Ordering, Pricing, and Lead-Time Quotation under Lead-Time and Demand Uncertainty

Publication Type

Working Paper

Publication Date



In this paper, we study the newsvendor problem with endogenous pricing in the presence of uncertain delivery lead-time. The problem can be observed in situations where final assembly or customization is required before the product delivery, or the actual shipping time cannot be accurately predicted. The demand for the product depends not only on the selling price, but also on the quoted lead-time. The firm has to carefully balance the holding cost and tardiness cost incurred from early and late completion of the product from the quoted lead-time. The paper determines the optimal selling price, quoted lead-time for delivery and the inventory level simultaneously. The paper makes three contributions. First, it combines the literature related to the Price-Setting Newsvendor Problem (PSNP) with that of setting price and quoted lead-time. The paper shows that the inclusion of lead-time uncertainty in PSNP cannot be treated as an increased level of demand uncertainty as the two forms of uncertainty have opposite effects on the optimal selling price. While demand uncertainty in the form of an additive random error term reduces the optimal selling price, lead-time uncertainty increases its value. Second, while consumers are always worse off when the firm can reduce demand uncertainty in PSNP (with an additive random error term), our paper shows that at least one segment of consumers, lead-time sensitive but price-insensitive, can benefit from reduced demand uncertainty. The paper describes the impact of both forms of uncertainty and problem parameters on the optimal choices for the selling price, stocking level, quoted lead-time, and the firm’s profits. Third, the paper makes a technical contribution. It introduces a widely applicable probability distribution for lead-time uncertainty, and presents a sequential approach to solve the joint optimization of lead-time quotation as well as pricing and stocking decisions.


newsvendor problem, pricing, lead-time quotation


Business Administration, Management, and Operations

Research Areas



Minor revision for Production and Operations Management

This document is currently not available here.