Price quotation for orders with different due dates

Pricing has been broadly used as an effective tool for companies to control demand. In most operations management models, the demand quantity of a product is formulated as a function of price, which garners the company flexibility to obtain tradeoff between revenue and cost. Such a price-demand function may not be suitable for make-to-order products with heterogeneous demands. To address such an issue, we study the price quotation and scheduling problem for a set of order inquiries. Specifically, a manufacturer receives multiple order inquiries from customers, and needs to quote a price for each inquiry. The quoted price will affect the probability of which the customer will accept the price and confirm the order. Then the manufacturer determines a schedule for processing the confirmed orders. The objective of the manufacturer is to maximize the expected profit, i.e., the total revenue from all confirmed orders less the delay penalty incurred by some orders. We show that the problem is NP-hard, design a heuristic to determine price quotes, and propose a method to find an upper bound of the optimal objective value. The efficiency of our heuristic is evaluated computationally. In general, our heuristic performs weaker with tighter due date, greater scheduling cost relative to order price, and nonlinear relationship between price quote and order placement probability.