the multi-compartment vehicle routing problem with flexible compartment sizes. Working Paper No. 04/2016, Fakultät für Wirtschaftswissenschaft, Otto-von-Guericke Universität Magdeburg.
Lahyani, R., Coelho, L. C., 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. (2009). Fifty years of vehicle routing. Transportation Science, 43, 408–416.
Mendoza, J. E., Castanier, B., Guéret, C., Medaglia, A. L., & Velasco, N. (2010). A memetic algorithm for the multi-compartment vehicle routing problem with stochastic demands. Computers & Operations Research, 37, 1886–1898.
Mendoza, J. E., Castanier, B., Guéret, C., Medaglia, A. L., & Velasco, N. (2011). Constructive heuristics for the multicompartment vehicle routing problem with stochastic demands. Transportation Science, 45, 346–363.
Muyldermans, L., & Pang, G. (2010). On the benefits of co-collection: Experiments with a multi-compartment vehicle routing problem. European Journal of Operational Research, 206, 93–103.
Rabbani, M., Farrokhi-asl, H., & Rafiei, H. (2016). A hybrid genetic algorithm for waste collection problem by heterogeneous fleet of vehicles with multiple separated compartments. Journal of Intelligent & Fuzzy Systems, 30, 1817–1830.
Ralphs, T. K., Kopman, L., Pulleyblank, W. R., & Trotter, L. E. (2003). On the capacitated vehicle routing problem. Mathematical Programming, Series B, 94, 343–359.
Reed, M., Yiannakou, A., & Evering, R. (2014). An ant colony algorithm for the multi-compartment vehicle routing problem. Applied Soft Computing, 15, 169–176.
Toth, P., & Vigo, D. (2014). Vehicle routing: Problems, methods, and applications (2nd ed.). Philadelphia: Society for Industrial and Applied Mathematics.
Vidović, M., Popović, D., & Ratković, B. (2014). Mixed integer and heuristics model for the inventory routing problem in fuel delivery. International Journal of Production Economics, 147, 593–604.
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Henke, T., Speranza, M.G. & Wäscher, G. A branch-and-cut algorithm for the multi-compartment vehicle routing problem with flexible compartment sizes. Ann Oper Res 275, 321–338 (2019). https://doi.org/10.1007/s10479-018-2938-4
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DOI: https://doi.org/10.1007/s10479-018-2938-4