modeling the multi-period and multi-product closedloop supply chain network design problem considering reused cost and capacity constraints

The importance of remanufacturing used products into new ones has been widely recognized in the literature and in practice. this is due to both of economic opportunities and environmental aspects. this paper aims to design a new integrated multi-period & multi-product closed-loop supply chain network considering reused cost and capacity constraints for all stages. in this problem the stages of supplier, assembler, retailer, customer, collection center, refurbishing center, and disassembler is regarded consequently. the considered objective function is total cost factors that consists of 7 components: costs of associated with locating the plants and retailers, purchasing, transportation, collection of used products from customers, disposal for subassemblies, refurbishing, and finally refund to customers. first, parameters and decision variables of this problem are defined, then a mixed integer linear programming mathematical model is presented. the proposed mathematical model is run applying the gams software. two real examples (shed light, and power-outlet) are considered to solve using the proposed mathematical model. these two examples were obtained based on data in two new references. since this problem is known as np-hard, the model is run just for small-sized problem consists of four suppliers, two disassemblers, two retailers, and two periods. the results are analysed and some sensitivity analysis have been done for the effective factors. these result show that, the demand has a less effect on total cost. but purchasing/refurbishing cost ratio has a high effect on the objective function. finally, the capacity of collection and refurbishing centers has a high effect in primary changes and this effect gradually reduced. so having the proper capacity for collection and refurbishing centers and also creating balance between different stages can reduce overall cost.