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Incentive Efficient Control of a Make-to-Stock Production System

Author

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  • Erica L. Plambeck

    (Graduate School of Business, Stanford University, Stanford, Calfornia 94305)

  • Stefanos A. Zenios

    (Graduate School of Business, Stanford University, Stanford, Calfornia 94305)

Abstract

This paper considers a principal-agent variant of the classical make-to-stock single-server queueing system. The principal incurs all costs for holding inventory and backordering demand. The agent dynamically controls the production rate at the server and incurs a convex production cost. The principal cannot monitor the production rate but can draw inference from increases in the inventory level. Furthermore, by making payments contingent on the inventory level, the principal motivates the agent to control the production rate in a manner that will minimize the principal's own total expected discounted cost. We show that an optimal incentive payment scheme consists of piece rates and inventory penalties that vary dynamically with the inventory level. This scheme coordinates the system if the agent is risk neutral. Otherwise, operational performance is degraded by the conflict in incentives between principal and agent. We identify some drivers of this agency loss: In addition to discounting and risk aversion in the agent's preferences, which are standard causes of friction in dynamic agency models, an increasing marginal cost of production and slack in the agent's capacity are also found to be lead contributors. Heavy traffic analysis supports these findings through closed-form expressions for the performance of the system under the optimal incentive scheme.

Suggested Citation

  • Erica L. Plambeck & Stefanos A. Zenios, 2003. "Incentive Efficient Control of a Make-to-Stock Production System," Operations Research, INFORMS, vol. 51(3), pages 371-386, June.
  • Handle: RePEc:inm:oropre:v:51:y:2003:i:3:p:371-386
    DOI: 10.1287/opre.51.3.371.14954
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    3. Hao Zhang & Mahesh Nagarajan & Greys Sošić, 2010. "Dynamic Supplier Contracts Under Asymmetric Inventory Information," Operations Research, INFORMS, vol. 58(5), pages 1380-1397, October.
    4. Wang, Yulan & Zipkin, Paul, 2009. "Agents' incentives under buy-back contracts in a two-stage supply chain," International Journal of Production Economics, Elsevier, vol. 120(2), pages 525-539, August.
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    6. Pascale Crama & Bert De Reyck & Zeger Degraeve, 2008. "Milestone Payments or Royalties? Contract Design for R&D Licensing," Operations Research, INFORMS, vol. 56(6), pages 1539-1552, December.
    7. Tinglong Dai & Kinshuk Jerath, 2016. "Technical Note—Impact of Inventory on Quota-Bonus Contracts with Rent Sharing," Operations Research, INFORMS, vol. 64(1), pages 94-98, February.
    8. Lee, Jun-Yeon & Schwarz, Leroy B., 2007. "Leadtime reduction in a (Q,r) inventory system: An agency perspective," International Journal of Production Economics, Elsevier, vol. 105(1), pages 204-212, January.
    9. Hongmin Li & Hao Zhang & Charles H. Fine, 2013. "Dynamic Business Share Allocation in a Supply Chain with Competing Suppliers," Operations Research, INFORMS, vol. 61(2), pages 280-297, April.
    10. Vibhuti Dhingra & Harish Krishnan, 2021. "Managing Reputation Risk in Supply Chains: The Role of Risk Sharing Under Limited Liability," Management Science, INFORMS, vol. 67(8), pages 4845-4862, August.
    11. Josh Reed & Bo Zhang, 2017. "Managing capacity and inventory jointly for multi-server make-to-stock queues," Queueing Systems: Theory and Applications, Springer, vol. 86(1), pages 61-94, June.
    12. Sang-Hyun Kim & Morris A. Cohen & Serguei Netessine & Senthil Veeraraghavan, 2010. "Contracting for Infrequent Restoration and Recovery of Mission-Critical Systems," Management Science, INFORMS, vol. 56(9), pages 1551-1567, September.
    13. Youngsoo Kim & Yuqian Xu, 2024. "Operational Risk Management: Optimal Inspection Policy," Management Science, INFORMS, vol. 70(6), pages 4087-4104, June.
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    15. Tinglong Dai & Kinshuk Jerath, 2013. "Salesforce Compensation with Inventory Considerations," Management Science, INFORMS, vol. 59(11), pages 2490-2501, November.

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