Journal of Business Economics

, Volume 84, Issue 5, pp 749–791 | Cite as

A vendor–purchaser economic lot size problem with remanufacturing

  • Grigory PishchulovEmail author
  • Imre Dobos
  • Barbara Gobsch
  • Nadezhda Pakhomova
  • Knut Richter
Original Paper


In this paper, we study a closed-loop supply chain in which a single purchaser orders a particular product from a single vendor and sells it on the market. A certain fraction of used items return from the market back to the purchaser, who is responsible for collecting and returning them to the vendor. In addition to manufacturing new items, the vendor is able to remanufacture the returns into as-good-as-new items which are subsequently used to serve market demand. Our framework features the conventional joint economic lot size (JELS) model extended to include the return flow of the used items. In line with the assumptions of the JELS model, we assume a deterministic constant demand for the product. The fraction of used items returning from the market is assumed to depend on the purchaser’s collection effort. To stimulate the returns, the vendor may offer the purchaser a transfer payment per item returned. The questions addressed by this study pertain to the optimal centralised control of this closed-loop supply chain, to the individually optimal policies of its members, and to the coordination within this supply chain under a decentralised control. In particular, we show that the transfer payment alone cannot coordinate the supply chain under consideration and may even fail to do so when combined with a two-part tariff—which is otherwise known to coordinate the corresponding forward supply chain. Our numerical study, though, has revealed that the combined contract is capable of substantially reducing the coordination deficit. We also introduce a novel three-part tariff which is shown to enable supply chain coordination in combination with the transfer payment.


EOQ Joint economic lot size Remanufacturing Closed-loop supply chain Coordination 

JEL Classification

C61 C71 M10 



The authors would like to thank two anonymous referees and Professor Peter Recht of TU Dortmund University for their many constructive comments on an earlier version of this paper. Imre Dobos gratefully acknowledges the financial support of the OTKA-105888 research programme and the Deutscher Akademischer Austauschdienst (DAAD). Knut Richter acknowledges the support of the Sankt Petersburg University in enabling him to continue his work on the area of closed-loop supply-chain management.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Grigory Pishchulov
    • 1
    Email author
  • Imre Dobos
    • 2
  • Barbara Gobsch
    • 3
  • Nadezhda Pakhomova
    • 4
  • Knut Richter
    • 4
  1. 1.Faculty of Business, Economics and Social SciencesTU Dortmund UniversityDortmundGermany
  2. 2.Institute of Business EconomicsCorvinus University of BudapestBudapestHungary
  3. 3.Faculty of Business Administration and EconomicsEuropean University ViadrinaFrankfurt (Oder)Germany
  4. 4.Faculty of EconomicsSaint Petersburg State UniversitySt. PetersburgRussia

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