Multi-period Newsvendor Model
Valentyn Khokhlov
TL;DR
The paper addresses the need for a multi-period, inventory-planning tool for manufacturing that carries over stock between periods while remaining aligned with generally accepted accounting principles. It extends the classic newsvendor framework to a multi-period setting (Model 3) with a closed-form optimal batch-size decision, incorporating lead time and a unified inventory holding cost term, and validates the approach via Monte Carlo simulations on real clothing-manufacturer data. The key contribution is showing that the proposed Model 3 often yields higher operating profits and fewer stock-outs than the original and extended models as well as a safety stock buffer, with robustness to demand-distribution misspecification. Practical guidance is provided on selecting model assumptions by SKU demand characteristics, highlighting that Model 3 offers strong performance under uncertainty and is broadly implementable within ERP environments.
Abstract
The newsvendor model is a well-known stochastic model for inventory management; however, it was originally developed for a single-period context and focuses on trading companies. This paper proposes an extension of the newsvendor model into a mutli-period setting, aiming to develop a decision-making tool for manufacturing firms to determine the optimal production batch size. The objective function is to maximize operating profit in accordance with generally accepted accounting principles. The model can also incorporate overhead costs, such as warehousing, shrinkage, cost of capital, and lead time between the production decision and output. Monte Carlo simulations demonstrate that the proposed model results in higher profitability compared to other newsvendor models used in our analysis, as well as the safety stock buffer approach. The key feature explaining its outperformance is better adaptability of the production batch size, that leads to fewer stock-outs relative to other newsvendor models and lower inventory levels compared to the safety stock buffer approach. The robustness analysis shows that the proposed model is quite tolerant of mismatches between the "model" and the "true" demand distributions. Finally, we provide some recommendations on selecting the appropriate "model" distribution for different SKUs.