A single-resource revenue management problem with random resource consumptions

Abstract

We study a single-resource multi-class revenue management problem where the resource consumption for each class is random and only revealed at departure. The model is motivated by cargo revenue management problems in the airline and other shipping industries. We study how random resource consumption distribution affects the optimal expected profit and identify a preference acceptance order on classes. For a special case where the resource consumption for each class follows the same distribution, we fully characterize the optimal control policy. We then propose two easily computable heuristics: (i) a class-independent heuristic through parameter scaling, and (ii) a decomposition heuristic that decomposes the dynamic programming formulation into a collection of one-dimensional problems. We conduct extensive numerical experiments to investigate the performance of the two heuristics and compared them with several widely studied heuristic policies. Our results show that both heuristics work very well, with class-independent heuristic slightly better between the two. In particular, they consistently outperform heuristics that ignore demand and/or resource consumption uncertainty. Our results demonstrate the importance of considering random resource consumption as another problem dimension in revenue management applications.

Keywords:

• revenue management
• dynamic programming
• transportation

Notes

1 According to a recent forecast report (Boeing, 2009), the world air cargo business, a 40-billion dollar industry worldwide, has been constantly growing at around 5% per year and is expected to triple in the next 20 years.

2 We assume the arrival probability for each customer class does not depend on t only for notational simplicity; all our results holds for non-stationary arrival probabilities.