Motivated by the observation that different ports are of nonuniform fee for each container shift, we propose a mixed integer programming (MIP) model for the problem to produce an optimal stowage planning with minimum total shifting fee in this work. Previous studies assume that each container shift consumes a uniform cost in all ports and thus focus on minimizing the total number of shifts or the turnaround time of the vessel. Each container shift via a quay crane induces one unit of shifting fee that depends on the charge policy of the local container port. Since the access to containers is in the top-to-bottom order for each stack, reshuffle operations occur when a target container to be unloaded at its destination port is not stowed on the top of a stack at the time. This paper studies the problem of stowage planning within a vessel bay in a multiple port transportation route, aiming at minimizing the total container shifting fee.
