Efficient Humanitarian Logistics: Multi-Commodity Location–Inventory Model Incorporating Demand Probability and Consumption Coefficients

<i>Background:</i> A logistics network plan could be a major key issue due to its effect on supply chain effectiveness and responsiveness. This study aims to investigate the inventory location in the humanitarian logistics response stage using a three-level logistics network to integrate location–allocation problems such as warehouse location and shelter allocation to each facility, and then determine the inventory level in each warehouse. <i>Methods</i>: In this research, the center and its distribution, as well as the reduction in service-level costs due to inventory deficit, have been considered to increase the level of shelter services. In order to investigate the network, in this study, bi-objective mixed-integer linear programming (BOMILP) is presented. <i>Results</i>: The first objective is to reduce location costs and inventory costs that take into account probable demand, consumption factors, and transportation costs, and the second objective is to raise the level of services offered to victims in the model. The software programs GAMS win32, 25.1.2 and MATLAB have been utilized with numerical examples in various dimensions. <i>Conclusions</i>: To maximize the efficiency and quality of the service, first, the model was numerically solved, and then the location where the most commodities could be transported at the lowest possible cost was identified.