Abstract

This paper presents an integrated network design model for a supply chain in which supplier and distribution centers are unreliable. When there is an unreliable supplier, the amount of yield which is received at each distribution center may be different from the original orders. Similarly, because of imperfect performances of distribution centers, the quantity of products which is transformed from each DC to each customer may be less than what was originally planned. In such a system, customers have random demands and there is flexibility in determining which customers must be served. The proposed model of this study is formulated as a nonlinear integer programming to minimize the expected total cost which includes the costs of location, inventory, transportation and lost sales. The model simultaneously determines the optimal location of distribution centers, the subset of customers to serve, the assignment of customers to distribution centers and the cycle order quantities at distribution centers. In order to solve the resulted mathematical model, an efficient solution methodology based on Lagrangian relaxation approach and genetic algorithm is developed. Finally, computational results for several instances of the problem are presented to imply the effectiveness of the proposed approach.

Key words: Lagrangian relaxation, integrated supply chain design model, uncertainty, location, inventory, genetic algorithm, birth-death process.