Dynamic pricing and inventory control for multiple products

A periodical multi–product pricing and inventory control problem with applications to production planning and airline revenue management is studied. The objective function of the single–period model is shown to be convex for certain types of demand distributions, thus tractable for large instances. A heuristic is proposed to solve the more complex multi–period problem, which is an interesting combination of linear and dynamic programming. Numerical experiments and theoretical bounds on the optimal expected revenue suggest that the extent to which a dynamic policy based on a stochastic model will outperform a simple static policy based on a deterministic model depends on the level of demand variability as measured by the coefficient of variation.