Vehicle Routing Problem with Transshipment: Mathematical Model and Algorithm

Abstract

This paper presents a new variant of vehicle routing problem with paired transshipment demands (VRPT) between retail stores (customers) in addition to the regular demand from depot to retail stores. The problem originates in a real distribution network of high-end retail department stores in Thailand. Transshipment demands arise for one-order-per-season expensive items, whose inventories at the depot may become shortage after the middle of a season, while they remain available at some retail stores. A transshipment demand is a request for items that need to be picked up from a specific store that has the items and delivered to the store that requests the items. The objective of solving the VRPT is to find delivery routes that can satisfy both regular demands and transshipment demands in the same routes without incurring too much additional transportation distance. A mixed integer linear programming model is formulated to represent the VRPT. Six small problem instances are used to test the model. A hybrid threshold accepting and neighborhood search heuristic is also developed to solve large problem instances of VRPT. The heuristic is further extended to include a forbidden list of transshipment demands that should not be included in the same routes. The purpose is to prevent incurring too much additional distance from satisfying transshipment demands. With the forbidden list, the problem becomes vehicle routing problem with optional transshipment demands (VRPOT). Computational testing shows promising results that indicate effectiveness of the proposed hybrid heuristics as well as the forbidden list.