Abstract
In this study, we introduce a routing problem with multiple uses of a single vehicle and service time in demand points, minimizing the sum of clients’ waiting time to receive service. This problem is relevant in the distribution of aid in disaster-stricken communities, in the recollection and/or delivery of perishable goods and personnel transportation, among other situations, where reaching clients to perform service, fast and fair, is a priority. We consider vehicle capacity and travel distance constraints, forcing multiple use of the vehicle during the planning horizon. This paper presents two mixed integer formulations for this problem, based on a multi-level network, as well as a metaheuristic algorithm. The proposed models can solve to optimality instances with up to 30 clients. The proposed metaheuristic algorithm obtains high-quality solutions in short computational times.
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Abeledo H, Fukasawa R, Pessoa AA and Uchoa E (2013). The time dependent traveling salesman problem: Polyhedra and algorithm. Mathematical Programming Computation 5 (1): 27–55.
Adenso-Diaz B and Laguna M (2006). Fine-tuning of algorithms using fractional experimental designs and local search. Operations Research 54 (1): 99–114.
Alonso F, Alvarez M and Beasley JE (2008). A tabu search algorithm for the periodic vehicle routing problem with multiple vehicle trips and accessibility restrictions. Journal of the Operational Research Society 59 (7): 963–976.
Angel-Bello F, Alvarez A and García I (2013). Two improved formulations for the minimum latency problem. Applied Mathematical Modelling 37 (4): 2257–2266.
Avella P, Boccia M and Sforza A (2004). Solving a fuel delivery problem by heuristic and exact approaches. European Journal of Operational Research 152 (1): 170–179.
Azi N, Gendreau M and Potvin J-Y (2007). An exact algorithm for a single-vehicle routing problem with time windows and multiple routes. European Journal of Operational Research 178 (3): 755–766.
Azi N, Gendreau M and Potvin J-Y (2010). An exact algorithm for a vehicle routing problem with time windows and multiple use of vehicles. European Journal of Operational Research 202 (3): 756–763.
Brandão J and Mercer A (1997). A tabu search algorithm for the multi-trip vehicle routing and scheduling problem. European Journal of Operational Research 100 (1): 180–191.
Camci F (2013). The travelling maintainer problem: Integration of condition-based maintenance with the travelling salesman problem. Journal of the Operational Research Society 65 (9): 1423–1436.
Christofides N, Mingozzi A, Toth P and Sandi C (eds) (1979). The vehicle routing problem. In: Combinatorial Optimization. Wiley: Chichester, pp 315–338.
Cordeau J-F, Gendreau M and Laporte G (1997). A tabu search heuristic for periodic and multi-depot vehicle routing problems. Networks 30 (2): 105–119.
Cornillier F, Laporte G, Boctor FF and Renaud J (2009). The petrol station replenishment problem with time windows. Computers & Operations Research 36 (3): 919–935.
Feo TA and Resende MG (1995). Greedy randomized adaptive search procedures. Journal of Global Optimization 6 (2): 109–133.
Festa P and Resende M (2011). GRASP: Basic components and enhancements. Telecommunication Systems 46 (3): 253–271.
Golden BL, Wasil EA, Kelly JP and Chao IM (1998). Metaheuristics in vehicle routing. In: Crainic TG and Laporte G (eds). Fleet Management and Logistics. Kluwer: Boston, MA, pp 33–56.
Gouveia L and Voss S (1995). A classification of formulations for the (time-dependent) traveling salesman problem. European Journal of Operational Research 83 (1): 69–82.
Ke L and Feng Z (2013). A two-phase metaheuristic for the cumulative capacitated vehicle routing problem. Computers & Operations Research 40 (2): 633–638.
Koc C and Karaoglan I (2011). A branch and cut algorithm for the vehicle routing problem with multiple use of vehicles. In: 41st International Conference on Computers & Industrial Engineering, pp 554–559.
Macedo R, Alves C, Valério de Carvalho J, Clautiaux F and Hanafi S. (2011). Solving the vehicle routing problem with time windows and multiple routes exactly using a pseudo-polynomial model. European Journal of Operational Research 214 (3): 536–545.
Martínez L and Amaya C (2012). A vehicle routing problem with multi-trips and time windows for circular items. Journal of the Operational Research Society 64 (11): 1–14.
Mattos Ribeiro G and Laporte G (2012). An adaptive large neighborhood search heuristic for the cumulative capacitated vehicle routing problem. Computers & Operations Research 39 (3): 728–735.
Méndez-Díaz I, Zabala P and Lucena A (2008). A new formulation for the traveling deliveryman problem. Discrete Applied Mathematics 156 (17): 3223–3237.
Ngueveu SU, Prins C and Calvo RW (2010). An effective memetic algorithm for the cumulative capacitated vehicle routing problem. Computers & Operations Research 37 (11): 1877–1885.
Olivera A and Viera O (2007). Adaptive memory programming for the vehicle routing problem with multiple trips. Computers & Operations Research 34 (1): 28–47.
Petch R and Salhi S (2003). A multi-phase constructive heuristic for the vehicle routing problem with multiple trips. Discrete Applied Mathematics 133 (1–3): 69–92.
Picard JC and Queyranne M (1978). The time-dependent traveling salesman problem and its application to the tardiness problem in one-machine scheduling. Operations Research 26 (1): 86–110.
Salehipour A, Sörensen K, Goos P and Bräysy O (2008). An efficient GRASP+VND metaheuristic for the traveling repairman problem. Technical report, University of Antwerp, Faculty of Applied Economics.
Salehipour A, Sörensen K, Goos P and Bräysy O (2011). Efficient GRASP+VND and GRASP+VNS metaheuristics for the traveling repairman problem. 4OR—A Quarterly Journal of Operations Research 9 (2): 189–209.
Şen A and Bülbül K (2008). A survey on multi trip vehicle routing problem. In: VI. International Logistics and Supply Chain Congress, Istanbul, Turkey. İstanbul Bilgi Üniversitesi.
Silva MM, Subramanian A, Vidal T and Ochi LS (2012). A simple and effective metaheuristic for the minimum latency problem. European Journal of Operational Research 221 (3): 513–520.
Taillard ED, Laporte G and Gendreau M (1995). Vehicle routeing with multiple use of vehicles. Journal of the Operation Research Society 47 (8): 1065–1070.
Toth P and Vigo D (eds) (2002). The Vehicle Routing Problem. Society for Industrial and Applied Mathematics: Philadelphia, PA.
Vidal T, Crainic T, Gendreau M and Prins C (2013). A unified solution framework for multi-attribute vehicle routing problems. Technical Report 2013-22, CIRRELT.
Wang Z, Liang W and Hu X (2014). A metaheuristic based on a pool of routes for the vehicle routing problem with multiple trips and time windows. Journal of the Operational Research Society 65 (1): 37–48.
Acknowledgements
This work is partially supported by the Research Chair in Industrial Engineering of Tecnológico de Monterrey (ITESM Research Fund CAT128) and the Universidad Autónoma de Nuevo León (PAICYT IT764-11). These grants are gratefully acknowledged.
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Martínez-Salazar, I., Angel-Bello, F. & Alvarez, A. A customer-centric routing problem with multiple trips of a single vehicle. J Oper Res Soc 66, 1312–1323 (2015). https://doi.org/10.1057/jors.2014.92
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DOI: https://doi.org/10.1057/jors.2014.92