An inventory model where customer demand is dependent on a stochastic price process

We investigate the optimal inventory operations of a firm selling an item whose price is driven by an exogenous stochastic price process which consequently impacts customer arrivals between ordering cycles. This case is typical for retailers that operate in different currencies, or trade products consisting of commodities or components whose prices are subject to market fluctuations. We assume that there is a stochastic input price process for the inventory item which determines purchase and selling prices according to a general selling price function. Customers arrive according to a doubly-stochastic Poisson process that is modulated by stochastic input prices. We analyze optimal ordering decisions for both backorder and lost-sale cases. We show that under certain conditions, a price-dependent base stock policy is optimal. Our analysis is then extended to a price-modulated compound Poisson demand case, and the case with fixed ordering cost where a price-dependent (s,S) policy is optimal. We present a numerical study on the sensitivity of optimal profit to various parameters of the operational setting and stochastic price process such as price volatility, customer sensitivity to price changes etc. We then make a comparison with a corresponding discrete-time benchmark model that ignores within-period price fluctuations and present the optimality gap when using the benchmark model as an approximation.