In this work, we consider the Vehicle Routing Problem with Simultaneous Delivery and Pickup, and constrained by time windows, to improve the performance and responsiveness of the supply chain by transporting goods from one location to another location in an efficient manner. In this class of problem, each customer demands a quantity to be delivered as a part of the forward supply service and another quantity to be picked up as a part of the reverse recycling service, and the complete service has to be done simultaneously in a single visit of a vehicle, and the objective is to minimize the total cost, which includes the traveling cost and dispatching cost for operating vehicles. We propose a Mixed Integer Linear Programming (MILP) model for solving this class of problem. In order to evaluate the performance of the proposed MILP model, a comparison study is made between the proposed MILP model and an existing MILP model available in the literature, with the consideration of heterogeneous vehicles. Our study indicates that the proposed MILP model gives tighter lower bound and also performs better in terms of the execution time to solve each of the randomly generated problem instances, in comparison with the existing MILP model. In addition, we also compare the proposed MILP model (assuming homogeneous vehicles) with the existing MILP model that also considers homogeneous vehicles. The results of the computational evaluation indicate that the proposed MILP model gives much tighter lower bound, and it is competitive to the existing MILP model in terms of the execution time to solve each of the randomly generated problem instances.
Supply chain transportation vehicle routing problem simultaneous delivery and pickup time windows integer programming model
This is a preview of subscription content, log in to check access.
We are thankful to the reviewers and the Editor for their valuable comments and suggestions to improve our manuscript.
Chopra S and Meindl P 2007 Supply chain management: strategy, planning and operation. New Jersey: Pearson Prentice HallGoogle Scholar
Toth P and Vigo D 2002 The vehicle routing problem. In: SIAM Monographs on Discrete Mathematics and Applications. Philadelphia, PA, USA: SIAMGoogle Scholar
Parragh S N, Doerner K F and Hartl R F 2008 A survey on pickup and delivery problems. J. Betriebswirtschaft 58: 21–51CrossRefGoogle Scholar
Wang H F and Chen Y Y 2012 A genetic algorithm for the simultaneous delivery and pickup problems with time window. Comput. Ind. Eng. 62: 84–95CrossRefGoogle Scholar
Min H 1989 The multiple vehicle routing problem with simultaneous delivery and pick-up points. Transp. Res. A Gen. 23: 377–386CrossRefGoogle Scholar
Dethloff J 2002 Relation between vehicle routing problems: an insertion heuristic for the vehicle routing problem with simultaneous delivery and pick-up applied to the vehicle routing problem with backhauls. J. Oper. Res. Soc. 53: 115–118CrossRefGoogle Scholar
Ganesh K and Narendran T T 2008 TASTE: a two-phase heuristic to solve a routing problem with simultaneous delivery and pick-up. Int. J. Adv. Manuf. Technol. 37: 1221–1231CrossRefGoogle Scholar
Ai T J and Kachitvichyanukul V 2009 A particle swarm optimization for the vehicle routing problem with simultaneous pickup and delivery. Comput. Oper. Res. 36: 1693–1702CrossRefGoogle Scholar
Liu R, Xie X, Augusto V and Rodriguez C 2013 Heuristic algorithms for a vehicle routing problem with simultaneous delivery and pickup and time windows in home health care. Eur. J. Oper. Res. 230: 475–486MathSciNetCrossRefGoogle Scholar
Wang C, Mu D, Zhao F and Sutherland J W 2015 A parallel simulated annealing method for the vehicle routing problem with simultaneous pickup–delivery and time windows. Comput. Ind. Eng. 83: 111–122CrossRefGoogle Scholar
Kallehauge B, Larsen J, Madsen O B and Solomon M M 2005. Vehicle routing problem with time windows. In: Desaulniers G, Desrosiers J and Solomon M M (Eds.) Column Generation. New York: Springer, pp. 67–98CrossRefGoogle Scholar
Polat O, Kalayci C B, Kulak O and Günther H O 2015 A perturbation based variable neighborhood search heuristic for solving the Vehicle Routing Problem with Simultaneous Pickup and Delivery with Time Limit. Eur. J. Oper. Res. 242: 369–382MathSciNetCrossRefGoogle Scholar
Solomon M M 1987 Algorithms for the vehicle routing and scheduling problems with time window constraints. Oper. Res. 35: 254–265MathSciNetCrossRefGoogle Scholar
Ramanathan R, George J and Ramanathan U 2014 The role of logistics in e-commerce transactions: an exploratory study of customer feedback and risk. In: Ramanathan U and Ramanathan R (Eds.) Supply Chain Strategies, Issues and Models. London: Springer, pp. 221–233CrossRefGoogle Scholar