The impact of subcontracting on service systems with time-sensitive strategic customers

Abstract

We consider a service system consisting of a provider who offers a service in a make-to-order fashion to a market of potential customers, and a subcontractor who can be recruited to speed up the service process. The provider operates a Markovian queue at a standard service rate and charges customers a fixed fee upon joining. At each busy cycle, the provider offers a salary to a subcontractor in exchange for increasing the service rate. The subcontractor decides whether to accept the offer while incurring a labor cost per unit of time. Arriving customers, who are strategic and time-sensitive, cannot observe the system’s queue length or the implemented service policy. They have a service value upon completion and incur a waiting cost per unit of time. Based on their utility maximization, they make individual join-or-balk decisions, considering both the behavior of other customers and the subcontractor’s strategic involvement.

We derive the equilibrium demand of customers as a response to the subcontractor’s commitment rate using a two-dimensional continuous-time Markov Chain. We define the collaboration regions based on salary thresholds, highlighting the reservation salaries that ensure collaboration between the two parties. Finally, using a Stackelberg game framework, we show that the subcontractor does not always opt for full commitment. When the provider relies less on subcontractor assistance, the subcontractor strategically prefers partial commitment, balancing the trade-off between idle periods and longer busy periods.