A four-echelon supply chain network design with shortage: Mathematical modeling and solution methods

Often, companies deliberately fulfill demands with delay since they can benefit from reducing transportation and setup costs. This paper aims at designing a four-echelon supply chain structure including multiple suppliers, multiple producers, multiple distributors and multiple customers. The objectives are to minimize the total operating costs of all the supply chain elements and to maximize the reliability of the system. A number of transportation systems with different reliability rates are considered. The paper mathematically formulates the problem as a mixed integer linear programming model. In order to solve the large-sized instances of the problem, the paper proposes a novel heuristic algorithm called Comparative Particle Swarm Optimization. This algorithm employs a mechanism in order to compare the generated solutions and to prevent from generating worse solutions. The results of different numerical experiments endorse the effectiveness of the proposed heuristic. (C) 2014 The Society of Manufacturing Engineers. Published by Elsevier Ltd. All rights reserved.