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

Abstract

This paper deals with inventory sharing in the context of a decentralized supply chain. The supply chain consists of a manufacturer who distributes a set of products through a network of independents Points of Sale (POS). The primary decision each player has to make is to optimize its service level while maintaining a minimum total cost. The POS share their inventory allowing transshipment to enhance their ability to face demand and to avoid shortages. The problem is modelled as a 1-leader, n-followers Stackelberg game. A mixed integer bi-level program is developed considering that the manufacturer decides first on inventory levels and routes to be constructed knowing each follower\’s (POS) response function arising from its own minimization of its total cost. In this game, a manufacturer incurs the vehicle routing cost for regular shipments. In addition to their own holding costs, it is assumed that the manufacturer and the POS each are willing to incur both a part of the cost of lost sales associated with the products shortage and a part of the cost of transshipment. To address the combinatorial complexity of the problem and to provide efficient solutions for large size instances, a hybrid Genetic Algorithm coupled with deep reinforcement learning is developed. Results show that Stackelberg mechanism for inventory sharing under certain conditions allows the network as a whole to achieve savings and improve its service level.