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Pooling of spare parts between multiple users: How to share the benefits?

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  • Karsten, Frank
  • Basten, Rob J.I.

Abstract

Companies that maintain capital goods (e.g., airplanes or power plants) often face high costs, both for holding spare parts and due to downtime of their technical systems. These costs can be reduced by pooling common spare parts between multiple companies in the same region, but managers may be unsure about how to share the resulting costs or benefits in a fair way that avoids free riders. To tackle this problem, we study several players, each facing a Poisson demand process for an expensive, low-usage item. They share a stock point that is controlled by a continuous-review base stock policy with full backordering under an optimal base stock level. Costs consist of penalty costs for backorders and holding costs for on-hand stock. We propose to allocate the total costs proportional to players’ demand rates. Our key result is that this cost allocation rule satisfies many appealing properties: it makes all separate participants and subgroups of participants better off, it stimulates growth of the pool, it can be easily implemented in practice, and it induces players to reveal their private information truthfully. To obtain these game theoretical results, we exploit novel structural properties of the cost function in our (S−1, S) inventory model.

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  • Karsten, Frank & Basten, Rob J.I., 2014. "Pooling of spare parts between multiple users: How to share the benefits?," European Journal of Operational Research, Elsevier, vol. 233(1), pages 94-104.
  • Handle: RePEc:eee:ejores:v:233:y:2014:i:1:p:94-104
    DOI: 10.1016/j.ejor.2013.08.029
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    References listed on IDEAS

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    2. Zhou, Weihua & Pu, Yaqi & Dai, Hongyan & Jin, Qingwei, 2017. "Cooperative interconnection settlement among ISPs through NAP," European Journal of Operational Research, Elsevier, vol. 256(3), pages 991-1003.
    3. Robin Molinier & Pascal da Costa, 2019. "Infrastructure sharing synergies and industrial symbiosis: optimal capacity oversizing and pricing," Post-Print hal-01792032, HAL.
    4. Olde Keizer, Minou C.A. & Teunter, Ruud H. & Veldman, Jasper, 2017. "Joint condition-based maintenance and inventory optimization for systems with multiple components," European Journal of Operational Research, Elsevier, vol. 257(1), pages 209-222.
    5. Lotty E. Westerink‐Duijzer & Loe P. J. Schlicher & Marieke Musegaas, 2020. "Core Allocations for Cooperation Problems in Vaccination," Production and Operations Management, Production and Operations Management Society, vol. 29(7), pages 1720-1737, July.
    6. Westerink-Duijzer, L.E. & Schlicher, L.P.J. & Musegaas, M., 2019. "Fair allocations for cooperation problems in vaccination," Econometric Institute Research Papers EI2019-06, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    7. Frank Karsten & Marco Slikker & Peter Borm, 2017. "Cost allocation rules for elastic single‐attribute situations," Naval Research Logistics (NRL), John Wiley & Sons, vol. 64(4), pages 271-286, June.
    8. Zheng, Meimei & Ye, Hongqing & Wang, Dong & Pan, Ershun, 2021. "Joint Optimization of Condition-Based Maintenance and Spare Parts Orders for Multi-Unit Systems with Dual Sourcing," Reliability Engineering and System Safety, Elsevier, vol. 210(C).
    9. Loe Schlicher & Marco Slikker & Geert-Jan Houtum, 2018. "Pooling of critical, low-utilization resources with unavailability," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 40(1), pages 233-263, January.
    10. Luo, Chunlin & Zhou, Xiaoyang & Lev, Benjamin, 2022. "Core, shapley value, nucleolus and nash bargaining solution: A Survey of recent developments and applications in operations management," Omega, Elsevier, vol. 110(C).
    11. Schlicher, L.P.J. & Musegaas, M. & Westerink-Duijzer, L.E., 2019. "Resource location games," Econometric Institute Research Papers EI2019-05, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    12. Wang, Wenbin & Yue, Shuai, 2015. "An inventory pooling model for spare units of critical systems that serve multi-companies," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 76(C), pages 34-44.
    13. Loe Schlicher & Marco Slikker & Geert‐Jan van Houtum, 2017. "Probabilistic resource pooling games," Naval Research Logistics (NRL), John Wiley & Sons, vol. 64(7), pages 531-546, October.
    14. Hezarkhani, Behzad & Slikker, Marco & Van Woensel, Tom, 2018. "Collaborative replenishment in the presence of intermediaries," European Journal of Operational Research, Elsevier, vol. 266(1), pages 135-146.
    15. Subiza, Begoña & Silva-Reus, José A. & Peris, Josep E., 2015. "Cost sharing solutions defined by non-negative eigenvectors," European Journal of Operational Research, Elsevier, vol. 244(2), pages 592-600.
    16. Ulaş Özen & Marco Slikker & Greys Sošić, 2022. "On the core of m$m$‐attribute games," Production and Operations Management, Production and Operations Management Society, vol. 31(4), pages 1770-1787, April.

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