A Stochastic Inventory Control Problem with Reputation-Dependent Demand

Abstract The paper addresses a problem of capacitated inventory control. It incorporates the reputation of the system as a key factor influencing the distribution of future demand. The reputation depends on the degree to which past demand was satisfied. The optimality conditions developed by means of a perturbation analysis technique allow formulating some structural properties of optimal dynamics of inventory and reputation. A numerical procedure is devised to calculate an optimal rule for inventory control. The rule determines the order quantity at each time period as a function of inventory and reputation of the system at the beginning of the period. A numerical example illustrates the applicability of the developed solution method.