Designing a Stochastic Multi-Product Closed Loop Supply Chain Network Considering the Discount and Solving Using the Firefly Algorithm with Decoding Based on Priority

The closed loop supply chain is becoming one of the industry's most important areas of business, due to environmental and business factors. Planning and implementing a closed loop supply chain network provide more profit, customer satisfaction, and a good social image to the company. While most supply chain networks are not equipped with back-up channels, this paper presents a mixed integer nonlinear scheduling model for minimizing shipping costs, operating costs, purchasing costs, and fixed costs for construction in a multi-product potential supply chain network. The proposed model is a multi-product supply chain supply model with the possibility of discounting the purchase of goods from the supplier. Since the design of the network is in the category of NP-hard problems, in this paper, the firefly algorithm is decoded with priority based on the optimal solution. In order to evaluate the performance of the proposed algorithm, it is compared with five algorithms (particle swarm algorithm, forest algorithm, ant colony algorithm, genetic algorithm and honey bee algorithm) in seven criteria. Comparing related numerical results with exact solutions, precise solution, as well as five proposed algorithms in a set of sample issues, indicates the provision of high-performance with high-frequency firefly algorithm with priority decoding.