A Game Theoretical Analysis for the Quantity Discount Problem with Weibull Ameliorating Items

  • Hidefumi Kawakatsu
  • Toshimichi Homma
  • Kiyoshi Sawada
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 186)


This paper presents a model for determining optimal all-unit quantity discount strategies in a channel of one seller (poultry farmer) and one buyer (retailer). The poultry farmer’s stock increases due to the growth of items. In contrast, the retailer purchases items as fresh chicken meat from the poultry farmer, the inventory level of the retailer is therefore depleted due to the combined effects of its demand and deterioration. The poultry farmer attempts to increase her profit by controlling the retailer’s ordering schedule through a quantity discount strategy. We formulate the above problem as a Stackelberg game between the poultry farmer and the retailer to analyze the existence of the poultry farmer’s optimal quantity discount pricing policy, which maximizes her total profit per unit of time. Numerical examples are presented to illustrate the theoretical underpinnings of the proposed formulation.


Ameliorating items Deteriorating items Quantity discounts Stackelberg game Total profit Weibull distribution 


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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Hidefumi Kawakatsu
    • 1
  • Toshimichi Homma
    • 2
  • Kiyoshi Sawada
    • 3
  1. 1.Department of Economics and Information ScienceOnomichi City UniversityOnomichiJapan
  2. 2.Faculty of Business Administration of Policy StudiesOsaka University of EconomicsOsakaJapan
  3. 3.Department of Policy StudiesUniversity of Marketing and Distribution SciencesKobeJapan

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