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Tractability of Revenue Management Models Using Discrete Distributions

Abstract

Most pricing and revenue management models have at their core an optimization problem; one needs to determine the optimal price or quantity to maximize a profit or revenue function. To ensure the tractability, conditions that assure the objective function has a unique solution are enormously helpful. So far, several technical assumptions have been proposed for the continuous case, but little attention is given to the discrete counterpart despite its prevalence in practice. Thus, this paper aims to develop new technical assumptions, built upon relevant economic concepts, to guarantee the tractability for revenue management models in discrete settings. In particular, we present two sufficient conditions for the revenue function to be concave, in terms of quantity or price and propose a discrete version of increasingly generalized failure rate (IGFR) which leads to a monotone elasticity condition. Our extension has appropriate economic interpretation and offers comparable properties to those of the continuous version. Finally, we show the IGFR property for several discrete distributions.

Type

Working Paper

Author(s)

Martin Lariviere, Zuo-Jun (Max) Shen

Date Published

2017

Citations

Lariviere, Martin, and Zuo-Jun (Max) Shen. 2017. Tractability of Revenue Management Models Using Discrete Distributions.

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