Acquisition Management Under Fluctuating Raw Material Prices

We study a continuous-review acquisition problem, in which the raw material price follows a discrete-state Markov process and demand is compound Poisson. We show that one optimal policy is of the order-up-to type. Under our mean reversion and time continuity conditions, we further show that the order-up-to levels are decreasing at the current price level. At the same time, our computational study verifies that both conditions are indispensable for the monotonicity result. The study also hints at the connection between discrete- and continuous-state price processes.