We investigate dynamic policies for allocating scarce inventory to stochastic demand for multiple fare classes,in a network environment so as to maximize total expected revenues. Typical applications include sequential reservations for an airline network,hotel,or car rental service. We propose and analyze a new algorithm based on approximate dynamic programming,both theoretically and computationally. This algorithm uses adaptive,nonadditive bid prices from a linear programming relaxation. We provide computational results that give insight into the performance of the new algorithm and the widely used bid-price control,for several networks and demand scenarios. We extend the proposed algorithm to handle cancellations and no-shows by incorporating oversales decisions in the underlying linear programming formulation. We report encouraging computational results that show that the new algorithm leads to higher revenues and more robust performance than bid-price control
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