A Comparison of Fixed and Dynamic Pricing Policies in Revenue Management

Abstract

We consider the problem of selling a fixed capacity or inventory of items over a finite selling period. Earlier research has shown that using a properly set fixed price during the selling period is asymptotically optimal as the demand potential and capacity grows large and that dynamic pricing has only a secondary effect on revenues. However, additional revenue improvements through dynamic pricing can be important in practice and need to be further explored. For example, in 2009, increasing the average price by one percent would increase the profitability of the largest airlines and rental car companies in the US by 67 percent and 30 percent, respectively. We suggest two simple dynamic heuristic heuristics that continuously updates prices based on remaining inventory and time in the selling period. The first heuristic is based on approximating the optimal expected revenue function and the second heuristic is based on the solution of the deterministic version of the problem. We show through a numerical study that the revenue impact of using these dynamic pricing heuristics rather than fixed pricing may be substantial. In particular, the revenue approximation heuristic has a consistent and remarkable performance leading to at most 0.2 percent gap compared to optimal dynamic pricing. We also show that the benefits of these dynamic pricing heuristics persist under a periodic setting. This is especially true for the revenue approximation heuristic for which the performance is monotone in the frequency of price changes.We finally show that both of these heuristics can be easily implemented for the multiple products case. We conclude that dynamic pricing should be considered as a more favorable option in practice.