A novel mix integer linear programming model for design of multi-level integrated supply chain

In the current century, the pattern of competition in production and services has shifted from competition among independent firms to competition among supply chains. Meanwhile, the issue of strategic design of the supply chain is one of the key issues in the field of supply chain management. In these issues, the aim is generally to provide a number of manufacturing facilities and distribution centers at the candidate sites (in different geometrical areas) in order to cover the demand for various products in the customer’s area. In the proposed model, demand for each product in customer areas is achieved through a number of distribution centers, while these distribution centers provide products from manufacturing factories, and these factories must purchase the requirement components to design and produce each product from suppliers. Here, a single-objective mathematical model of mix integer linear programming is proposed that simultaneously considers the facility location problem in addition to the design of the multi-level supply chain. In this model, there are various objectives, such as minimizing the costs of the procurement and production of components, the preparation and production of products, storage and dispatch the products to distribution centers, sending to customer areas and the cost of building factories and distribution centers. To evaluate the proposed model, the mathematical model is first coded with GAMS optimization software, and then solved for large-scale problems with particle swarm optimization algorithm and imperialist competitive algorithm. Statistical analysis of the results indicates the quality of the model and the proposed solving procedure.