Supply Chain Network Design with Time and Capacity Requirements

An efficient supply chain network is crucial to the logistics of a modern business. Careful design of the supply chain network will lead to enormous cost saving and market opportunity. In the supply chain network design, how to determine the best location and capacity configurations of the Distribution Centers (DCs) and the distribution paths is a challenging issue. Intensive researches have tackled this problem. However, in this paper, for the first time, we consider the supply chain network design problem with time and capacity constraints. The supply chain network considered here is composed of several potential locations for the DCs and predetermined locations and traffic requirements for the supplier (origin) and consumer nodes (destination). The origin can only make the shipment to the destination via DCs without the possibility of shipping to the destination directly. In this paper, only the traffic requirements (including the amount of goods to be shipped and the shipping time requirement) of each origin and destination pair (O-D pair) is known in advance. We try to determine the best locations for these DCs and their associated optimal capacity configurations, and to establish the optimal routing assignment for each O-D pair in order to meet the traffic requirements. The objective of supply chain design problem is to minimize the total DCs construction cost (in terms of the capacity configurations for the DCs) and the transportation cost (in terms of the capacity configurations for the transporting vehicles), where the capacity and time requirements are explicitly enforced in the constraints. The capacity constraints include the capacity constraints for the DCs and the transporting vehicles. The capacity constraints for the DCs require that the amount of the distributed goods should not exceed the capacity of the DCs. The capacity constraints for the transporting vehicles require that the amount of transported goods should not exceed the capacity of the transporting vehicles. The transportation time constraints require that the end-to-end transportation time should not exceed the maximum allowable end-to-end delay for each O-D pair. In this paper, we assume the transporting time to be a function of the associated distance, and the time function does not need to be a linear function of distance, and even non-convex functions could be handled. The problem is formulated as a non-linear and non-convex combinatorial optimization problem. The Largragean relaxation method is applied to solve this problem. From the computational results, by assessing the gap between heuristic upper bounds and the Lagrangean lower bounds and the computational time, we propose the high efficiency and effectiveness algorithms for the supply-chain network design problem.