Bi-objective reliable location-inventory-routing problem with partial backordering under disruption risks: A modified AMOSA approach

In this paper, we present a reliable model of multi-product and multi-period Location-Inventory-Routing Problem (LIRP) considering disruption risks. An inventory system with stochastic demand in which the supply of the product is randomly disrupted in distribution centers, is considered in this paper. Partial backordering is used in case stock out occurs by considering the probability of the confronting defects in distribution centers in time of disruption. We presented a bi-objective mixed-integer nonlinear programming (MINLP) model. The first objective minimizes the locating, routing and transportation costs and inventory components which consist of ordering, holding and partial backordering costs. The second objective is to minimize the total failure costs related to disrupted distribution centers that leads to reliability of the supply chain network. Because of NP-hardness of the proposed model, we modified Archived Multi-Objective Simulated Annealing (AMOSA) meta-heuristic algorithm to solve the bi-objective problem in large scales and compared the results with three other algorithms. To improve performance of the algorithms Taguchi method is used to tune parameters. Finally, several numerical examples are generated to evaluate solution methods and five multi-objective metrics are calculated to compare results of the algorithms.