The Nonstationary Newsvendor: Data-Driven Nonparametric Learning

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 family of nonparametric dynamic ordering policies, termed two-stage estimation (2SE) policies, that track the shifts in the unknown demand level while accounting for the unobservable random demand shocks. To compute the order quantity in each period, these policies only need the past demand observations, without any access to the underlying demand distribution. For a finite variation “budget,” we prove that our ordering policies are first-order optimal in the sense that their regrets grow 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 policies can save 15-80% 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