A distribution-free-based approach for stochastic food closed-loop supply chain
研究了食品行业中带可回收运输物品的闭环供应链优化问题，提出无分布方法处理不确定需求，相比传统方法大幅降低计算时间，并给出延长保质期和适度扩大产能可降低总成本的见解。
Resource scarcity has driven growing interest in circular economy (CE). Closed-loop supply chain (CLSC) with returnable transport items (RTIs) in the food industry is an important component of CE. However, existing works on food CLSC with RTIs have not simultaneously considered the perishability, facility location, and uncertain demand under limited information. Therefore, this work addresses a new food CLSC optimisation problem. We first propose a non-linear chance-constrained programming model. It is then transformed into a mixed-integer linear programming model via using the distribution-free (DF) method and sample average approximation (SAA) method, respectively. An illustrative example reveals that the DF method needs only 10.50% of the computation time of the SAA method. To address large-scale problems, an improved Lagrangian relaxation (LR) method is developed. To address the computational challenge in large-scale problems, an improved Lagrangian relaxation (LR) algorithm is developed. Results show that CPLEX achieves a gap of 75.57%, while the LR surpasses it by finding near-optimal solutions with a gap of 1.22%, using only 31.82% of the computation time required by CPLEX. For this work, the main insights are summarised: (1) extending product shelf life can reduce the total cost; and (2) to alleviate uncertain demand and production risks, production capacity and product inventory capacity can be appropriately expanded, but excessive investment may not improve returns.