Designing a portfolio-based closed-loop supply chain network for dairy products with a financial approach: Accelerated Benders decomposition algorithm

Abstract

Product portfolio design is one of the important and effective factors in the financial and physical flows of various supply chains, especially dairy products. Accordingly, the financial and physical flows of the portfolio should be taken into consideration during the supply chain design. In this study, a closed-loop supply chain (CLSC) network is designed for dairy products aiming at maximizing the net cash flow from assets and maximizing the amounts paid to shareholders simultaneously. To find the optimal policy, an accelerated Benders decomposition (ABD) algorithm is implemented to tackle the complexity of the model. Moreover, three multi-objective optimization solution approaches of the weighted sum method (WSM), augmented ε-constraint (AEC), and fuzzy multi-objective programming (FMOP) are implemented to tackle the bi-objectiveness of the model. Next, a real case study in Iran is investigated to reveal the applicability of the developed methodology. Numerical results reveal that the ABD method reduces CPU time by about 10.8%. Moreover, the results of the case study demonstrate that by integrating financial and physical flows, an improvement of 4.8478% in the net cash flow from assets and a 2.3% improvement in the amounts paid to shareholders compared to the current situation.