A hybrid system dynamics and two-stage mixed integer stochastic programming approach for closed-loop battery supply chain optimization

Abstract

Used lead-acid batteries contain a large amount of lead, which poses a threat to the environment; however, since it is valuable economically, recycling function is very important. Previous studies have not consistently examined closed-loop supply chain (CLSC) from two macro and micro perspectives. In this study, System Dynamics (SD) and mathematical programming are integrated for the first time in the field of CLSC in order to optimize the lead-acid battery CLSC for a focal company that faces the shortage of recycled lead, and therefore, increased economic costs and environmental pollution due to the purchasing of raw lead. First, the CLSC of lead-acid battery was simulated using SD under four scenarios for economic situation. Then the network is optimized using a two-stage stochastic mixed programming under the uncertainty of demand using the parameters estimated by SD. Considering the importance of supply chain (SC) financing, financial flows like trade and bank credits are also integrated. The results indicated that authorized delay in repayment without interest and interest rate for delay in repayment play an important role in making a decision to whether or not receive trade or bank credit, selection of suppliers and banks, and when to repay the trade or bank credit. Eventually, due to the need for the use of bank credit, a repayment of 2% more than using trade credit has been imposed on the company. Physical flows showed that shortage of recycled lead supply is, to some extent, due to failing to collect sufficient number of batteries. It was found that when recycling capacity increases by adopting such policies as product exchange, maximum capacity is not used. Moreover, limited recycling capacity causes this shortage that makes it necessary to make more to investments expand the recycling capacity. Increasing the recycling capacity to 12.5% in the growth scenario will result in the economic saving of 10.8%.