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Optimal Contract Design of Supplier-Led Outsourcing Based on Pontryagin Maximum Principle

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  • Jianxiong Zhang

    (Tianjin University)

  • Lin Feng

    (Tianjin University)

  • Wansheng Tang

    (Tianjin University)

Abstract

This paper provides a supplier-led outsourcing model to maximize the supplier’s profits based on a principal-agent framework with both asymmetric cost information and uncertain market demand information described by continuous random variables. The salvage value of the unsold product is processing-cost dependent. By converting the proposed model, which is a dynamic optimization problem, to an optimal control problem, we obtain the analytical form of the optimal supplier outsourcing contract composed of the wholesale price and the transfer payment by applying Pontryagin’s maximum principle. It is shown that the optimal contract is directly related to the supplier’s beliefs about the manufacturer’s unit cost and the salvage value function. The Pontryagin’s maximum principle-based solution method serves as a powerful tool to support the decision making for the best sourcing strategy, and it provides analytical insights for outsourcing management. Finally, numerical examples are presented to illustrate the validness of the theoretical results.

Suggested Citation

  • Jianxiong Zhang & Lin Feng & Wansheng Tang, 2014. "Optimal Contract Design of Supplier-Led Outsourcing Based on Pontryagin Maximum Principle," Journal of Optimization Theory and Applications, Springer, vol. 161(2), pages 592-607, May.
    • Handle: RePEc:spr:joptap:v:161:y:2014:i:2:d:10.1007_s10957-013-0415-4
    DOI: 10.1007/s10957-013-0415-4
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    References listed on IDEAS

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    Cited by:

    1. Zhang, Jianxiong & Tang, Wansheng & Hu, Mingmao, 2015. "Optimal supplier switching with volume-dependent switching costs," International Journal of Production Economics, Elsevier, vol. 161(C), pages 96-104.
    2. Thyago Celso Cavalcante Nepomuceno & Késsia Thais Cavalcanti Nepomuceno & Thiago Poleto & Victor Diogho Heuer de Carvalho & Ana Paula Cabral Seixas Costa, 2022. "When Penalty Fails: Modeling Contractual Misincentives With Evidence From Portugal ITO Agreements," SAGE Open, , vol. 12(4), pages 21582440221, December.

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