Two-Phase Newsvendor with Optimally Timed Additional Replenishment: Model, Algorithm, Case Study

Dina Smirnov, Yale T. Herer, Assaf Avrahami

Research output: Contribution to journalArticlepeer-review


Recent advancements in Information Technology have provided an opportunity to significantly improve the effectiveness of inventory systems. The use of in-cycle demand information enables faster reaction to demand fluctuations. In particular, for the newsvendor (NV) system, we exploit the newly available data to perform an additional review (AR) of inventory at an endogenously determined, a priori set time during the sales period, and perform an additional replenishment if necessary. We implemented our innovative model at a market-leading media group. The results of the initial pilot were dramatic, indicating that the proposed model achieves an increase of 4%–24% in profits compared to the policy before implementation. As a result, the company started following the proposed model for all their printed magazines and observed a significant reduction in operational costs. In a generalized setting, we provide a tractable search-based optimization algorithm, based on the problem's structural properties, for determining the optimal initial quantity, AR timing, and quantity to restock at that time. Based on these theoretical results, we propose a simple heuristic that can be used for many practical situations including our implementation at Yedioth. Through a computational experiment, we show that our algorithm finds the optimal solution quickly and that the proposed heuristic performs well. We also provide additional insights into the problem—for instance, that our system exhibits properties similar to inventory pooling, provided that the demand rate is large enough.

Original languageEnglish
Pages (from-to)2871-2889
Number of pages19
JournalProduction and Operations Management
Issue number9
StatePublished - Sep 2021


  • additional review
  • newsvendor
  • print industry
  • replenishment timing
  • two phases

All Science Journal Classification (ASJC) codes

  • Management of Technology and Innovation
  • Industrial and Manufacturing Engineering
  • Management Science and Operations Research


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