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

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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.

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Acknowledgements

This work was supported by National Natural Foundation of China No. 61004015, 71131007, the Program for New Century Excellent Talents in Universities of China No. NCET-11-0377.

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Authors and Affiliations

  1. Institute of Systems Engineering, Tianjin University, Tianjin, 300072, China

    Jianxiong Zhang, Lin Feng & Wansheng Tang

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  1. Jianxiong Zhang
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  2. Lin Feng
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  3. Wansheng Tang
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Corresponding authors

Correspondence to Jianxiong Zhang or Lin Feng.

Additional information

Communicated by Francesco Zirilli.

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Zhang, J., Feng, L. & Tang, W. Optimal Contract Design of Supplier-Led Outsourcing Based on Pontryagin Maximum Principle. J Optim Theory Appl 161, 592–607 (2014). https://doi.org/10.1007/s10957-013-0415-4

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  • DOI: https://doi.org/10.1007/s10957-013-0415-4

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