1. By:Maasoomeh Karimi Fall 2008 In the name of God

2. content An introduction to Container Stowage planning Some definitions Problem importance Problem complexity Models and solution techniques Case study Reference 2

3. Some definitions Primary definitions containerisationContainer shipsRe-handlTEU 3 (Anna Sciomachen, Elena Tanfani, )

4. problem importance Containerization 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). 4

5. 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). 5

6. Problem complexity 6 The constraints of the problem The structure of container ship

7. The structure of container ship (Daniela Ambrosino, Anna Sciomachen, Elena Tanfani, 2004) counted from bow to stern Bay I counted from the centre to outside Row J counted from the bottom to the top of the ship Tier K 7 In particular, each location is addressed by the following indices:

8. The structure of container ship (cont’d) 8 Numbering of tiers Numbering of rows Numbering of bays (I.D. WILSON AND P.A. ROACH, 1999)

9. The structure of container ship (cont’d) 9

10. The constraints of the problem (Anna Sciomachen, Elena Tanfani, 2007; Daniela Ambrosino, Anna Sciomachen, Elena Tanfani, 2004) constraints Size of container Type of container Weight constraints Operational and security constraints Destination constraints 10

11. Size of container constraints (Anna Sciomachen, Elena Tanfani, 2007)  Constraints related to 40 feet containers  Constraints related to 20 feet containers 11

12. Type of container constraints (I.D. Wilson, P.A. Roach, J.A. Ware, 2001; Anna Sciomachen, Elena Tanfani, 2007)  Reefer containers  ‘Out of gauge’ containers  Empty and open top containers  Fantainers  Hazardous containers 12

13. 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. 13

14. Operational and security constraints: (Daniela Ambrosino, Anna Sciomachen, Elena Tanfani, 2004; Anna Sciomachen, Elena Tanfani, 2007)  Cross equilibrium (Q 1 )  Horizontal equilibrium (Q 2 )  Vertical equilibrium (Q 3 ) 14

15. 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. 15

16. Objective function classification (Akio Imai, Kazuya Sasaki, Etsuko Nishimura, Stratos Papadimitriou, 2006; Anna Sciomachen, Elena Tanfani, 2007 ) Objective functionArticles 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 timeAmbrosino, Sciomachen and Tanfani (2004) Minimization of the rahandlesKim et al. (2000); Taleb-Ibrahimi et al. (1993); Kim and Kim (1994); I.D. Wilson, P.A. Roach, J.A. Ware (2001) 16

17. Models classification Daniela Ambrosino, Anna Sciomachen, Elena Tanfani, 2004 Linear programming model I.D. Wilson, P.A. Roach, J.A. Ware, 2001 Wilson and Roach 1999 Wilson et al. 2001 Breaking the container stowage process into two phases Kim et al., 2000 Dynamic Programming Multi-objective integer programming(Akio Imai, Kazuya Sasaki, Etsuko Nishimura, Stratos Papadimitriou, 2006) Mixed Integer programming (Kim and Kim, 1994) 0-1 Integer Programming (Avriel and Penn, 1993; Avriel et al., 1998; Imai and Miki, 1989) Integer Programming 17

18. 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). 18

19. A 0-1 Linear programming model (Daniela Ambrosino, Anna Sciomachen, Elena Tanfani, 2004) 19 (1) (2) (3) (4) (5) (6) (7)

20. A 0-1 Linear programming model (cont’d) (Daniela Ambrosino, Anna Sciomachen, Elena Tanfani, 2004) 20 (8) (9) (10) (11) (12) (13)

21. A 0-1 Linear programming model (cont’d) (Daniela Ambrosino, Anna Sciomachen, Elena Tanfani, 2004) 21 (14) (15) (16) (17) (18)

22. 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 process o Solution technique: Tabu search 22

23. 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 rehandle Solution technique: Genetic algorithm 23

24. 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 techniquesarticles Simulation based upon probabilityJ.J. Shields (1984) Heuristic drivenAnna Sciomachen and Elena Tanfani (2007), G.L. Martin (1988), Haghani and Kaisar (2001) Rule-based expert systemsN.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 systemsD.J. Saginaw, A.N.Perakis (1989), G.J.P. Lang (1985), H. Sansen (1989) Rule-based decision systemsAmbrosino 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)

25. 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. 25

26. 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 26

27. 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 27

28. 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. 28

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