An optimum closed loop supply chain network model in a stochastic product life cycle context

Abstract

Nowadays, closed loop supply chain network (CLSCN) receives considerable attention due to the growing awareness of the environmental destruction and depletion of natural resources. The establishment of a CLSCN is considered as a strategic decision that requires a lot of effort and intensive capital resources. Therefore, it is very crucial to make CLSCN design decisions taking into account multiple facets of uncertainties. Literature reviews to date reveals that uncertainties in product life cycle (PLC) or what has been called “product diffusion” have been vastly ignored. Particularly, the deterministic nature of the proposed diffusion models is a severe defect that can hinder the involvement of real-world uncertainties in design of a CLSCN. This study is an attempt to fill this gap by developing a costefficient CLSCN model for a product with dynamic and stochastic diffusion into the market that leads to an optimum design of the targeted CLSCN. Firstly, a geometric Brownian motion (GBM)-based diffusion forecast method was proposed and validated using a conventional approach namely, Holt’s method. Then, a two-stage stochastic programming mathematical model for optimum design of the targeted CLSCN was developed. The developed stochastic CLSCN model provides the optimum design of the targeted CLSCN utilizing the values predicted for the product diffusion through the PLC based on the proposed forecast method. The developed mathematical model addresses two types of decisions namely, “here and now” and “wait and see” decisions within the PLC. The “here and now” decisions were made in the first stage. The results show optimum values for decisions concerning configuration of the CLSCN as well as dynamic capacity allocation and expansion decisions through the PLC. However, the “wait and see” decisions are made in the second stage within the frame provided by the first-stage solutions. Here, the results portray optimum values for decisions concerning with the flow quantities between the CLSCN facilities, backorder and inventory levels, and recovery of returns through the PLC. In order to test the applicability of the developed CLSCN model, the mathematical model was coded by CPLEX software and solved for secondary data from the case study from previous case study in literature. Finally, a sensitivity analysis was performed to investigate the effect of diffusion uncertainty on the total cost of the CLSCN, its configuration, and production capacity allocations and expansions. The results of the sensitivity analysis revealed that, for the higher levels of diffusion uncertainty, the total cost imposed to the supply chain increases due to the increase in the allocated production capacity as well as the increase in the number of involved facilities.