Optimal sales policy for a class of non-perishable items from fixed capacity over finite horizons

In this paper, we consider the problem of presetting the optimal batch quantities to be sold in each period for a class of non-perishable products with fixed inventory in the face of price and demand uncertainty. More specifically, we suppose that the demand in each period is an independent random variable with known distribution function, and the price is determined exogenously and fluctuates according to AR process. First, we develop a finite horizon model for the problem with the objective of maximizing total expected discounted revenue. Second, we discuss existence of the optimal sales policy and characterize structural properties of its. Finally, we examine the analytic results and characterize how system parameters affect the optimal policy and corresponding optimal revenue value through a series of numerical experiments.