An Exact Algorithm for the Integrated Planning of Berth Allocation and Quay Crane Assignment

In this paper we study the simultaneous optimization of berth allocation and quay crane assignment in seaport container terminals. We propose a model based on an exponential number of variables that is solved via column generation. An exact branch and price algorithm is implemented to produce optimal integer solutions to the problem. In particular, we present several accelerating techniques for the master and the pricing problem that can be generalized to other branch and price schemes. Computational results show that the proposed approach outperforms commercial solvers. Furthermore, the developed algorithm allows for a comparative analysis between the hierarchical and the integrated solution approach that confirms the added value of integration in terms of cost reduction and efficient use of resources. To the best of our knowledge, this is the first exact branch and price algorithm for both the berth allocation problem and the berth allocation problem with quay crane assignment.

[1]  Michel Bierlaire,et al.  Optimization at Container Terminals: Status, Trends and Perspectives (revised version) , 2007 .

[2]  Kjetil Fagerholt,et al.  Ship Routing and Scheduling: Status and Perspectives , 2004, Transp. Sci..

[3]  Akio Imai,et al.  The Dynamic Berth Allocation Problem for a Container Port , 2001 .

[4]  Alberto Ceselli,et al.  Exactly solving a two-level location problem with modular node capacities , 2012, Networks.

[5]  Marshall Conley,et al.  Canadian shipping policies and the United Nations Conference on Trade and Development: an analysis of UNCTAD V , 1982 .

[6]  Giovanni Righini,et al.  A column generation algorithm for the vehicle routing problem with soft time windows , 2011, 4OR.

[7]  Michel Gendreau,et al.  Interior point stabilization for column generation , 2007, Oper. Res. Lett..

[8]  Kap Hwan Kim,et al.  A scheduling method for Berth and Quay cranes , 2003 .

[9]  Ilaria Vacca.  Container Terminal Management , 2011 .

[10]  Giovanni Righini,et al.  New dynamic programming algorithms for the resource constrained elementary shortest path problem , 2008, Networks.

[11]  Jacques Desrosiers,et al.  Selected Topics in Column Generation , 2002, Oper. Res..

[12]  Giovanni Righini,et al.  A Branch-and-Price Approach to the Vehicle Routing Problem with Simultaneous Distribution and Collection , 2006, Transp. Sci..

[13]  Christian Bierwirth,et al.  A survey of berth allocation and quay crane scheduling problems in container terminals , 2010, Eur. J. Oper. Res..

[14]  Marielle Christiansen,et al.  A Branch-and-Price Method for a Liquefied Natural Gas Inventory Routing Problem , 2010, Transp. Sci..

[15]  Gilbert Laporte,et al.  Models and Tabu Search Heuristics for the Berth-Allocation Problem , 2005, Transp. Sci..

[16]  Cynthia Barnhart,et al.  Applications of Operations Research in the Air Transport Industry , 2003, Transp. Sci..

[17]  Alexandre César Muniz de Oliveira,et al.  A Hybrid Column Generation Approach for the Berth Allocation Problem , 2008, EvoCOP.

[18]  Stefan Voß,et al.  Operations research at container terminals: a literature update , 2007, OR Spectr..

[19]  Sylvie Gélinas,et al.  A new branching strategy for time constrained routing problems with application to backhauling , 1992, Ann. Oper. Res..

[20]  Matteo Salani,et al.  Modeling and Solving the Tactical Berth Allocation Problem , 2010 .

[21]  Stefan Voß,et al.  Container terminal operation and operations research - a classification and literature review , 2004, OR Spectr..

[22]  Nicos Christofides,et al.  An algorithm for the resource constrained shortest path problem , 1989, Networks.

[23]  Diego Klabjan,et al.  Multiship Crane Sequencing with Yard Congestion Constraints , 2009, Transp. Sci..

[24]  Pierre Hansen,et al.  Stabilized column generation , 1998, Discret. Math..

[25]  Giovanni Righini,et al.  New dynamic programming algorithms for the resource constrained elementary shortest path problem , 2008 .

[26]  Jesper Larsen,et al.  Models for the discrete berth allocation problem: A computational comparison , 2011 .

[27]  Akio Imai,et al.  The simultaneous berth and quay crane allocation problem , 2008 .

[28]  Giovanni Righini,et al.  Symmetry helps: Bounded bi-directional dynamic programming for the elementary shortest path problem with resource constraints , 2006, Discret. Optim..

[29]  Alberto Ceselli,et al.  A branch-and-cut-and-price approach for a two-level hierarchical location problem , 2009 .

[30]  Michel Bierlaire,et al.  Optimization of operations in container terminals: hierarchical vs integrated approaches , 2010 .

[31]  Christian Bierwirth,et al.  Heuristics for the integration of crane productivity in the berth allocation problem , 2009 .

[32]  Iris F. A. Vis,et al.  Transshipment of containers at a container terminal: An overview , 2003, Eur. J. Oper. Res..