A Multi-Product Production/Distribution System Design Problem with Direct Shipments and Lateral Transshipments

In this paper, we investigate a multi-product, three-stage production/distribution system design problem (PDSD) with direct shipment and lateral transshipment capabilities. Our overall goal is to find the most efficient network design to minimize the total fixed facility and transportation costs. Specifically, we locate p capacitated distribution centers in the second stage from a set of candidate locations. At the same time, our design allows for direct shipments between first (suppliers) and third stages (customers) and lateral transshipments among the distribution centers in the second stage. The PDSD problem is known to be NP-hard, and prior studies have explored several heuristic methods including scatter search, tabu search, and genetic algorithms to solve the problem. In this paper, we propose two solution algorithms based on simulated annealing and GRASP heuristics. We apply both long-term and short-term memory lists to maintain an efficient local search, combined with a custom greedy solver that can effectively evaluate the quality of a solution candidate. We conduct a series of computational experiments to validate the proposed algorithms. Compared with the optimal solution, the simulated annealing algorithm presents an average optimality gap of 0.07% and an average time of 25.56% of optimal solution time, while the GRASP algorithm achieves a solution gap of 0.11% with 17.85% of optimal running time. The experimental results also show that the simulated annealing and GRASP algorithms outperform the best-reported heuristic in the literature based on scatter search regarding both solution quality and duration, especially for large-scale problem instances with tighter capacities.