Simultaneous and sequential price quotations for uncertain order inquiries with production scheduling cost

Abstract

This article studies the coordination between pricing and production scheduling decisions of a manufacturer who quotes prices for a set of order inquiries. Each inquiry is either canceled or confirmed by its owner following a certain probability distribution that depends on the quoted price. The manufacturer then incurs a production scheduling cost for processing each firm order. Two types of price quotation schemes, simultaneous and sequential quotations, are investigated. A simultaneous quotation quotes all order inquiries simultaneously. The problem is formulated with a specific form of price function as a quadratic program that can be solved efficiently. Properties of optimal quotations are provided. A sequential quotation quotes order inquiries one at a time. For the problem, optimal algorithms are developed using implicit enumeration and design-efficient heuristics. Simultaneous and sequential quotations and several managerial insights are obtained in computational studies. The conditions under which the simultaneous quotation performs close to sequential quotation and conditions under which heuristic sequential quotation performs near optimal are highlighted.

Keywords:

• Price quotation
• production scheduling
• coordination