Two-echelon multiple-vehicle location–routing problem with time windows for optimization of sustainable supply chain network of perishable food

Increasing environmental, legislative, and social concerns are forcing companies to take a fresh view of the impact of supply chain operations on environment and society when designing a sustainable supply chain. A challenging task in today's food industry is distributing high quality perishable foods throughout the food supply chain. This paper proposes a multi-objective optimization model by integrating sustainability in decision-making, on distribution in a perishable food supply chain network (SCN). It introduces a two-echelon location–routing problem with time-windows (2E-LRPTW) for sustainable SCN design and optimizing economical and environmental objectives in a perishable food SCN. The goal of 2E-LRPTW is to determine the number and location facilities and to optimize the amount of products delivered to lower stages and routes at each level. It also aims to reduce costs caused by carbon footprint and greenhouse gas emissions throughout the network. The proposed method includes a novel multi-objective hybrid approach called MHPV, a hybrid of two known multi-objective algorithms: namely, multi-objective particle swarm optimization (MOPSO) and adapted multi-objective variable neighborhood search (AMOVNS). MHPV features two strategies for leader selection procedures (LSP), (i.e. Grids) and crowding distance is compared to common genetic algorithms based on metaheuristics (i.e. MOGA, NRGA and NSGA-II). Results indicate that the hybrid approach achieves better solutions compared to others, and that crowding distance method for LSP outperforms the former Grids method.