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Dual bounds of a service level assignment problem with applications to efficient pricing

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  • Pavlin, J. Michael

Abstract

We extend the classical continuous assignment problem to allow for the assignment of multiple service levels. This formulation encompasses an important class of lead-time allocation problems in queues where congestion may impact feasible assignments of customers to service levels. Through analysis of the dual program we show a number of results which include existence of welfare maximizing prices for a more general set of operational settings than previously reported. Further, we show that the duality gap provides a bound on welfare loss that can be calculated from operational information in a service system with priced service levels. For systems where total expected delay is a convex function of the customer arrival rate, this bound is shown to be an upper bound on the difference between current and maximum welfare and provide a sufficient condition for maximizing welfare. We demonstrate how this bound may be used to evaluate and improve a current set of prices through use as a measure to guide an adaptive pricing algorithm. The adaptive pricing algorithm is shown through computational experiments to find pricing schemes which deliver near optimal welfare.

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  • Pavlin, J. Michael, 2017. "Dual bounds of a service level assignment problem with applications to efficient pricing," European Journal of Operational Research, Elsevier, vol. 262(1), pages 239-250.
    • Handle: RePEc:eee:ejores:v:262:y:2017:i:1:p:239-250
    DOI: 10.1016/j.ejor.2017.03.078
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