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

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