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A two-stage linear production planning model with partial cooperation under stochastic demands

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Abstract

We consider two-stage stochastic linear production planning problems with partial cooperation including resource pooling, technology transfer and product transshipment, and employ a two-stage programming model with simple recourse to address uncertain demands. At the first stage, each manufacturer individually determines the production level according to its own technology and transferred technologies. After the demands are realized, multiple manufacturers jointly produce the products using pooled resources, and surplus products are transshipped to manufacturers with residual demands. Using the core solution concept from cooperative game theory, the additional profit obtained at the second stage is divided among all manufacturers. We develop a method to find a Nash equilibrium point such that the sum of the profits earned by all manufacturers is maximized. To demonstrate the validity of the proposed model, numerical examples are presented.

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Acknowledgements

This work was supported by JSPS KAKENHI Grant Numbers: 18K18923 and 21H01565.

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Authors and Affiliations

  1. Graduate School of Advanced Science and Engineering, Hiroshima University, Higashi-Hiroshima, 739-8527, Japan

    Ichiro Nishizaki, Tomohiro Hayashida, Shinya Sekizaki & Kojiro Furumi

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  1. Ichiro Nishizaki
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  2. Tomohiro Hayashida
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  3. Shinya Sekizaki
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  4. Kojiro Furumi
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Correspondence to Ichiro Nishizaki.

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Nishizaki, I., Hayashida, T., Sekizaki, S. et al. A two-stage linear production planning model with partial cooperation under stochastic demands. Ann Oper Res 320, 293–324 (2023). https://doi.org/10.1007/s10479-022-05056-w

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