Multiobjective bi-level programming for shared inventory with emergency and backorders

The goal of this study is to model a shared inventory model as a bilevel programming problem. The model considers both emergency and backorders so decision makers have flexibility in meeting customer needs and extends the satisfaction level is higher than the simple model with no emergency and backorders. We focus on the interaction between decision makers in an uncertain environment. The considered situation consists in a large corporation that owns a warehouse and two concurrent chains. The company opted for shared inventory policy. The corporation is looking into minimizing its inventory and reducing the overtime for its personnel. The chains, independently, are trying to minimize their inventory costs. The chains are allowed to submit emergency and backorders to minimize their inventory cost while increasing their customers’ satisfaction. The warehouse plays the role of a leader and optimizes its objectives first then the two chains, as followers, try to satisfy their objectives independently. The problem is formulated into a decentralized bilevel programming problem where the leader has multiple objectives. We formulate the situation as a biobjective bilevel the mathematical program and we propose ways to solve it. . Our simulation, inspired from a real case, shows a cost reduction of up to 8.9 % compared to regular use of inventory model.