Transportation Science · 2009 · 225 citations · 16 references
ManagementDecision SciencesEconomicsMarkov Decision ProcessesOptimizationRevenue ManagementChoice ModelingCombinatorial OptimizationDiscrete Choice ModelsDiscrete Choice TheoryNetwork Revenue ManagementRevenue OptimizationApproximate Dynamic ProgrammingChoice-based Revenue ManagementColumn GenerationDiscrete Choice ModellingMarkov Decision ModelsMarkov-process ApproximationState-value FunctionStochastic Revenue Management
The paper studies network revenue management with customer choice modeled by a prespecified choice model. The authors formulate the problem as an MDP, approximate the value function affinely, and use column generation to solve a multinomial logit model with disjoint consideration sets, also deriving a decomposition‑based bound. The approach yields a tighter bound than the choice‑based linear program and produces policies that outperform its heuristics in numerical experiments.
We consider a network revenue management problem where customers choose among open fare products according to some prespecified choice model. Starting with a Markov decision process (MDP) formulation, we approximate the value function with an affine function of the state vector. We show that the resulting problem provides a tighter bound for the MDP value than the choice-based linear program. We develop a column generation algorithm to solve the problem for a multinomial logit choice model with disjoint consideration sets (MNLD). We also derive a bound as a by-product of a decomposition heuristic. Our numerical study shows the policies from our solution approach can significantly outperform heuristics from the choice-based linear program.
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