The Incremental Cost Matrix Procedure for Locating Repair Service Centers in Multinational Reverse Logistics

This study provides a heuristic algorithm to solve the locating problem of repair service centers (RSCs). To enhance the customer service level with more satisfaction and quicker responsiveness, the locating problem of RSCs has become one of the important issues in reverse supply chain management. This problem is formulated as a zero-one mixed integer programming in which an exiting distributor will be considered to be an un-capacitated repair service center for the objective of cost-minimizing. Since logistical costs are highly interrelated with the multinational location of distributors and RSCs, the fixed cost for setting a repair service center, variable cost, transportation cost, and exchange rates are considered in this study. Recognizing the selection of un-capacitated RSCs' locations is a combinatorial optimization problem and is a zero-one mixed integer programming with NP-hard complexity, we provide a heuristic algorithm named as incremental cost matrix procedure (ICMP) to simplify the solving procedure. By using the concise and structural cost matrix, ICMP can efficiently screen the potential location with cost advantage and effectively decide which distributor should be a RSC. Results obtained from the numerical experiments conducted in small scale problem have shown the fact that ICMP is an effective and efficient heuristic algorithm for solving the RSCs locating problem. In the future, using the extended ICMP to solve problems with larger industrial scale or problems with congestion effects caused by the variation of customer demand and the restriction of the RSC capacity is worth a further investigation.