Application of Benders Decomposition in Closed-loop Supply Chain Models with Uncertain Scenarios

This paper explores an efficient algorithm for a closed-loop supply chain (CLSC). The CLSC problem is formulated as a Mixed-integer Linear Programming (MILP) with multiple scenarios. The variables in the model, such as the location selection of factories and collection centers, are integer variables, whereas the transportation flow between nodes in the model are continuous variables. Due to the inclusion of multiple scenarios, the number of constraints in the continuous problem part is significantly large. Furthermore, the presence of integer variables extends the computation time required for direct calculations. This paper attempts to use Benders Decomposition to divide the integer and continuous parts of the model into two steps of solution, aiming to reduce the computation time. This paper extends the original model, which considers random demand quantities and recovery rates as stochastic scenarios, to include scenarios for insufficient raw material supply and fluctuating recycling values. The original model is transformed into a multidimensional stochastic model, and the practicality of Benders Decomposition is demonstrated.