A stochastic model for dynamic capacity allocation of container shipping two-dimensional revenue management

A stochastic model for dynamic capacity allocation with multiple container types of container shipping two-dimensional revenue management is constructed. The difficulty of computing the optimal strategy is analyzed in a special example with two container types. Then bounds of the value function of the model are proved and the two-dimensional problem is decomposed into two one-dimensional problems which are more practical in computing. Furthermore, a characteristic problem with four container types is studied with the model built, the solution algorithm put forward and a numerical example given. The analysis results show that the expected marginal value of a 20 or 40-foot container slot is not necessarily monotonic, but the approximate expected marginal value is non-decreasing in time for any given volume and weight capacity left. The research result also indicates that the ratio of the maximal expected revenue of the optimal strategy to that of the heuristic is close to one when two-dimensional capacity becomes relatively larger.