Multi‐objective location‐allocation‐routing problem of perishable multi‐product supply chain with direct shipment and open routing possibilities under sustainability

Abstract In this study, a multi‐objective formulation is proposed for designing a supply chain of perishable products including suppliers, plants, distributors, and customers under sustainable development. In addition to the studies of the literature, direct shipment between producers and customers and also alternative products possibility are allowed. In this problem, the objectives, such as facilities establishment costs, transportation costs, negative environmental impacts, and social impact (fixed and variable employment rates) are optimized simultaneously. As in real situations, most of the transportation activities of such supply chain are performed by hiring transportation devices, the open routing logic is applied to form the traveling path of each hired transportation device. Furthermore, the possibility of direct shipment from the plants to the customers is considered in order to increase profitability of the plants. Because of the NP‐hard nature of the supply chain design problems, some meta‐heuristic solution approaches of the literature are modified to multi‐objective form and applied to solve the problem. Several test problems from small to large sizes are generated randomly to evaluate the meta‐heuristic algorithms. As a result, among the proposed algorithms, the multi‐objective gray wolf optimizer (MGWO) performs better than others by considering four well‐known evaluation metrics. Finally, a case study from perishable products supply chain of Iran is solved and analyzed to show the applicability of the proposed problem.