Joint pricing and inventory policies for make-to-stock products with deterministic price-sensitive demand

In this paper, we focus on a firm selling a single make-to-stock product to price-sensitive end customers. We develop an integrated operations–marketing model that can help determine the relevant profit-maximizing decision variable values for two pricing policies that the firm might follow – price as a decision variable, which is advocated by academicians, and mark-up pricing, used by most practitioners. We first consider an EOQ-based model with price and order quantity as independent decision variables. We then develop an analogous model where price is a mark-up over operating costs per unit, and order quantity becomes the sole decision variable. We are able to ascertain the optimal decision variable values for each model for log-linear and linear demand functions. We prove that for such profit-maximizing models, the optimal batch size is not necessarily monotone increasing in set-up cost. Interestingly, our numerical/analytical evidence suggests that from a profit perspective it is better for managers to be aggressive on price rather than reducing price too much, especially for highly price-sensitive and non-linear demand. Moreover, we establish that, in general, the profit penalty for not including inventory costs in determining the optimal batch size, or ignoring the batch size optimization issue in a mark-up price model is not significant. Only when the set-up cost is quite high and/or the firm faces non-linear demand from highly price-sensitive end consumers does it become crucial for managers to determine the “exact” optimal batch size and base the mark-up price on the entire unit operating cost, not only the unit (variable) production cost.