Efficient frontiers in revenue management

We consider the problem of generating the efficient frontier (or Pareto set) between two business goals in a pricing and revenue management context. We show that, under standard conditions on the demand function, the efficient frontier between revenue and profit will be continuous, bounded, downward-sloping and concave when pricing a single product. For the single-leg revenue management problem, we show that the efficient frontier between any two goals that are linear in load, such as revenue, load factor and operating contribution, can be efficiently generated using a weighted-sum (or scalarization) approach. We give some numerical examples of the weighted sum approach applied to the discrete-time single leg revenue management problem, as well as applied to an Expected Marginal Seat Revenue heuristic. We discuss possible extensions to a general choice model and to a full network.