An incentive for coordination in a decentralised service chain with a Weibull lifetime distributed facility

This article deals with a decentralised service chain consisting of a service provider and a facility owner. The revenue allocation and service price are, respectively, determined by the service provider and the facility owner in a non-cooperative manner. To model this decentralised operation, a Stackelberg game between the two parties is formulated. In the mathematical framework, the service system is assumed to be driven by Poisson customer arrivals and exponential service times. The most common log-linear service demand and Weibull facility lifetime are also adopted. Under these analytical conditions, the decentralised decisions in this game are investigated and then a unique optimal equilibrium is derived. Finally, a coordination mechanism is proposed to improve the efficiency of this decentralised system.