An Interactive Possibilistic Programming Approach to Designing a 3PL Supply Chain Network Under Uncertainty

The design of closed-loop supply chain networks has attracted increasing attention in recent decades with environmental concerns and commercial factors. Due to the rapid growth of knowledge and technology, the complexity of the supply chain operations is increasing daily and organizations are faced with numerous challenges and risks in their management. Most organizations with limited resources, capabilities, and knowledge outsource their logistics services to reduce costs and increase customer satisfaction. The Third-Party Logistics (3PL) Providers have been set up to outsource various supply chain activities to specialized companies. This paper proposes a bi-objective possibilistic mixed-integer nonlinear programming model for designing a closed-loop supply chain network from the perspective of 3PL. To solve the proposed multi-objective model, a two-stage solving approach was applied first to converting the possibilistic model into its equivalent crisp counterpart and second, to converting the crisp multi-objective model into a single-objective one. Using this approach, a single-objective equivalent auxiliary crisp model was obtained and solved optimally by IBM ILOG CPLEX software. Solving numerical examples proved the effectiveness of the proposed bi-objective, possibilistic framework. Several sensitivity analyses were performed to gain managerial insights.