Sensitivity of optimal prices to system parameters in a steady-state service facility
We consider the problem of maximizing the long-run average reward in a service facility with dynamic pricing. We investigate sensitivity of optimal pricing policies to the parameters of the service facility which is modelled as an M/M/s/K queueing system. Arrival process to the facility is Poisson with arrival rate a decreasing function of the price currently being charged by the facility. We prove structural results on the optimal pricing policies when the parameters in the facility change. Namely, we show that optimal prices decrease when the capacity of the facility or the number of servers in the facility increase. Under a reasonable assumption, we also show that optimal prices increase as the overall demand for the service provided by the facility increases or when the service rate of the facility decreases. We illustrate how these structural results simplify the required computational effort while finding the optimal policy.
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- Knudsen, Niels Chr, 1972. "Individual and Social Optimization in a Multiserver Queue with a General Cost-Benefit Structure," Econometrica, Econometric Society, vol. 40(3), pages 515-528, May.
- Shaler Stidham, 1992. "Pricing and Capacity Decisions for a Service Facility: Stability and Multiple Local Optima," Management Science, INFORMS, vol. 38(8), pages 1121-1139, August.
- Sanjeev Dewan & Haim Mendelson, 1990. "User Delay Costs and Internal Pricing for a Service Facility," Management Science, INFORMS, vol. 36(12), pages 1502-1517, December.
- Edelson, Noel M & Hildebrand, David K, 1975. "Congestion Tolls for Poisson Queuing Processes," Econometrica, Econometric Society, vol. 43(1), pages 81-92, January.
- Albert Y. Ha, 1998. "Incentive-Compatible Pricing for a Service Facility with Joint Production and Congestion Externalities," Management Science, INFORMS, vol. 44(12-Part-1), pages 1623-1636, December.
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