Benders’ decomposition for concurrent redesign of forward and closed-loop supply chain network with demand and return uncertainties

• A stochastic MILP model for CLSCND problem is solved using Benders’ decomposition.
• We consider uncertainty in products’ demands and the amount of returned products.
• The problem is developed in the multi-period and multi-product contexts.
• Cholesky’s factorization and k-means clustering methods are utilized to generate scenarios.
• The method is tested on a case study in cell phone SC.

This paper attempts to design a reverse supply chain network (SCN), add it to an existing multi-product forward SCN and simultaneously redesign the existing forward supply chain (SC). The problem considers uncertainty on products demand and and also returned products in multi-period context. Benders’ decomposition is applied to solve the stochastic mixed-integer model to optimality. The scenarios are generated based on the demand distribution function using Cholesky’s factorization method to consider correlation among different products’ demands. To decrease the computational effort, the number of scenarios is reduced using k-means clustering algorithm. The method is tested on a cell phone SC.