Revised solution technique for a bi-level location-inventory-routing problem under uncertainty of demand and perishability of products

Bi-level programming is an efficient tool to tackle decentralized decision-making processes in supply chains with upper level (i.e., leader) and lower level (i.e., follower). The leader makes the first decision while the follower makes the second decision. In this research, a bi-level programming formulation for the problem of location-inventory-routing in a two-echelon supply chain, including a number of central warehouses in the first echelon and retailers in the second echelon with perishable products under uncertain demand, is proposed. The total operational costs at both levels are minimized considering capacity constraints. Due to the uncertain nature of the problem, a scenario-based programming is utilized. The economic condition or unforeseen events such as COVID-19 or Russia-Ukraine war can be good examples for uncertainty sources in today’s world. The model determines the optimal locations of warehouses, the routes between warehouses and retailers, number of received shipments and the amount of inventory held at each retailer. A revised solution method is designed by using multi-choice goal programming for solving the problem. The given revised method attempts to minimize the deviations of each decision maker’s solution from its ideal value assuming that the upper level is satisfied higher than the lower level. Base on some numerical analysis, the proposed solution technique is more sensitive to the upper bounds of the goals rather than the lower bounds.