Multi-periods Inventory Game Under Uncertainty

The inventory is an important competitive factor for the enterprise.This thesis focuses the substitute inventory management problems in the competitive setting.Keep the enterprise guarantee supply and reduce the operational risk by optimizing the order decision.In this thesis,the inventory games,in which demands information are updating in every periods and supply uncertainty is studied.In particular,the thesis focus on multi-periods two-person non-cooperative inventory games under unknown demand distribution function and random yield,respectively.First,the thesis addresses the multi-period inventory game of two new substitutable products with learning,in which the demand distribution form in each period is known but one or more parameters and shortage are unknown in advance.The retailers update the estimates of the unknown parameters using the historical demand information as the transaction proceeds.The thesis model the problem as a dynamic Bayesian game with multi-dimension state-space.Second,based on the conclusion of previous issue,the thesis assumed that shortage quantity is unknown.So retailers cannot obtain complete demand information if shortage in some period and a new variable emergent to denote the accuracy of the historical data.The new variables result in three-dimensional state space of the game,which means the problem is more complicated.Finally,the thesis assumed the yield quantity is a random variable and considered a multi-period two-person inventory game,in which both supply and demand are uncertain.The main conclusion as follows:In shortage-known game model,it can be found that under certain conditions the state-space in each period can be reduced.The thesis prove the existence and uniqueness of Nash equilibrium and show that the equilibrium ordering strategy is the order-up-to policy,the computation of the optimal inventory levels can be reduced to a more simply game with one-dimension state-space.Moreover,for the case with perishable product,the computation of the base-stock levels can be reduced to the Newsboy game.The thesis also analyzed how the substitution rate impacts the payoff by numerical study.In shortage-unknown game model,after the dimension reduction process same with previous,the thesis give the conditions in which the game has at least one Nash equilibrium order quantity.In numerical study,the thesis analyzed the impact of new state variables.In the yield uncertain game model,the thesis give the conditions that multi-period inventory game has unique Nash equilibrium and how the substitute rate impact ordering decisions and how the yield reliability factors affect the payoff.In numerical example the thesis show the multiple Nash equilibrium,and analyzed the impact of substitute rate,reliability factor on the payoff and equilibrium ordering strategy.The innovations of this thesis are three points.The thesis extends the two-person inventory game into multi-period setting,in which inventory is inter-dependent between periods.The thesis considered the inventory game with demand information update process,and the characters of Nash equilibrium.The thesis presented a new multi-period inventory game model,in which yield and demand uncertain.