Allocating containers to ships with fixed departure times

We consider the problem of allocating containers to ships in which the size of container is 1 or 2, and each ship has its own capacity and fixed departure time. The fixed departure times implies the completion times of containers belonging to the same ship are identical. As objectives, Lmax, ∑wjCj, ∑wjUj and ∑Tj are considered. We verify the problems are closely related with the scheduling problem with eligibility constraint or the generalized assignment problem. The polynomial-time algorithms are developed for each problem, and moreover the more efficient algorithms are presented for the cases with ∑Cj and ∑Uj,