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

• The paper considers different transportation systems with different reliability rates in designing the supply chain.
• We have developed a novel PSO based heuristic entitled “Comparative Particle Swarm Optimization” in order to solve the problem.
• A fourth level (suppliers) is added to the initial supply chain and considering this level in the final integration.

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.