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An Integrated Production-Supply System with Uncertain Demand, Nonlinear Lead Time and Allowable Shortages

Author

Listed:
  • Hengameh Tahmasebi

    (Boeing, Seattle, WA, USA)

  • Junfang Yu

    (Department of Engineering Management, Information & Systems, Lyle School of Engineering, Southern Methodist University, Dallas, TX, USA)

  • Bhaba R. Sarker

    (Department of Industrial Engineering, Louisiana State University, Baton Rouge, LA, USA)

Abstract

A supply chain consisting of a single-supplier and a single-buyer is modeled and compared in two different modes: non-coordinated and coordinated. The model is established based on the fact that the demand is uncertain and shortages are considered as lost sales. The buyer’s order lead time is a nonlinear function of the buyer’s order size and the number of shipments from the supplier. Quantity discount offers are used as a tool to achieve the coordination between both parties. In non-coordinated mode the total annual profits of both parties are maximized using partial derivative and a lower and an upper bound are obtained for the supplier’s wholesale price. For the coordinated mode total annual profit of the whole supply chain system is maximized using partial derivatives and coordination may increase the total annual profit of the whole system is mathematically proved. In order to encourage the both parties to coordinate, a fair profit-sharing method is proposed based on the total costs that each party incurs. The supplier’s wholesale price is evaluated such that coordination seems appealing and profitable for both parties.

Suggested Citation

  • Hengameh Tahmasebi & Junfang Yu & Bhaba R. Sarker, 2012. "An Integrated Production-Supply System with Uncertain Demand, Nonlinear Lead Time and Allowable Shortages," International Journal of Operations Research and Information Systems (IJORIS), IGI Global, vol. 3(4), pages 1-18, October.
    • Handle: RePEc:igg:joris0:v:3:y:2012:i:4:p:1-18
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