# Calibrating Sales Forecast in a Pandemic Using Online Non-Parametric Regression Model

35 Pages Posted: 13 Aug 2020 Last revised: 19 Feb 2021

See all articles by David Simchi-Levi

## David Simchi-Levi

Massachusetts Institute of Technology (MIT) - School of Engineering

Alibaba Group US

## Michelle Xiao Wu

Massachusetts Institute of Technology (MIT) - Institute for Data, Systems, and Society (IDSS)

## Ruihao Zhu

Massachusetts Institute of Technology (MIT) - School of Engineering

Date Written: August 9, 2020

### 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 online learning and pandemic modeling to develop a data-driven \emph{online non-parametric regression} method. Specifically, the method takes the future COVID-19 case number estimates, which can be simulated via the SIR (\ie, Susceptible-Infectious-Removed) epidemic model, as an input, and outputs the level of calibration of the baseline sales forecast generated by AB InBev's offline learning algorithm. To generate the calibration level, we focus on an online non-parametric regression setting, where our algorithm sequentially predicts the label (\ie, the level of calibration) of a random covariate (\ie, the current active case numbers) given past observations and the generative process (\ie, the SIR epidemic model) of future covariates. We evaluate the performance of our algorithm by \emph{regret}, which is the difference between the squared $\ell_2$-norm associated with labels generated by the algorithm and labels generated by an adversary and the squared $\ell_2$-norm associated with labels generated by the best isotonic (non-decreasing) function in hindsight and the adversarial labels. We develop a computationally-efficient algorithm that attains the minimax-optimal worst case regret over all possible choices of the labels. We demonstrate the performances of our algorithm on both synthetic and AB InBev’s datasets of three different geographical regions. The AB InBev’s numerical experiments show that our method is capable of reducing the forecasting error in terms of WMAPE (\ie, weighted mean absolute percentage error) and MSE (\ie, mean squared error) by more than 50\% in the monthly forecast (AB InBev's main focus) and 15\% in the weekly forecast.

Keywords: sales forecast, COVID-19 pandemic, online learning, isotonic regression

Suggested Citation

Simchi-Levi, David and Sun, Rui and Wu, Michelle Xiao and Zhu, Ruihao, Calibrating Sales Forecast in a Pandemic Using Online Non-Parametric Regression Model (August 9, 2020). Available at SSRN: https://ssrn.com/abstract=3670264 or http://dx.doi.org/10.2139/ssrn.3670264