Distribution with Quality of Service Considerations:The Capacitated Routing Problem with Profits and Service Level Requirements

Inspired by a problem arising in cash logistics, we propose the Capacitated Routing Problem with Profits and Service Level Requirements (CRPPSLR). The CRPPSLR extends the class of Routing Problems with Profits by considering customers requesting deliveries to their (possibly multiple) service points. Moreover, each customer imposes a service level requirement specifying a minimum-acceptable bound on the fraction of its service points being delivered. A customer-specific financial penalty is incurred by the logistics service provider when this requirement is not met. The CRPPSLR consists in finding vehicle routes maximizing the difference between the collected revenues and the incurred transportation and penalty costs in such a way that vehicle capacity and route duration constraints are met. A fleet of homogeneous vehicles is available for serving the customers. We design a branch-and-cut algorithm and evaluate the usefulness of valid inequalities that have been effectively used for the capacitated vehicle routing problem and, more recently, for other routing problems with profits. A real-life case study taken from the cash supply chain in the Netherlands highlights the relevance of the problem under consideration. Computational results illustrate the performance of the proposed solution approach under different input parameter settings for the synthetic instances. For instances of real-life problems, we distinguish between coin and banknote distribution, as vehicle capacities only matter when considering the former. Finally, we report on the effectiveness of the valid inequalities in closing the optimality gap at the root node for both the synthetic and the real-life instances and conclude with a sensitivity analysis on the most significant input parameters of our model

A Branch-Price-and-Cut Algorithm for the Min-Max k -Vehicle Windy Rural Postman Problem

[EN] The min-max k -vehicles windy rural postman problem consists of minimizing the maximal distance traveled by a vehicle to find a set of balanced routes that jointly service all the required edges in a windy graph. This is a very difficult problem, for which a branch-and-cut algorithm has already been proposed, providing good results when the number of vehicles is small. In this article, we present a branch-price-and-cut method capable of obtaining optimal solutions for this problem when the number of vehicles is larger for the same set of required edges. Extensive computational results on instances from the literature are presented.Contract grant sponsor: Ministerio de Education y Ciencia of Spain: Contract gram number: MTM2006-14961-C05-02 Canadian Natural Sciences and Engineering Research Council; Contract grant number: 157935-07Benavent Lopez, E.; Corberán, A.; Desaulniers, G.; Lessard, F.; Plana, I.; Sanchís Llopis, JM. (2014). A Branch-Price-and-Cut Algorithm for the Min-Max k -Vehicle Windy Rural Postman Problem. Networks. 63(1):34-45. https://doi.org/10.1002/net.21520S3445631Baldacci, R., Mingozzi, A., & Roberti, R. (2011). New Route Relaxation and Pricing Strategies for the Vehicle Routing Problem. Operations Research, 59(5), 1269-1283. doi:10.1287/opre.1110.0975Barnhart, C., Johnson, E. L., Nemhauser, G. L., Savelsbergh, M. W. P., & Vance, P. H. (1998). Branch-and-Price: Column Generation for Solving Huge Integer Programs. Operations Research, 46(3), 316-329. doi:10.1287/opre.46.3.316Benavent, E., Corberán, A., Plana, I., & Sanchis, J. M. (2009). Min-MaxK-vehicles windy rural postman problem. Networks, 54(4), 216-226. doi:10.1002/net.20334Benavent, E., Corberán, Á., & Sanchis, J. M. (2009). A metaheuristic for the min–max windy rural postman problem with K vehicles. Computational Management Science, 7(3), 269-287. doi:10.1007/s10287-009-0119-2Benavent, E., Corberán, A., Plana, I., & Sanchis, J. M. (2011). New facets and an enhanced branch-and-cut for the min-max K-vehicles windy rural postman problem. Networks, 58(4), 255-272. doi:10.1002/net.20469Boland, N., Dethridge, J., & Dumitrescu, I. (2006). Accelerated label setting algorithms for the elementary resource constrained shortest path problem. Operations Research Letters, 34(1), 58-68. doi:10.1016/j.orl.2004.11.011Corberán, A., Plana, I., & Sanchis, J. M. (2008). The Windy General Routing Polyhedron: A Global View of Many Known Arc Routing Polyhedra. SIAM Journal on Discrete Mathematics, 22(2), 606-628. doi:10.1137/050640886Á. Corberán I. Plana J.M. Sanchis Arc routing problems: Data instances www.uv.es/corberan/instancias.htm 2007Dantzig, G. B., & Wolfe, P. (1960). Decomposition Principle for Linear Programs. Operations Research, 8(1), 101-111. doi:10.1287/opre.8.1.101Desaulniers, G., Desrosiers, J., & Spoorendonk, S. (2011). Cutting planes for branch-and-price algorithms. Networks, 58(4), 301-310. doi:10.1002/net.20471Desaulniers, G., Lessard, F., & Hadjar, A. (2008). Tabu Search, Partial Elementarity, and Generalizedk-Path Inequalities for the Vehicle Routing Problem with Time Windows. Transportation Science, 42(3), 387-404. doi:10.1287/trsc.1070.0223Dror, M. (1994). Note on the Complexity of the Shortest Path Models for Column Generation in VRPTW. Operations Research, 42(5), 977-978. doi:10.1287/opre.42.5.977Gilmore, P. C., & Gomory, R. E. (1961). A Linear Programming Approach to the Cutting-Stock Problem. Operations Research, 9(6), 849-859. doi:10.1287/opre.9.6.849Hadjar, A., Marcotte, O., & Soumis, F. (2006). A Branch-and-Cut Algorithm for the Multiple Depot Vehicle Scheduling Problem. Operations Research, 54(1), 130-149. doi:10.1287/opre.1050.0240Hoffman, K. L., & Padberg, M. (1993). Solving Airline Crew Scheduling Problems by Branch-and-Cut. Management Science, 39(6), 657-682. doi:10.1287/mnsc.39.6.657Jepsen, M., Petersen, B., Spoorendonk, S., & Pisinger, D. (2008). Subset-Row Inequalities Applied to the Vehicle-Routing Problem with Time Windows. Operations Research, 56(2), 497-511. doi:10.1287/opre.1070.0449Lübbecke, M. E., & Desrosiers, J. (2005). Selected Topics in Column Generation. Operations Research, 53(6), 1007-1023. doi:10.1287/opre.1050.0234Padberg, M. W., & Rao, M. R. (1982). Odd Minimum Cut-Sets andb-Matchings. Mathematics of Operations Research, 7(1), 67-80. doi:10.1287/moor.7.1.67Pearn, W. L. (1994). Solvable cases of the k-person Chinese postman problem. Operations Research Letters, 16(4), 241-244. doi:10.1016/0167-6377(94)90073-6Righini, G., & Salani, M. (2006). Symmetry helps: Bounded bi-directional dynamic programming for the elementary shortest path problem with resource constraints. Discrete Optimization, 3(3), 255-273. doi:10.1016/j.disopt.2006.05.007Righini, G., & Salani, M. (2008). New dynamic programming algorithms for the resource constrained elementary shortest path problem. Networks, 51(3), 155-170. doi:10.1002/net.20212Ropke, S., & Cordeau, J.-F. (2009). Branch and Cut and Price for the Pickup and Delivery Problem with Time Windows. Transportation Science, 43(3), 267-286. doi:10.1287/trsc.1090.027

Aesthetic considerations for the min-max K-Windy Rural Postman Problem

[EN] The aesthetic quality of routes is a feature of route planning that is of practical importance, but receives relatively little attention in the literature. Several practitioners have pointed out that the visual appeal of a proposed set of routes can have a strong influence on the willingness of a client to accept or reject a specific routing plan. While some work has analyzed algorithmic performance relative to traditional min-sum or min-max objective functions and aesthetic objective functions, we are not aware of any work that has considered a multi-objective approach. This work considers a multi-objective variant of the Min-Max K-Vehicles Windy Rural Postman Problem, discusses several formulations of the problem, and presents computational experiments with a heuristic algorithm. After exploring several formulations, we choose to study the problem with a bi-objective function that includes contributions from the route overlap index and average task distance aesthetic measures. The heuristic extends the cluster-first procedure presented in Lum et al. (Networks 69 (2017), 290-303) by incorporating the new objective function into the improvement phase and adding a perturbation routine. (c) 2017 Wiley Periodicals, Inc.Contract grant sponsor: Spanish Ministerio de Economia y Competitividad and Fondo Europeo de Desarrollo Regional (FEDER); Contract grant number: project MTM2015-68097-P (MINECO/FEDER). Contract grant sponsor: Generalitat Valenciana; Contract grant number: project GVPROMETEO2013-049Corberán, A.; Golden, B.; Lum, O.; Plana, I.; Sanchís Llopis, JM. (2017). Aesthetic considerations for the min-max K-Windy Rural Postman Problem. Networks. 70(3):216-232. https://doi.org/10.1002/net.21748S216232703Baños, R., Ortega, J., Gil, C., Márquez, A. L., & de Toro, F. (2013). A hybrid meta-heuristic for multi-objective vehicle routing problems with time windows. Computers & Industrial Engineering, 65(2), 286-296. doi:10.1016/j.cie.2013.01.007Attea, B. A., Khalil, E. A., & Cosar, A. (2014). Multi-objective evolutionary routing protocol for efficient coverage in mobile sensor networks. Soft Computing, 19(10), 2983-2995. doi:10.1007/s00500-014-1462-yBenavent, E., Corberán, Á., Desaulniers, G., Lessard, F., Plana, I., & Sanchis, J. M. (2013). A branch-price-and-cut algorithm for the min-maxk-vehicle windy rural postman problem. Networks, 63(1), 34-45. doi:10.1002/net.21520Benavent, E., Corberán, A., Piñana, E., Plana, I., & Sanchis, J. M. (2005). New heuristic algorithms for the windy rural postman problem. Computers & Operations Research, 32(12), 3111-3128. doi:10.1016/j.cor.2004.04.007Benavent, E., Corberán, A., Plana, I., & Sanchis, J. M. (2009). Min-Max K -vehicles windy rural postman problem. Networks, 54(4), 216-226. doi:10.1002/net.20334Benavent, E., Corberán, A., Plana, I., & Sanchis, J. M. (2011). New facets and an enhanced branch-and-cut for the min-max K -vehicles windy rural postman problem. Networks, 58(4), 255-272. doi:10.1002/net.20469Benavent, E., Corberán, Á., & Sanchis, J. M. (2009). A metaheuristic for the min–max windy rural postman problem with K vehicles. Computational Management Science, 7(3), 269-287. doi:10.1007/s10287-009-0119-2Bode, C., & Irnich, S. (2012). Cut-First Branch-and-Price-Second for the Capacitated Arc-Routing Problem. Operations Research, 60(5), 1167-1182. doi:10.1287/opre.1120.1079Bräysy, O., & Hasle, G. (2014). Chapter 12: Software Tools and Emerging Technologies for Vehicle Routing and Intermodal Transportation. Vehicle Routing, 351-380. doi:10.1137/1.9781611973594.ch12Constantino, M., Gouveia, L., Mourão, M. C., & Nunes, A. C. (2015). The mixed capacitated arc routing problem with non-overlapping routes. European Journal of Operational Research, 244(2), 445-456. doi:10.1016/j.ejor.2015.01.042Cordeau, J.-F. (2006). A Branch-and-Cut Algorithm for the Dial-a-Ride Problem. Operations Research, 54(3), 573-586. doi:10.1287/opre.1060.0283Gulczynski, D., Golden, B., & Wasil, E. (2011). The period vehicle routing problem: New heuristics and real-world variants. Transportation Research Part E: Logistics and Transportation Review, 47(5), 648-668. doi:10.1016/j.tre.2011.02.002He, R., Xu, W., Sun, J., & Zu, B. (2009). Balanced K-Means Algorithm for Partitioning Areas in Large-Scale Vehicle Routing Problem. 2009 Third International Symposium on Intelligent Information Technology Application. doi:10.1109/iita.2009.307Janssens, J., Van den Bergh, J., Sörensen, K., & Cattrysse, D. (2015). Multi-objective microzone-based vehicle routing for courier companies: From tactical to operational planning. European Journal of Operational Research, 242(1), 222-231. doi:10.1016/j.ejor.2014.09.026G. Karypis V. Kumar METIS-unstructured graph partitioning and sparse matrix ordering systemKarypis, G., & Kumar, V. (1998). A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs. SIAM Journal on Scientific Computing, 20(1), 359-392. doi:10.1137/s1064827595287997Lu, Q., & Dessouky, M. M. (2006). A new insertion-based construction heuristic for solving the pickup and delivery problem with time windows. European Journal of Operational Research, 175(2), 672-687. doi:10.1016/j.ejor.2005.05.012Lum, O., Cerrone, C., Golden, B., & Wasil, E. (2017). Partitioning a street network into compact, balanced, and visually appealing routes. Networks, 69(3), 290-303. doi:10.1002/net.21730Magaia, N., Horta, N., Neves, R., Pereira, P. R., & Correia, M. (2015). A multi-objective routing algorithm for Wireless Multimedia Sensor Networks. Applied Soft Computing, 30, 104-112. doi:10.1016/j.asoc.2015.01.052Mandal, S. K., Pacciarelli, D., Løkketangen, A., & Hasle, G. (2015). A memetic NSGA-II for the bi-objective mixed capacitated general routing problem. Journal of Heuristics, 21(3), 359-390. doi:10.1007/s10732-015-9280-7Matis, P. (2008). DECISION SUPPORT SYSTEM FOR SOLVING THE STREET ROUTING PROBLEM. TRANSPORT, 23(3), 230-235. doi:10.3846/1648-4142.2008.23.230-235Melián-Batista, B., De Santiago, A., AngelBello, F., & Alvarez, A. (2014). A bi-objective vehicle routing problem with time windows: A real case in Tenerife. Applied Soft Computing, 17, 140-152. doi:10.1016/j.asoc.2013.12.012Ombuki, B., Ross, B. J., & Hanshar, F. (2006). Multi-Objective Genetic Algorithms for Vehicle Routing Problem with Time Windows. Applied Intelligence, 24(1), 17-30. doi:10.1007/s10489-006-6926-zPoot, A., Kant, G., & Wagelmans, A. P. M. (2002). A savings based method for real-life vehicle routing problems. Journal of the Operational Research Society, 53(1), 57-68. doi:10.1057/palgrave/jors/260125