Computational Management Science

, Volume 9, Issue 2, pp 273–286 | Cite as

DCA for solving the scheduling of lifting vehicle in an automated port container terminal

  • Hoai Minh LeEmail author
  • Adnan Yassine
  • Riadh Moussi
Original Paper


The container was introduced as a universal carrier for various goods in the 1960s and soon became a standard worldwide transportation. The competitiveness of a container seaport is marked by different success factors, particularly the time in port for ships. Operational problems of container terminals is divided into several problems, such as assignment of vessels, loading/unloading and storage of the containers, quay cranes scheduling cite, planning yard cranes cite and assignment of storage containers cite. In this work, the study will focus on piloting yard trucks. Two different types of vehicles can be used, namely automated guided vehicles (AGVs) and lifting vehicles (LVs). An AGV receives a container from a quay crane and transports containers over fixed path. LVs are capable of lifting a container from the ground by itself. The model that we consider is formulated as a mixed integer programming problem, and the difficulty arises when the number of binary variables increases. There are a lot of algorithms designed for mixed integer programming problem such as Branch and Bound method, cutting plane algorithm, . . . By using an exact penalty technique we treat this problem as a DC program in the context of continuous optimization. Further, we combine the DCA with the classical Branch and Bound method for finding global solutions.


Automated lifting vehicle Container port terminal Programmation DC DCA Branch and Bound 

Mathematics Subject Classification (2000)

90C26 90C27 90B06 


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  1. An LHA, Tao DP (1997) Solving a class of linearly constrained indefinite quadratic problems by DC algorithms. J Global Optimiz 11(3): 253–285CrossRefGoogle Scholar
  2. An LTH, Tao PD (2001) A continuous approach for globally solving linearly constrained quadratic zero—once programming problems. Optimization 50: 93–120CrossRefGoogle Scholar
  3. An LTH, Tao PD (2002) DC programming: theory, algorithms and applications. In: The State of the Art (28 pages), Proceedings (containing the refereed contributed papers) of The First International Workshop on Global Constrained Optimization and Constraint Satisfaction (Cocos’ 02), Valbonne-Sophia Antipolis, France, October 2–4Google Scholar
  4. An LTH, Tao DP (2005) The DC (Difference of convex functions) programming and DCA revisited with DC models of real world nonconvex optimization problems. Ann Oper Res 133: 23–46CrossRefGoogle Scholar
  5. An LTH, Tao DP, Muu LD (1999) Exact penalty in D. C. programming. Vietnam J Math 27(2): 169–178Google Scholar
  6. Imai A, Nishimura E, Papadimitriou S (2001) The dynamic berth allocation problem for a container port. Transport Res Part B 35(4): 401–417CrossRefGoogle Scholar
  7. Imai A, Sasaki K, Nishimura E, Papadimitriou S (2006) Multi-objective simultaneous stowage and load planning for a container ship with container rehandle in yard stacks. Er J Oper Res 171(2): 373–389CrossRefGoogle Scholar
  8. Kim KH, Jong WB (2004) A look-ahead dispatching method for automated guided vehicles in automated port container terminals. Transp Sci 38(2): 224–234CrossRefGoogle Scholar
  9. Lee DH, Cao Z, Meng Q (2007) Scheduling of two-transtainer systems for loading outbound containers in port container terminals with simulated annealing algorithm. Int J Product Econom 107(1): 115–124CrossRefGoogle Scholar
  10. Lee LH, Chew EP, Tan KC, Han Y (2006) An optimization model for storage yard management in transshipment hubs. OR Spectrum 28(4): 539–556CrossRefGoogle Scholar
  11. Lee DH, Wang HQ, Miao LX (2008) Quay crane scheduling with non-interference constraints in port container terminals. Transport Res Part E 44(1): 124–135CrossRefGoogle Scholar
  12. Nguyen VD, Kim KH (2009) A dispatching method for automated lifting vehicles in automated port container terminals. Comput Ind Eng 56(3): 1002–1020CrossRefGoogle Scholar
  13. Tao PD (1988) Duality in DC (Difference of convex functions) optimization, subgradient methods, trends in mathematical optimization. Int Ser Number Math Birkhauser 84: 277–293Google Scholar
  14. Tao PD, An LTH (1997) Convex analysis approach to DC programming: theory, algorithms and applications. Acta Math Vietnamica, dedicated to Professor Hoang Tuy on the occasion of his 70th birthday 22(1):289–355Google Scholar
  15. Vis IFA, Harika I (2004) Comparison of vehicle types at an automated container terminal. OR Spectrum 26(1): 117–143CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Laboratoire de Mathématique Appliquée du HavreLe HavreFrance
  2. 2.Institut Supérieur d’Etudes Logistiques (ISEL), Quai FrissardLe Havre CedexFrance

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