A multi-objective mixed-integer linear model for sustainable fruit closed-loop supply chain network

Purpose: This paper aims to present a closed-loop supply chain (CLSC) optimization problem for a perishable agricultural product to achieve three pillars of sustainability, including minimizing total network costs and carbon dioxide emissions from different network activities and maximizing responsiveness to demands simultaneously. 

Design/methodology/approach: The research problem is formulated as a multi-objective mixed-integer linear programming model, and classical approaches, including the LP-Metric and weighted Tchebycheff method, have been applied to solve the optimization model. A set of test problems has been proposed to validate the model, and the results are presented. 

Findings: Computational time to find Pareto optimal solutions by using the weighted Tchebycheff method was twice as much as that of the LP-Metric method. Also, the result of the study is a mathematical model that can be applied to other products that are close to the fruit, such as vegetables. Research limitations/implications: The present study is limited to fruits supply chains and the inventory is considered at the distribution centers only. The study also considers only one type of transport. Practical implications: The paper can assist supply chain managers to define strategies to achieve a sustainable CLSC network configuration for the fruits. 

Originality/value: This study is one of the early studies to consider environmental indicators in fruits supply chain design along with two other indicators of sustainability, namely, economic and social indicators. Therefore, this can help supply chain managers to achieve sustainability by optimizing location decisions, inventory quantities and flow between facilities.