Managing Uncertain Capacities for Network Revenue Optimization

problem definition:We study the problem of managing uncertain capacities forrevenue optimization over a network of resources. The uncertainty could be due to (i) theneed to reallocate initial capacities among resources or (ii) the random availability of physi-cal capacities by the time of service execution. Academic/practical relevance:The analyzedcontrol policy is aligned with the current industry practice, with a virtual capacity and abid price associated with each network resource. The seller collects revenues from an arriv-ing stream of customers. Admitted requests that cannot be accommodated within thefinal,effective capacities incur a penalty cost. The objective is to maximize the total cumulativenet revenue (sales revenue minus penalty cost). The problem arises in practice, for instance,when airlines are subject to last-minute change of aircrafts and in cargo revenue manage-ment where the capacity left by the passengers'load is used for freight. Methodology: Wepresent a stochastic dynamic programming formulation for this problem and propose astochastic gradient algorithm to approximately solve it. All limit points of our algorithmare stationary points of the approximate expected net revenue function.Results:Throughan exhaustive numerical study, we show that our controls are computed efficiently and de-liver revenues that are almost consistently higher than the ones obtained from benchmarksbased on the widely adopted deterministic linear programming model. Managerial impli-cations:We obtain managerial insights about the impact of the timing of the capacity un-certainty clearance, the capacity heterogeneity, the network congestion, and the penalty fornot being able to accommodate the previously accepted demand. Our approach tends tooffer the best performance across different parameterizations of the problem.