Several mixed integer programming (MIP) models for discrete DBAP have been proposed in the literature.
Christensen and Holst  modeled the discrete DBAP as a generalized set-partitioning problem (GSPP) which assumed that the time measurements were integers (discrete time periods).
Lai and Shih  developed a heuristic algorithm for solving the DBAP by considering the first-come-first-served rule and evaluated three different berthing policies using simulation experiments.
 extended the DBAP to the multiwater depth configuration in a public berth system and proposed a genetic algorithm (GA) to solve the problem.
 proposed a population training algorithm with linear programming (PTA/LP) to solve discrete DBAP. PTA/LP improved incoming columns in the column generation problem.
 proposed a Tabu search ([T.sup.2][S.sup.*]) approach and a Tabu search with path relinking ([T.sup.2][S.sup.*] + PR) approach to solve the discrete DBAP. [T.sup.2][S.sup.*] was an improved version of T2S  that employed different neighborhood structure, and [T.sup.2][S.sup.*] + PR added the path-relink techniques to the [T.sup.2][S.sup.*] [T.sup.2]S, [T.sup.2][S.sup.*], and [T.sup.2][S.sup.*] + PR were tested using the instances from Cordeau et al.
To clearly illustrate the process, Tables 1 and 2 together give a small discrete DBAP instance with 15-ship and 3-berth.
Tables 3-6 list the computational results for the discrete DBAP. The optimal solution was provided by the GSPP model using CPLEX 11 .
At a confidence level of 95%, Tables 7 and 8 show that the proposed IG algorithm outperforms the PTA/LP in terms of the best objective value obtained for discrete DBAP (PTA/LP for the I3 set).