Games of Decentralized Inventory Management

Abstract

Any decentralized retail or wholesale system of competing entities requires a benefit sharing arrangement when competing entities collaborate after their demands are realized. For instance, consider a distribution system similar to the observed behavior of independent car dealerships. If a dealership does not have in stock the car requested by a customer, it might consider acquiring it from a competing dealer. Such behavior raises questions about competitive procurement strategies that achieve system optimal outcomes. This dissertation consists of three main bodies of work contained respectively in chapters 2, 3, and 4. In the first work -- chapter 2, we examine a decentralized system that adopts an ex-post agreed transfer payment approach proposed by Anupindi et al. (Manuf. Serv. Oper.Manag. 4(3):349-368, 2001). In particular, we state a set of conditions on cost parameters and distributions that guarantee uniqueness of pure strategy Nash equilibrium. In the second work -- chapter 3, we introduce a multilevel graph framework that links decentralized inventory distribution models as a network of stochastic programming with recourse problems. This framework depicts independent retailers who maximize their individual expected profits, with each retailer independently procuring inventory in the ex-ante stage in response to forecasted demand and anticipated cooperative recourse action of all retailers in the system. The graph framework clarifies the modeling connection between problems in a taxonomy of decentralized inventory distribution models. This unifying perspective links the past work and shades light on future research directions. In the last work -- chapter 4, we examine and recast the biform games modeling framework as two-stage stochastic programming with recourse. Biform games modeling framework addresses two-stage games with competitive first stage and cooperative second stage without ex-ante agreement on profit sharing scheme. The two-stage stochastic programming view of biform games is demonstrated on examples from all the known examples regarding operational decision problems of competing firms from the literature. It allows an “old” mathematical methodology to showcase its versatility in modeling combined competitive and cooperative game options. In short, this dissertation provides important insights, clarifications, and strategic limitations regarding collaborations in decentralized distribution system.