The Nonstationary Newsvendor: Data-Driven Nonparametric Learning

35 Pages Posted: 15 Jun 2021

See all articles by N. Bora Keskin

N. Bora Keskin

Duke University - Fuqua School of Business

Xu Min

Tsinghua University - Tsinghua University School of Economics and Management

Jing-Sheng Jeannette Song

Duke University - Fuqua School of Business

Date Written: June 13, 2021

Abstract

We study a newsvendor problem with unknown demand distribution in a nonstationary demand environment over a multi-period time horizon. The demand in each period consists of a time-varying demand level and an additive random shock. Neither the demand level nor the random shock is separately observable. The amount of change in the demand level over the time horizon is measured by a cumulative variation metric. The problem has widespread applications, such as perishable inventory planning, staffing, and medical resource capacity planning in the wake of COVID-19. We design a nonparametric dynamic ordering policy, termed the moving window ordering policy, that tracks the shifts in the unknown demand level while accounting for the unobservable random demand shocks. To compute the order quantity in each period, this policy only needs the past demand observations, without any access to the underlying demand distribution. For a finite variation "budget," we prove that our ordering policy is first-order optimal in the sense that its regret grows at the smallest possible rate. We also extend our analysis to the case of asymptotically large variation budgets. Through case studies based on real-life data, we show that our policy can save 20-80% of overage and underage costs, relative to policies widely used for perishable inventory replenishment and nurse staffing.

Keywords: newsvendor, nonstationary demand learning, nonparametric estimation, inventory management, optimal staffing

Suggested Citation

Keskin, N. Bora and Min, Xu and Song, Jing-Sheng Jeannette, The Nonstationary Newsvendor: Data-Driven Nonparametric Learning (June 13, 2021). Available at SSRN: https://ssrn.com/abstract=3866171 or http://dx.doi.org/10.2139/ssrn.3866171

N. Bora Keskin (Contact Author)

Duke University - Fuqua School of Business ( email )

100 Fuqua Drive
Durham, NC 27708-0120
United States

HOME PAGE: http://faculty.fuqua.duke.edu/~nk145/

Xu Min

Tsinghua University - Tsinghua University School of Economics and Management ( email )

Beijing
China

Jing-Sheng Jeannette Song

Duke University - Fuqua School of Business ( email )

100 Fuqua Drive
Duke University
Durham, NC 27708
United States

HOME PAGE: http://people.duke.edu/~jssong/

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