The capital cost of holding inventory with stochastically mean-reverting purchase price

Most models of inventory control assume that the per unit purchase price is constant. The capital cost of holding inventory can then be taken into account by adding a fixed interest rate, r, times the purchase price, C, to the out-of pocket holding cost. However, it is not uncommon that the purchase price varies over time. How the capital cost then should be calculated is the focus of the present paper. The paper studies the common single-item inventory model with a fixed set-up cost and assumes that the stochastic purchase price follows the mean-reverting Ornstein–Uhlenbeck process. Methods for computing an adjusted interest rate, r, are suggested along with modifications of well-known heuristics and formulas for lot-sizing. Simulation tests, where the optimal policy has been compared to policies obtained using modified versions of the Silver–Meal method, the Part Period algorithm and the EOQ formula, suggest that r should be estimated as the sum of the unadjusted interest rate and the average expected purchase price decrease, measured over a period between 1/3 and 2/3 of the length of the order cycle.