Dynamic facility location with supplier selection under quantity discount

Abstract

Retailers have to consider several factors when making facility location decisions including suppliers’ and customers’ locations, customer demand and price offered by suppliers. In this study, we analyze the multi-period facility location decisions of a retailer which procures the products from multiple suppliers under an incremental quantity discount scheme and in turn satisfies an exogenous demand. The retailer decides (i) where and when to open a facility, (ii) how much to order from each supplier in each time period, and (iii) from which facility locations to satisfy the demand. We formulate the problem as a mixed-integer mathematical model. To handle large instances, we develop a decomposition-based solution approach which considers the decisions in the first echelon (suppliers and facilities) and the second echelon (facilities and customers) in an iterative manner until convergence. We propose two implementations of the proposed solution approach. The first one limits the search space by considering only a subset of the facility locations for each customer. In the second implementation of the proposed solution approach, we develop a novel two-phase strategy where we first eliminate some of the facility locations entirely from the problem using a simplified version of the first approach and then implement the first approach to the reduced set of facility locations. We demonstrate the effectiveness of the heuristic approaches through an extensive computational study. The proposed heuristics provide significantly better results compared to a simple heuristic inspired by a related study. Moreover, we observe that for small instances both heuristics provide solutions with quite low optimality gaps and for larger instances they find better solutions in less amount of time when compared against CPLEX results obtained within a 12-h time limit.