Bi-level programming for modeling inventory sharing in decentralized supply chains

This paper deals with inventory sharing and routing in the context of decentralized supply chains. The supply chain considered in this paper consists of a single manufacturer distributing its products through a network of independents Points of Sale (POS). The problem is modeled as a 1-leader - n-followers Stackelberg game. A new mixed-integer bi-level program is developed, in which the manufacturer decides first on inventory levels and the distribution routes, considering each follower’s (POS) response function that minimizes the follower’s own cost. A trade-off solution to manage conflict of interests between the parties involved in the supply chain is also proposed. To solve the mixed-integer bi-level program an original hybrid Genetic Algorithm coupled with deep reinforcement learning is developed and used to solve a set of large-size instances. The gap analysis shows that the proposed hybrid algorithm performs quite well and that inventory sharing allows the network to improve its service level