Mathematical models for green vehicle routing problems with pickup and delivery: A case of semiconductor supply chain

In this paper, we consider a special case of vehicle routing problem that addresses the routing problem in a semiconductor supply chain. This paper proposes two Mixed Integer Linear Programming (MILP) models for solving the Green Vehicle Routing Problems with Pickups and Deliveries in a Semiconductor Supply Chain (G-VRPPD-SSC). The first MILP model considers the basic G-VRPPD-SSC problem, and the objective is to find the set of minimum cost routes and schedules for the alternative fuel vehicles in order to satisfy a set of requests which comprise pickup and delivery operations, without violating the product and vehicle compatibility, vehicle capacity, request-priorities and request-types, and start/completion time constraints. The second model extends the first model in order to handle the scenario of having different fuel prices at different refueling stations, and the objective is to minimize the sum of costs of operating alternative fuel vehicles, which include both the routing cost and the refueling cost. To relatively evaluate the performance of the proposed MILP models, we consider the Pickup and Delivery Problem in a Semiconductor Supply Chain (PDP-SSC) without the presence of alternative fuel vehicles, and we present the corresponding MILP model. Our model is compared with an MILP model present in the literature. Our study indicates that the proposed model for the PDP-SSC gives better lower bounds than that by the existing work, apart from performing better than the existing work in terms of requiring less CPU time. In all cases, the proposed three MILP models preform quite good in terms of the execution time to solve the generated problem instances.