An Effective Ship Berthing Algorithm

Singapore has one of the busiest ports in the world. Ship berthing is one of the problems faced by the planners at the port. In this paper , we study the ship berthing problem. We first provide the problem formulation and study the complexity of the problem with different restrictions. In general, the ship berthing problem is NP-complete, although, some of its variants may be solved quickly. While a geometrical model is intuitive, the model cannot be easily extended to handle clearance constraints and berth restriction. Rather than solving the problem geometrically, we transform the problem t nto the problem of fixing directionsof edges ,n graph to form directed acyclic graph with minimal lonqest path. Since the problem is NP-complete, solving the problem exactly in polynomial time is highly unlikely. As a result, we devise a fast and effective greedy algorithm to can generate good solutions. The greedy method together with a tabu search like post optimization algorithm is able to return optimal or near optimal solutions. 1 Introduction Situated at the crossroads of the world, the Port of Sin-gapore is one of the world's busiest port. Every few minutes a ship arrives or departs the port. Every month the port handles more than one million transhipment containers. When a ship arrives at the port, the planners must first decide where to berth the ship for the unloading and loading of containers. For the containers that are to be unloaded, the planners must decide where to place these containers in the yard. The wharf line of the port is divided into sections, and no ship can be berthed across any two sections. Which section to assign a ship to and exactly where to berth a ship within a section depend on factors like the locations of containers to be loaded and unloaded, the physical (i.e. depth of the berth) and resource limitations (i.e. suitably of quay crane) of each berth. A sketch of a port is given in Figure 1. The allocation of ships to sections and placement of containers in the yard is studied by Lim [Lim, 1998]. The approach used is a variant of graph partitioning problem. Allocation of vessels to sections were also studied by Brown [Brown et al., 1994; 1997]. One of the subproblems in [Lim, 1998] is the ship berthing problem. The ship berthing problem was studied by HenglHeng, Khoong, and Lim, 1996J using a …