Dynamic pricing strategies for multi-product revenue
management problems
Costis Maglaras and Joern Meissner, Submitted July
2003.
Abstract:
Consider a monopolist firm that owns a fixed capacity
of a resource that is consumed in the production of multiple products. There is
a finite horizon over which the resource must be used, and the firm's problem
is to choose a dynamic pricing strategy for each product in order to maximize
its total expected revenues. This paper shows that this problem is equivalent
to one where the firm controls the aggregate rate at which all products jointly
consume resource capacity, rather than the multi-dimensional product pricing
strategies. Given the desired aggregate capacity consumption rate, the product
prices are chosen so as to maximize the instantaneous revenue rate subject to
the constraint that all products jointly use up capacity at the specified rate.
This defines an efficient frontier for multi-product pricing problems. Other
applications of this idea are pursued in settings where the firm uses capacity
rather than pricing controls and in network revenue management problems.
Overall, the reduction in the control dimension leads to algorithmic
simplifications and highlights the essential features of good
pricing/allocation policies.
Keywords: revenue management, dynamic
pricing, capacity controls, fluid approximations, efficient frontier
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