Emergency supply contracts for a service provider with limited local resources

S. Rahimi-Ghahroodi*, A. Al Hanbali, W. H.M. Zijm, J. B. Timmer

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


We study a problem faced by a service provider, who is responsible for the repair of a group of assets subject to random failures. In case of a failure, both an engineer and a spare part of the right kind need to be available to carry out the repair. A limited number of engineers are employed while also stocks of the various spare parts are limited. In case any resource (engineer or spare part) is not immediately available, the service provider may follow a full backlogging policy. Alternatively, in case of spare parts stock out, he has the option to revert to an emergency supplier with ample capacity of resources. We present an original model to analyze the problem dynamics between this service provider and the emergency supplier. Especially, we determine the optimal emergency shipment cost and the optimal multi-resource level of the service provider. To this end, we propose a computationally efficient algorithm to find the Stackelberg equilibrium. Furthermore, we design a revenue-sharing cooperative contract between these players which always results in coordination. Finally, we examine the risk of uncertainties in such a contract and find the optimal contract parameters by considering the utility functions of the players.

Original languageEnglish
Pages (from-to)445-460
Number of pages16
JournalReliability Engineering and System Safety
StatePublished - Sep 2019

Bibliographical note

Funding Information:
This publication was made possible by the NPRP award [ NPRP 7-308-2-128 ] from the Qatar National Research Fund (a member of The Qatar Foundation). The statements made herein are solely the responsibility of the authors.

Publisher Copyright:
© 2019 Elsevier Ltd


  • After-sales service logistics
  • Coordination
  • Game theory
  • Service engineers
  • Spare parts inventory

ASJC Scopus subject areas

  • Safety, Risk, Reliability and Quality
  • Industrial and Manufacturing Engineering


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