A credibility-constrained programming for closed-loop supply chain network design problem under uncertainty

Document Type: Original Article


Department of Industrial Engineering, Masjed-Soleiman Branch, Islamic Azad University, Masjed-Soleiman, Iran


A closed-loop supply chain network (CLSCN) is consisted of both forward and reverse supply chains. In this paper, a CLSCN is including multiple plants, collection centers, demand markets, products and disposal centers. The plants manufacture the new products, then the new products are distributed to the demand market locations and the returned products are collected for sending to the collection centers. Collection centers have important role in recognizing the returned products conditions and the next action of supply chain as follows: inspection and/or separation of the collected products to check whether they are recoverable for sending to remanufacturing plants or unrecoverable ones to be sent to the disposal centers. A mixed-integer linear programming model is proposed to minimize the total cost. Since the uncertain parameters including cost, capacity, demand and the returned products influence the proposed CLSCN, a trapezoidal fuzzy model has been proposed to cope with the vagueness. The expected value is applied to the objective function and the chance constrained programming approach is used to model the uncertain constraint with fuzzy parameters. The numerical examples are coded and solved by GAMZ software. The computational results demonstrate the applicability of the proposed model and solution approach.


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