Stowage planning for container ships to reduce the number of shifts

This paper deals with a stowage plan for containers in a container ship. Containers on board a container ship are placed in vertical stacks, located in many bays. Since the access to the containers is only from the top of the stack, a common situation is that containers designated for port J must be unloaded and reloaded at port I (before J) in order to access containers below them, designated for port I. This operation is called "shifting". A container ship calling at many ports may encounter a large number of shifting operations, some of which can be avoided by efficient stowage planning. In general, the stowage plan must also take into account stability and strength requirements, as well as several other constraints on the placement of containers. In this paper, we only deal with stowage planning in order to minimize the number of shiftings, without considering stability and several other constraints. First, we briefly present a 0-1 binary Linear programming formulation that can find the optimal solution for stowage planning. However, finding the optimal solution using this model is quite limited because of the large number of binary variables and constraints needed for the formulation. Moreover, in [3] the stowage planning problem is shown to be NP-complete. For these reasons, the Suspensory Heuristic Procedure was developed.