Inventory Management under Periodic Profit Targets

Managers seek to meet quarterly profit targets because missing a target affects both the stock price and bonuses. To capture how these targets can affect a retailer’s procurement decisions, we analyze a periodic-review inventory model with a chance constraint in each period that requires meeting a profit target with a given probability, while maximizing expected profit. Corporate profits are reported using accrual accounting, but inventory models typically use cash-basis accounting. We consider both methods. The optimal policy under accrual accounting is quite complicated, involving a state-dependent disposal policy, so we focus on the class of policies in which, in each period, the disposal quantity is increasing in the remaining inventory after demand has occurred, and show that the optimal policy consists of an order-up-to level and a dispose-down-to level in each period. These values may depend upon the constraint in that period and in all subsequent periods, so each constraint may have far-reaching effects. We also derive the optimal policy under cash-basis accounting for the infinite horizon stationary case and find that it is state- and demand dependent, even in this “easy” case. We offer insights into how the chance constraints affect the optimal procurement decisions and profits under both accounting schemes, and show that the chance constraints can lead to perverse behavior under cash-basis accounting.