By:Maasoomeh Karimi

Fall 2008

In the name of God

contentAn introduction to Container Stowage

planning Some definitions Problem importance

Problem complexityModels and solution techniquesCase studyReference

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Some definitions

3(Anna Sciomachen , Elena

Tanfani, )

problem importanceContainerization has increasingly facilitated

the transportation of cargo since the 1970s (I.D. Wilson, P.A. Roach, J.A. Ware, 2001).

The standard frame and dimentions of containers allows containerized cargo to be transported by rail, truck or sea (I.D. Wilson, P.A. Roach, J.A. Ware, 2001).

The fast ship turnaround at a container terminal is essential for the economic performance of shipping companies (Akio Imai, Kazuya Sasaki, Etsuko Nishimura, Stratos Papadimitriou, 2006).

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problem importance (cont’d)

The turnaround time of a ship includes the time for berthing, unloading, loading and departure (Akio Imai, Kazuya Sasaki, Etsuko Nishimura, Stratos Papadimitriou, 2006).

Determining a viable arrangement of containers that facilitates loading and unloading process, in a cost-effective way, makes up the container stowage problem (I.D. Wilson, P.A. Roach, J.A. Ware, 2001).

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Problem complexity

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The structure of container ship (Daniela Ambrosino, Anna Sciomachen, Elena Tanfani, 2004)

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In particular, each location is addressed by the following indices:

The structure of container ship (cont’d)

8Numbering of tiers

Numbering of rows Numbering of bays (I.D. WILSON AND P.A. ROACH,

1999)

The structure of container ship (cont’d)

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The constraints of the problem (Anna Sciomachen, Elena Tanfani, 2007; Daniela Ambrosino, Anna Sciomachen, Elena Tanfani, 2004)

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Size of container constraints(Anna Sciomachen, Elena Tanfani, 2007)

Constraints related to 40 feet containers

Constraints related to 20 feet containers

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Type of container constraints (I.D. Wilson, P.A. Roach, J.A. Ware, 2001; Anna Sciomachen, Elena Tanfani, 2007)

Reefer containers‘Out of gauge’ containersEmpty and open top containersFantainersHazardous containers

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Weight constraints (Daniela Ambrosino, Anna Sciomachen, Elena Tanfani, )

The total weight of all containers cannot exceed the maximum weight capacity.

the weight of a stack of three containers of 20 feet and 40 feet cannot be greater than an a priori established value.

the weight of a container located in a tier cannot be greater than the weight of the container located in a lower tier having the same row and bay.

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Operational and security constraints:(Daniela Ambrosino, Anna Sciomachen, Elena Tanfani, 2004; Anna Sciomachen, Elena Tanfani, 2007)

Cross equilibrium (Q1)

Horizontal equilibrium (Q2)

Vertical equilibrium (Q3)

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Destination constraints:(Daniela Ambrosino, Anna Sciomachen, Elena Tanfani, 2004)

Loading first those containers having as

destination the final stop of the ship and consequently load last those containers that have to be unloaded first.

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Objective function classification (Akio Imai, Kazuya Sasaki, Etsuko Nishimura, Stratos Papadimitriou, 2006; Anna Sciomachen, Elena Tanfani, 2007)

Objective function Articles

Minimization of the loading-related rehandle and maximization of ship stability

Imai and Miki (1989); Imai et al. (2002); Akio Imai, Kazuya Sasaki, Etsuko Nishimura, Stratos Papadimitriou (2006)

Minimization of the unloading-related rehandles without any consideration for ship’s stability

Avriel and Penn (1993) and Avriel et al. (1998)

Minimization of the container unloading-related rehandle cost, while keeping the ship stability acceptable

Haghani and Kaisar (2001); Wilson and Roach (1999, 2000)

Minimization of the number unloading-related rehandles and minimization of the transtainer movement time

Martin et al. (1988)

Minimization of the total stowage time

Ambrosino , Sciomachen and Tanfani (2004)

Minimization of the rahandles Kim et al. (2000); Taleb-Ibrahimi et al. (1993); Kim and Kim (1994); I.D. Wilson, P.A. Roach, J.A. Ware (2001)

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Models classification

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A 0-1 Linear programming model (Daniela Ambrosino, Anna Sciomachen, Elena Tanfani, 2004)

Formally, the master bay plan problem (MBPP) involves determining how to stow a set C of m containers of different types into a set S of n available locations within a containership, with respect to some structural and operational constraints related to both the containers and the ship, whilst minimising the total stowage time (see, e.g., Ambrosino and Sciomachen, 1998).

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A 0-1 Linear programming model (Daniela Ambrosino, Anna Sciomachen, Elena Tanfani, 2004)

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(1)

(2)

(3)

(4)

(5)

(6)

(7)

A 0-1 Linear programming model (cont’d) (Daniela Ambrosino, Anna Sciomachen, Elena Tanfani, 2004)

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(8)

(9)

(10)

(11)

(12)

(13)

A 0-1 Linear programming model (cont’d) (Daniela Ambrosino, Anna Sciomachen, Elena Tanfani, 2004)

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(14)

(15)

(16)

(17)

(18)

A model divided into sub-problems (I.D. Wilson, P.A. Roach, J.A. Ware, 2001)

underlying heuristics used to generate stowage solution and their subsequent evaluation.

Decomposing the planning process into two sub-process:A strategic planning process

o Solution technique: branch and bound search

A tactical planning processo Solution technique: Tabu search

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A multi-objective integer programming(Akio Imai, Kazuya Sasaki, Etsuko Nishimura, Stratos Papadimitriou, 2006)

relationship between ship stability and the loading-related rehandle

Employing the weighting method (Cohon, 1978)

Objective function: maximization of the ship atability,

minimization of the loading related rehandleSolution technique: Genetic algorithm

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Solution techniques (I.D. Wilson, P.A. Roach, J.A. Ware, 2001; Akio Imai, Kazuya Sasaki, Etsuko Nishimura, Stratos Papadimitriou, 2006; Anna Sciomachen, Elena Tanfani, 2007 )

Solution techniques articles

Simulation based upon probability J.J. Shields (1984)

Heuristic driven Anna Sciomachen and Elena Tanfani (2007), G.L. Martin (1988), Haghani and Kaisar (2001)

Rule-based expert systems N.Perakis, J.T. Dillingham (1987), J.T. Dillingham , A.N.Perakis (1986), I.D.Wilson (1997), I.D.Wilson , P.A. Roach (1997), I.D.Wilson , P.A. Roach (1999), K. Sato, H.Itoh, Y. Awashima (1992), Ratcliffe and Sen (1987), Saginaw and Parakis (1989)

Decision support systems D.J. Saginaw, A.N.Perakis (1989), G.J.P. Lang (1985), H. Sansen (1989)

Rule-based decision systems Ambrosino and Sciomachen (1998)

Metaheuristic approaches (genetic algorithm and tabu search)

Dubrovsky et al. (2002), Wilson and Roach (1999), Wilson et al. (2001), I.D. Wilson, P.A. Roach and J.A. Ware (2001); Akio Imai, Kazuya Sasaki, Etsuko Nishimura, Stratos Papadimitriou, 2006

Exact method (branch and bound search) Wilson and Roach (1999), Wilson et al. (2001), I.D. Wilson, P.A. Roach and J.A. Ware (2001), Ambrosino et al. (2006)

Local search algorithms and techniques based on combinatorial optimisation

Wilson and Roach (1999) and Wilson et al. (2001)

Case study (Daniela Ambrosino, Anna Sciomachen, Elena Tanfani, 2004)

the Chiwaua containership, that is a ‘‘client’’ of the maritime terminal in Genoa (Italy)

It is a 198 TEU containership, with 11 bays, four rows and five tiers (three in the hold and two in the upper deck, respectively)

Testing the approach deducing the master bay plan by referring to 13 cases, reported in Table 1.

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Case study (cont’d) (Daniela Ambrosino, Anna Sciomachen, Elena Tanfani, 2004)

The impact of the destination constraints (15) in the cases 9 and 11, computational time

reduces respectively from 103 to 22 min in the relaxed model, and from 112 to 35 min on the same platform.

Manually compiling the corresponding master bay plans takes about from 60 to 90 min

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Case study (cont’d) (Daniela Ambrosino, Anna Sciomachen, Elena Tanfani, 2004)

Achievement 26 container movements/hour, versus the same

index in the present operational scenario at the maritime terminal that is about 24.

28,500 variables for case 1 up to 45,030 for case13

from 14,015 to 18,231 constraints for the same cases

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Refrence Anna Sciomachen, Elena Tanfani, 2007. A 3D-BPP approach for optimising

stowage plans and terminal productivity. European Journal of Operational Research 183, 1433–1446.

Akio Imai, Kazuya Sasaki, Etsuko Nishimura, Stratos Papadimitriou, 2006. Multi-objective simultaneous stowage and load planning for a container ship with container rehandle in yard stacks. European Journal of Operational Research 171, 373–389.

Daniela Ambrosino, Anna Sciomachen, Elena Tanfani, 2004. Stowing a containership: the master bay plan problem. Transportation Research Part A 38, 81–99.

Wilson, I.D., Roach, P.A., Ware, J.A., 2001. Container stowage pre-planning: Using search to generate solutions, a case study. Knowledge-Based Systems 14, 137–145.

Wilson, I.D., Roach, P.A., 1999. Principles of combinatorial optimization applied to container-ship stowage planning. Journal of Heuristics 5, 403–418.

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