A 3D-BPP approach for optimising stowage plans and terminal productivity

https://doi.org/10.1016/j.ejor.2005.11.067Get rights and content

Abstract

This paper addresses the problem of determining stowage plans for containers in a ship, that is the so-called master bay plan problem (MBPP).

MBPP is NP-complete [Botter, R.C., Brinati, M.A., 1992. Stowage container planning: A model for getting an optimal solution. IFIP Transactions B (Applications in Technology) B-5, 217–229; Avriel, M., Penn, M., Shpirer, N., 2000. Container ship stowage problem: Complexity and connection to the colouring of circle graphs. Discrete Applied Mathematics 103, 271–279]. We present a heuristic method for solving MBPP based on its relation with the three-dimensional bin packing problem (3D-BPP), where items are containers and the only bin is the ship. We look for stowage plans that take into a proper account structural and operational constraints, related to both the containers and the ship, and maximise some important terminal performance indexes, such as the effective and mean net crane productivity.

Our aim is to evaluate how stowage plans can influence the performance of the quay. A validation of the proposed approach with some test cases related to containership docks at the port of Genoa (Italy) is given. The results of real instances of the problem and the comparison with a validated heuristic for MBPP, show the effectiveness of the proposed approach in producing stowage plans that minimise the total loading time and allow an efficient use of the quay equipment.

Section snippets

Introduction and literature review

During the past 30 years the container handling revolution has increased the efficiency of worldwide trade. The container is a universal transportation method capable of being moved by sea, road or rail with relative ease. With the increasing level of world trade and the corresponding increase in size of containerships (up to around 8000 containers by the year 2000) one of the main areas for cost and efficiency gains now occurs in port whilst performing container loading, unloading and

Comparison of 3D-BPP and MBPP via a simple example

As has already been said, the proposed heuristic procedure for maximising quay terminal productivity is based on the relation of MBPP with the three-dimensional bin packing problem.

Given a set of n rectangular-shaped items, each one characterised by width wj, height hj, and depth dj, (j  J = {1,  , n}), and an unlimited number of identical three-dimensional containers (bins) having width W, height H, and depth D, 3D-BPP consists of orthogonally packing all items into the minimum number of bins.

In

Terminal productivity

The ever increasing number of container shipments is causing higher demands on the seaport container terminals, the whole container logistics chain and management, as well as the technical equipment. Consequently, the competition between seaports, especially between geographically closed ones, is increasing too. The competitiveness of a container seaport is based on different factors, such as transhipment time combined with low rates for loading and discharging. Therefore, a crucial competitive

A MBPP heuristic procedure for evaluating the terminal productivity

We present the main steps of an algorithm for MBPP which is an extension of the heuristic procedure given in Sciomachen and Tanfani (2003) for minimising the total loading time in the definition of stowage plans. Here we want to include in the analysis the quay cranes used for the loading operations with the aim of maximising the terminal productivity indexes introduced in Section 3. We consider the constraints described in Section 2 and use the positioning pattern, and the corresponding

Computational experiments

The proposed loading procedure has been used to solve commercial instances of MPBB. Here we present two different series of computational experiments. The first experiments regard the comparison between the solutions of 15 real instances obtained by using two strategies of the present approach and their optimal solutions obtained by solving the 0–1 Linear Programming model for MBPP reported in Ambrosino et al. (2004). The comparison is aimed at showing the effectiveness of the proposed approach

Conclusions

In this paper, we have presented a heuristic algorithm for MBPP based on its connection to 3D-BPP. The proposed solution method has very good performances in terms of both solution quality and computational time. In particular, the most important consideration about the performance of our heuristic algorithm is the possibility of finding stowage plans for maximising the quay terminal productivity. Moreover, our algorithm enables the loading operations of each portion of the ship to be performed

Acknowledgements

The authors wish to thank the terminal management office of the terminal SECH for the fruitful support. Special thanks are to the anonymous referee for the valuable remarks and helpful comments and suggestions.

References (27)

  • D. Ambrosino et al.

    A Bay Assignment Algorithm for the containership stowage problem

    Journal of Heuristics

    (2006)
  • Atkins, W.H., 1991. Modern Marine Terminal Operations and Management Boyle,...
  • R.C. Botter et al.

    Stowage container planning: A model for getting an optimal solution

    IFIP Transactions B (Applications in Technology)

    (1992)
  • Cited by (68)

    • A decision framework for decomposed stowage planning for containers

      2024, Transportation Research Part E: Logistics and Transportation Review
    • Literature survey on the container stowage planning problem

      2023, European Journal of Operational Research
    • Multi-objective optimization of the 3D container stowage planning problem in a barge convoy system

      2022, Computers and Operations Research
      Citation Excerpt :

      First, a general loading plan is created by distributing the containers in the bays of the ships. Then, to determine the position of each container, a phase of planning the exact locations follows and focuses on each bay at a time (Wilson and Roach, 1999; Wilson and Roach, 2000; Sciomachen & Tanfani, 2007; Delgado et al., 2012). Ambrosino et al. (2004) proposed a three-phase algorithm to solve the MBPP.

    • A hybrid approach for a multi-compartment container loading problem

      2019, Expert Systems with Applications
      Citation Excerpt :

      However, it considers several objects (compartments) in a same vehicle respecting, for example, the load balancing and/or multiple destinations of the boxes. It is also related to the Master Bay Plan Problem, which consists in determining stowage plans for containers in a ship (see, e.g., Pacino & Jensen, 2012; Sciomachen & Tanfani, 2003, 2007; Araújo, Chaves, Salles Neto & Azevedo, 2016). In that problem, the containers, the ship and its bays can be viewed as the items, the object and its compartments of the present problem, respectively.

    View all citing articles on Scopus

    This work has been developed within the research area: “The harbour as a logistic node” of the Italian Centre of Excellence on Integrated Logistics (CIELI) of the University of Genoa, Italy.

    View full text