Integrated pricing and production scheduling of multiple customized products with a common base product

Make-To-Order (MTO) is a popular production strategy commonly used by manufacturers selling customized products. Dynamic pricing is a popular tactical tool commonly used by sellers to match supply with demand when there is a limited capacity and high demand uncertainty over time. In this article, we consider joint pricing and production scheduling decisions faced by a manufacturer that uses an MTO strategy to sell a number of customized products made from a common base product. At the beginning of each period in a planning horizon, the manufacturer sets the price of the base product, which in turn sets the prices for the customized products accordingly. Given the prices, orders for the products arrive. In each period, together with the pricing decision, the manufacturer needs to make a production scheduling decision for processing accepted orders on a single production line. The manufacturer’s objective is to maximize the total revenue of the processed orders minus a scheduling penalty over the planning horizon. Three specific problems with different order acceptance rules and objective functions are studied. In the first problem, the manufacturer has to accept all the incoming orders and treats the total weighted completion time of the orders as a part of the objective function. In the second problem, the manufacturer has to accept all incoming orders, but is allowed to complete some orders after their due dates with tardiness penalties. In the third problem, the manufacturer may reject some incoming orders, but must complete all the accepted orders by their due dates. We show that all these problems are NP-hard, propose optimal pseudo-polynomial-time dynamic programming algorithms and fully-polynomial-time approximation schemes for solving these problems, and conduct computational experiments to show the performance of the proposed algorithms. Furthermore, we derive several managerial insights through computational experiments.