FINANCIALLY OPTIMAL INVENTORY POLICIES WITH NON-LINEAR REPLENISHMENT COSTS

We model the inventory decisions of a firm that maximizes its market value, namely, the expected present value of the time stream of dividends issued to its shareholders. The firm is single-product and equity-owned, it orders products from an outside supplier, its only short-term borrowing is for solvency if necessary, and it issues dividends to its shareholders while facing financial and market risks (uncertain demand). The distinguishing features of the model are the financial criterion, hence joint selection of operational and financial decisions, and non-linear replenishment costs. If the non-linearity is due to a setup cost, we show that an (s, S) replenishment policy is optimal. The analysis is not a straightforward variant of Scarf's argument. If the non-linearity is due to bilinear smoothing costs, we show that the optimal replenishment policy has the same form as in the traditional smoothing cost model. These seem to be the first instances in which the optimization of a model with a financial criterion and non-linear replenishment costs yields policies having the same forms as in the corresponding cost minimization problems.