Department of Industrial Engineering & Decision Analytics [Joint IEDA/ISOM] seminar - History-Dependent Fluid Approximations and Performance Guarantees for Revenue Management with Markov-Modulated Demands

A common approach for modeling the demand in revenue management systems is based on dividing the selling horizon into a number of time periods such that there is at most one customer arrival at each time period and the products requested by different customers are independent of each other. This approach rules out the possibility of modeling dependence between the demands from different customers. In this talk, we study revenue management models that use Markov-modulated demands to incorporate dependence between the demands from different customers. In our problem setting, we have a modulating Markov chain that makes transitions over the time periods. The probability distribution for the product requested by each arriving customer depends on the state of the Markov chain. We can give dynamic programming formulations for such revenue management models by keeping track of the remaining resource capacities and state of the Markov chain in the state variable, but solving these dynamic programs is intractable. We seek to formulate the corresponding fluid approximation with the goal of obtaining approximate policies with performance guarantees. We give a family of history-dependent fluid approximations, where the probability of accepting a product request depends on the history of the Markov chain. Our fluid approximations yield upper bounds on the optimal total expected revenue and these upper bounds get tighter as we use longer histories. Furthermore, our approximate policy is asymptotically optimal as the capacities of the resources get large and its performance guarantee gets stronger as we use a larger number of time periods in the history of the Markov chain. Our numerical work shows that the right fluid approximation under Markov-modulated demands can make a dramatic impact.