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Due to increasing air pollution, which is a consequence of the environmental effects of production in various industries, green supply chain management (GSCM) has attracted the attention of both scholars and practitioners. Green supplier selection is an important problem in GSCM and seeks to satisfy a firm's environmental goals as well as its economic targets. In this paper, for the first time, a green supplier selection problem considering both green and non-green evaluation criteria in a closed-loop supply chain is studied, and a cap-and-trade mechanism as a way of controlling the air pollution caused by manufacturers is proposed. To solve this particular problem, we propose a multi-objective robust optimization (RO) model. This specific model is an effective approach to handle uncertainty. A numerical example using randomly generated data, accompanied by subsequent discussion of the proposed approach, is deployed to validate the model. The results prove that the developed model for green supplier selection is able to effectively enhance the decision-making process of the experts. By illustrating the trade-off in robustness between the model and proposed solutions, as well as the effect of the deviation penalty on the closeness of results to the achieved solution, we show how firms can make optimal decisions when assigning the parameters. Furthermore, analyses show that decreasing the allowance amount (cap) and increasing the allowance prices in the cap-and-trade system escalate the firms' costs, but lower the amount of carbon released. Finally, we show that the cap-and-trade mechanism results in a better solution in terms of the total utility of the supply chain compared to the penalty-based system for a specific range of carbon allowance. • This paper generalizes the green supplier selection and order allocation problem. • A mathematical model for the problem is developed. • A robust optimization approach to handle the model uncertainty is developed. • The impact of changes in model parameters on the objective functions is analyzed. • The cap-and-trade mechanism is compared with a penalty-based mechanism. [ABSTRACT FROM AUTHOR]

Highlights • We model a new quantity discounts supply chain planning problem. • The model is very hard to solve using leading commercial solvers. • We develop MIP-based local search algorithms for our problem. • We apply our model to a realistic food supply chain. • We show the efficiency of our algorithms in getting high quality solutions quickly. Abstract Supplier selection with quantity discounts has been an active research problem in the literature. In this paper, we focus on a new real-world quantity discounts scheme, where suppliers are selected in the beginning of a strategic planning period (e.g., 5 years). Monthly orders are placed from the selected suppliers, but the quantity discounts are based on the aggregated annual order quantities. We incorporate this type of cost structure in a multi-period, multi-product, multi-echelon supply chain planning problem, and develop a mixed integer linear programming (MIP) model for it. Our model is highly intractable; leading commercial solvers cannot construct high quality feasible solutions for realistic instances even after multiple hours of solution time. We develop an algorithm that constructs an initial feasible solution and a large neighborhood search method that combines two customized iterative algorithms based on MIP-based local search and improves such solution. We report numerical results for a food supply chain application and show the efficiency of using our methodology in getting very high quality primal solutions quickly. [ABSTRACT FROM AUTHOR]

Forward and reverse supply chains form a closed-loop supply chain. In this paper, a mathematical model is proposed for a closed-loop supply chain network by considering global factors, including exchange rates and customs duties. The model is a multi-objective mixed-integer linear programming model under uncertain demand. A solution approach based on fuzzy programming is developed for solving the optimization problem. The model is then applied in a network, which is located in Southwestern Ontario, Canada. A sensitivity analysis is provided to validate the model. This model considers global factors, multiobjectives, and uncertainty simultaneously in a closed-loop supply chain network. [ABSTRACT FROM AUTHOR]

With the growing level of public environmental consciousness, sustainability has become an important issue in the area of supply chain management. This paper focuses on a channel coordination problem in a two-echelon sustainable supply chain involving one socially responsible manufacturer and one fair-minded retailer. Constructing mathematical models to characterize the problem, four particular contracts are developed to investigate the environmental performance and channel profit under the framework of two non-cooperative contracts: wholesale price and two-part tariff, and two cooperative contracts: Nash bargaining and Rubinstein bargaining. Theoretical analysis verified by numerical experiments shows that the wholesale price contract performs worse than the other three in terms of the carbon emission per unit product and channel profit. In addition, the two-part tariff contract can partially coordinate the supply chain, whereas both bargaining contracts can achieve perfect coordination to provide outcomes of the centralized decision. Comparing with the fair-neutral scenarios, we find that the fairness behavior promotes the retailer's profit, but reduces the manufacturer's profit under different contracts. Sensitivity analysis reveals that with intensified fairness concerns, the sustainability level and channel profit diminish under non-cooperative contracts, but remain the same under cooperative contracts. The Nash bargaining and Rubinstein bargaining contracts are robust to the degree of the retailer's fairness behavior and could be the best choice for the socially responsible manufacturer. • A channel coordination issue in a two-echelon sustainable supply chain is studied. • Four contracts are developed to examine the impact of retailer's fairness behavior. • Fairness behavior worsens wholesale price contract compared to two-part tariff one. • Nash and Rubinstein bargaining contracts are robust to levels of fairness concerns. • Both bargaining contracts achieve perfect coordination in reducing carbon emission. [ABSTRACT FROM AUTHOR]