Channel coordination in a HMMS-type supply chain with profit sharing contract

  • Imre Dobos
  • Barbara Gobsch
  • Nadezhda Pakhomova
  • Grigory Pishchulov
  • Knut Richter
Conference paper
Part of the Operations Research Proceedings book series (ORP)


We investigate a supply chain with a single supplier and a single manufacturer. The manufacturer is supposed to know the demand for the final product which is produced from a raw material ordered from the supplier just in time—i.e., the manufacturer holds no raw material inventory. Her costs consist of the linear purchasing cost, quadratic production cost and the final product quadratic holding costs. It is assumed that the market price of the final product is known as well, hence the sales of the manufacturer are known in advance. Her goal is to maximize her cumulated profits. The supplier’s costs are the quadratic manufacturing and inventory holding costs; his goal is to maximize the revenues minus the relevant costs.We will not examine the bargaining process that determines the adequate price and quantity. The situation is modeled as a differential game. The decision variables of the supplier are the sales price and the production quantity, while the manufacturer chooses a production plan that minimizes her costs, so maximizing the cumulated profits. The basic problem is a Holt-Modigliani-Muth-Simon (HMMS) problem extended to linear purchasing costs. We examine two cases: the decentralized Nash-solution and a centralized Pareto-solution to optimize the behavior of the players of the game.


Supply Chain Differential Game Wholesale Price Reverse Logistics Pareto Solution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Imre Dobos
    • 1
  • Barbara Gobsch
    • 2
  • Nadezhda Pakhomova
    • 3
  • Grigory Pishchulov
    • 4
  • Knut Richter
    • 3
    • 5
  1. 1.Institute of Business EconomicsCorvinus University of BudapestBudapestHungary
  2. 2.Faculty of Business Administration and EconomicsEuropean University ViadrinaFrankfurt (Oder)Germany
  3. 3.Faculty of EconomicsSt. Petersburg State UniversitySt. PetersburgRussia
  4. 4.European University ViadrinaFrankfurt (Oder)Germany
  5. 5.Faculty of Business Administration and EconomicsEuropean University ViadrinaFrankfurtGermany

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