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.