Optimal procurement policies under price-dependent demand

We study a periodic-review inventory model where, in addition to the procurement quantity, price is also a decision variable. We develop a model where demand in each period is a random variable having a price- and, possibly, period-dependent probability distribution, with the expected demand decreasing in price. The model includes price limits and fixed ordering costs in addition to unit procurement holding and shortage costs. We study the optimal policies which jointly maximize the discounted expected profit over a finite planning horizon. We characterize the form of the optimal procurement policy under a general price–demand relationship and give a sufficient condition for it to be (sn, Sn) type. We also discuss some special cases and extensions to the basic model, including the infinite horizon problem.