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Non-parametric generalised newsvendor model.

Soham Ghosh1, Sujay Mukhoti2

  • 1Humanities and Social Sciences, Indian Institute of Technology Indore, Indore, Madhya Pradesh 453552 India.

Annals of Operations Research
|December 19, 2022
PubMed
Summary

This study introduces a newsvendor problem model for perishable goods with complex costs and unknown demand. A non-parametric estimator for optimal order quantity proves efficient and consistent, validated with real-world data.

Keywords:
Monte-Carlo simulationNewsvendor problemNon-linear optimisationNon-parametric estimationStochastic programmingStrong consistency

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Area of Science:

  • Operations Research
  • Supply Chain Management
  • Econometrics

Background:

  • The classical newsvendor problem assumes linear costs, which may not accurately reflect critical perishable commodities.
  • Perishable goods often incur more severe costs (e.g., spoilage, obsolescence) than linear models allow.
  • Stochastic demand for such items frequently follows unknown probability distributions.

Purpose of the Study:

  • To generalize the newsvendor problem for perishable commodities with non-linear, piecewise polynomial cost functions.
  • To develop a non-parametric estimator for the optimal order quantity under unknown demand distributions.
  • To assess the efficiency and consistency of the proposed estimator and demonstrate its real-world applicability.

Main Methods:

  • Generalization of the newsvendor problem using piecewise polynomial cost functions.
  • Development of a non-parametric estimator based on an estimating equation from a random sample.
  • Theoretical proof of strong consistency for the estimator, including cases with unique and multiple optimal solutions.
  • Simulation studies to evaluate the estimator's efficiency (Mean Squared Error).

Main Results:

  • A novel non-parametric estimator for optimal order quantity in the generalized newsvendor problem was developed.
  • Strong consistency of the estimator was theoretically established for both unique and multiple optimal order quantity solutions.
  • Simulation results demonstrated the estimator's efficiency, outperforming alternatives in terms of Mean Squared Error.
  • The estimator was successfully applied to real-world datasets, including avocado demand and COVID-19 test kit demand.

Conclusions:

  • The proposed non-parametric approach effectively addresses the newsvendor problem for critical perishables with complex cost structures and unknown demand.
  • The developed estimator offers a statistically robust and efficient method for determining optimal order quantities in uncertain environments.
  • Empirical validation with avocado and COVID-19 test kit data confirms the practical utility and reliability of the non-parametric estimator in supply chain management.