Cargo Revenue Management: Bid-Prices for a 0-1 Multi Knapsack Problem

Revenue management is the practice of selecting those customers that generate the maximum revenue from a fixed and perishable capacity. Cargo revenue management differs from the well-known passenger revenue management problem by the fact that its capacity constraint is 2-dimensional, i.e. weight and volume, and that the weight, volume and profit of each booking request are random and continuous variables. This leads to a multi-dimensional on-line knapsack problem. We show that a bid-price acceptance policy is asymptotically optimal if demand and capacity increase proportionally and the bid-prices are set correctly. We provide a heuristic to set the bid-prices based on a greedy algorithm for the multi-knapsack problem proposed by Rinnooy Kan et al. (1993). A test case shows that these bid-prices perform better than the traditional LP-based bid-prices that do not perform well at all for this problem.