Sourcing with demand updates
File(s)
Accepted version
Author(s)
Federgruen, Awi
Liu, Zhe
Lu, Jiaqi
Type
Journal Article
Abstract
We study a two-stage newsvendor model where the initially uncertain mean demand is revealed midstream, allowing for a second, costlier order to be placed. The two-stage process is relevant to many retailers who have access to two supply options: a long-lead, low-cost option where orders need to be placed under much demand uncertainty, and a short-lead, high-cost option after a signal is revealed that updates the mean demand. We introduce a forecast evolution model that describes how the initial forecast for mean demand varies in response to the signal, which generalizes the popular additive and multiplicative martingale model of forecast evolution (MMFE). We show that the optimal first-stage order solves a simple ordinary differential equation (ODE), whereas the second-stage order is analytically available. We characterize asymptotics for the first-stage order and expected profit as the forecasted mean demand grows, and propose a simple, asymptotically optimal heuristic. We apply our study to data from a national retail chain, where we calibrate our model by maximum likelihood estimation (MLE). The comparison of several heuristic policies, as well as two benchmarks, shows the efficacy of our method. When the signal is more uncertain (e.g., for product lines with impulse- and trend-driven purchases), our heuristic with a simple adjusted critical fractile outperforms benchmarks; otherwise, the classic newsvendor solution performs well and is asymptotically optimal. We also extend the approach to distribution-free settings and capacitated systems.
Date Acceptance
2025-10-28
Citation
Management science
ISSN
0025-1909
Publisher
Institute for Operations Research and Management Sciences
Journal / Book Title
Management science
Copyright Statement
Copyright © 2026 Copyright Owner. This is the author’s accepted manuscript made available under a CC-BY licence in accordance with Imperial’s Research Publications Open Access policy (www.imperial.ac.uk/oa-policy)
License URL
Subjects
demand updates
Publication Status
Accepted
Article Number
mnsc.2024.04692
Date Publish Online
2026-03-19