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Stochastic Predictive Analytics for Stocks in the Newsvendor Problem

Pedro A. Pury

TL;DR

This work addresses stockout forecasting within the Newsvendor setting by modeling the time evolution of inventory stock without presupposing a fixed demand distribution. It builds a stochastic, Markovian stock process with state probabilities P(n,k) and a first-passage stockout distribution P(0,k), and derives closed-form recurrences for both generic and parametric demand forms (Deterministic, Poisson, Binomial, Negative Binomial) as well as a naive frequentist alternative. The framework is validated on a large e-commerce dataset (MercadoLibre MELI) using the Ranked Probability Score to assess full distribution forecasts, demonstrating robust performance even with very short training histories and offering a practical, low-cost forecasting tool for inventory managers. The work also provides a mechanism to quantify frustrated sales and discusses extensions to incorporate cross-SKU effects, contributing to interpretable, scalable stockout forecasting in real-world marketplaces.

Abstract

This work addresses a key challenge in inventory management by developing a stochastic model that describes the dynamic distribution of inventory stock over time without assuming a specific demand distribution. Our model provides a flexible and applicable solution for situations with limited historical data and short-term predictions, making it well-suited for the Newsvendor problem. We evaluate our model's performance using real-world data from a large electronic marketplace, demonstrating its effectiveness in a practical forecasting scenario.

Stochastic Predictive Analytics for Stocks in the Newsvendor Problem

TL;DR

This work addresses stockout forecasting within the Newsvendor setting by modeling the time evolution of inventory stock without presupposing a fixed demand distribution. It builds a stochastic, Markovian stock process with state probabilities P(n,k) and a first-passage stockout distribution P(0,k), and derives closed-form recurrences for both generic and parametric demand forms (Deterministic, Poisson, Binomial, Negative Binomial) as well as a naive frequentist alternative. The framework is validated on a large e-commerce dataset (MercadoLibre MELI) using the Ranked Probability Score to assess full distribution forecasts, demonstrating robust performance even with very short training histories and offering a practical, low-cost forecasting tool for inventory managers. The work also provides a mechanism to quantify frustrated sales and discusses extensions to incorporate cross-SKU effects, contributing to interpretable, scalable stockout forecasting in real-world marketplaces.

Abstract

This work addresses a key challenge in inventory management by developing a stochastic model that describes the dynamic distribution of inventory stock over time without assuming a specific demand distribution. Our model provides a flexible and applicable solution for situations with limited historical data and short-term predictions, making it well-suited for the Newsvendor problem. We evaluate our model's performance using real-world data from a large electronic marketplace, demonstrating its effectiveness in a practical forecasting scenario.

Paper Structure

This paper contains 21 sections, 64 equations, 4 figures, 5 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Stochastic Model for Stocks
  3. Markov model
  4. Recursive Solutions
  5. Frustrated Sales
  6. Demand distributions
  7. Naive frequentist distribution
  8. Deterministic distribution
  9. Poisson distribution
  10. Binomial distribution
  11. Negative Binomial distribution
  12. Forecasting of Stockouts
  13. Forecasting metric
  14. Uniform distribution of stockout time
  15. Forecasting a single day at random
  16. ...and 6 more sections

Figures (4)

  • Figure 1: Boxplots of the total number of feasible evaluations in March based on days with sales in February. The numbers inside the boxes indicate the number of SKUs with that number of sales in February. Circles represent outliers.
  • Figure 2: Histogram of RPS values from evaluations using the BNBP model.
  • Figure 3: Boxplots of RPSs from BNBP model evaluations versus days with sales in February (training set). The number of evaluations is indicated within each box. The red line indicates the baseline value, and the blue line represents the benchmark. Outliers are represented by circles.
  • Figure 4: Medians and means of RPSs from BNBP model evaluations versus days with sales in February (training set). The numbers of evaluations are indicated aligned with each pair of dots. The red line indicates the baseline value, and the blue line represents the benchmark.