Calibrating Sales Forecasts in a Pandemic Using Competitive Online Nonparametric Regression

David Simchi-Levi (), Rui Sun (), Michelle Xiao Wu () and Ruihao Zhu ()
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David Simchi-Levi: Institute for Data, Systems, and Society, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139; Department of Civil and Environmental Engineering, Cambridge, Massachusetts 02139; Operations Research Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
Rui Sun: Amazon, Seattle, Washington 98109
Michelle Xiao Wu: Institute for Data, Systems, and Society, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
Ruihao Zhu: SC Johnson College of Business, Cornell University, Ithaca, New York 14853

Management Science, 2024, vol. 70, issue 10, 6502-6518

Abstract: Motivated by our collaboration with Anheuser-Busch InBev (AB InBev), a consumer packaged goods (CPG) company, we consider the problem of forecasting sales under the coronavirus disease 2019 (COVID-19) pandemic. Our approach combines nonparametric regression, game theory, and pandemic modeling to develop a data-driven competitive online nonparametric regression method. Specifically, the method takes the future COVID-19 case estimates, which can be simulated via the susceptible-infectious-removed (SIR) epidemic model as an input, and outputs the level of calibration for the baseline sales forecast generated by AB InBev. In generating the calibration level, we focus on an online learning setting where our algorithm sequentially predicts the label (i.e., the level of calibration) of a random covariate (i.e., the current number of active cases) given past observations and the generative process (i.e., the SIR epidemic model) of future covariates. To provide robust performance guarantee, we derive our algorithm by minimizing regret, which is the difference between the squared ℓ 2 -norm associated with labels generated by the algorithm and labels generated by an adversary and the squared ℓ 2 -norm associated with labels generated by the best isotonic (nondecreasing) function in hindsight and the adversarial labels. We develop a computationally efficient algorithm that attains the minimax-optimal regret over all possible choices of the labels (possibly non-i.i.d. and even adversarial). We demonstrate the performances of our algorithm on both synthetic and AB InBev’s data sets of three different markets (each corresponds to a country) from March 2020 to March 2021. The AB InBev’s numerical experiments show that our method is capable of reducing the forecast error in terms of weighted mean absolute percentage error (WMAPE) and mean squared error (MSE) by more than 37% for the company.

Keywords: sales forecast; online learning; nonparametric regression; COVID-19 pandemic (search for similar items in EconPapers)
Date: 2024
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