Bi-objective integrating sustainable order allocation and sustainable supply chain network strategic design with stochastic demand using a novel robust hybrid multi-objective metaheuristic

objective integrating sustainable order allocation and sustainable supply chain network strategic design with stochastic demand using a novel robust hybrid multi-objective metaheuristic, This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. ďƐƚƌĂĐƚ͗ Sustainability has been considered as a growing concern in supply chain network design (SCND) and in the order allocation problem (OAP). Accordingly, there still exists a gap in the quantitative modeling of sustainable SCND that consists of OAP. In this article, we cover this gap through simultaneously considering the sustainable OAP in the sustainable SCND as a strategic decision. The proposed supply chain network is composed of five echelons including suppliers classified in different classes, plants, distribution centers that dispatch products via two different ways, direct shipment, and cross-docks, to satisfy stochastic demand received from a set of retailers. The problem has been mathematically formulated as a multi-objective optimization model that aims at minimizing the total costs and environmental effect of integrating SCND and SMP, simultaneously. To tackle the addressed problem, a novel multi-objective hybrid approach called MOHEV with two strategies for its best particle selection procedure (BPSP), minimum distance, and crowding distance is proposed. MOHEV is constructed through hybridization of two multi-objective algorithms, namely the adapted multi-objective electromagnetism mechanism algorithm (AMOEMA) and adapted multi-objective variable neighborhood search (AMOVNS). According to achieved results, MOHEV achieves better solutions compared with the others, and also crowding distance method for BPSP outperforms minimum distance. Finally, a case study for an automobile industry is used to demonstrate the applicability of the approach.