  We consider the canonical (quantity-based) network revenue management
problem, where a firm accepts or rejects incoming customer requests irrevocably
in order to maximize expected revenue given limited resources. Due to the curse
of dimensionality, the exact solution to this problem by dynamic programming is
intractable when the number of resources is large. We study a family of
re-solving heuristics that periodically re-optimize an approximation to the
original problem known as the deterministic linear program (DLP), where random
customer arrivals are replaced by their expectations. We find that, in general,
frequently re-solving the DLP produces the same order of revenue loss as one
would get without re-solving, which scales as the square root of the time
horizon length and resource capacities. By re-solving the DLP at a few selected
points in time and applying thresholds to the customer acceptance
probabilities, we design a new re-solving heuristic whose revenue loss is
uniformly bounded by a constant that is independent of the time horizon and
resource capacities.

Optimization and Control