Dario Pacino

On the complexity of container stowage planning problems

The optimization of container ship and depot operations embeds the k-shift problem, in which containers must be stowed in stacks such that at most k containers must be removed in order to reach containers below them. We first solve an open problem introduced by Avriel et al. (2000) by showing that changing from uncapacitated to capacitated stacks reduces the complexity of this problem from NP-complete to polynomial. We then examine the complexity of the current state-of-the-art abstraction of container ship stowage planning, wherein containers and slots are grouped together. To do this, we define the hatch overstow problem, in which a set of containers are placed on top of the hatches of a container ship such that the number of containers that are stowed on hatches that must be accessed is minimized. We show that this problem is NP-complete by a reduction from the set-covering problem, which means that even abstract formulation of container ship stowage planning is intractable.

A Survey on the Ship Loading Problem

Recent statistics show that large container terminals can process more than 30 million containers a year, and are constantly in search for the better ways to optimize processing time, deliver high quality and profitable services. Some of the terminal decisions are, however, dependent on externalities. One of those is the ship loading process. Based on the stowage plan received by liner shippers, terminal operators plan the execution of load and discharge operations. In this paper we present a literature review for the Ship Loading Problem, where stowage and loading sequencing and scheduling are integrated to improve the efficiency of the ship handling operations. We present a survey of the state-of-the-art methods and of the available benchmarking data.

An LNS Approach for Container Stowage Multi-port Master Planning

The generation of competitive stowage plans have become a priority for the shipping industry. Stowage planning is NP-hard and is a challenging optimization problem in practice. Two-phase decomposition approaches have proved to give viable solutions. We propose a large neighborhood search (LNS) to solve the first of the two phases, the multi-port master planning problem. Our approach combines the strength of mathematical modeling with the flexibility of a local search. We show how the new approach can solve more instances than previous mathematical models, and present an analysis of its performance.

Crane Intensity and Block Stowage Strategies in Stowage Planning

The increasing size of container vessels is raising the complexity of daily operations of both the carrier and the terminal. This paper focuses on stowage planning, the problem of assigning container to positions in a vessel. In particular, it studies the implementation of known planning strategies within an optimisation framework. Block stowage and crane intensity are presented and mathematically modelled on a simplified version of the problem. An experimental evaluation, on a large set of novel benchmark instances, shows that even in this simplified version the problem is not trivially solved. A matheuristic based on large neighbourhood search is presented, which is able to find a solution to all instances in short computational times.