Simulated annealing with different vessel assignment strategies for the continuous berth allocation problem



The berth allocation problem is an optimization problem concerning seaside operations at container terminals. This study investigates the dynamic and continuous berth allocation problem (BAP), whose objective is to minimize the total weighted service time and the deviation cost from vessels’ preferred position. The problem is formulated as a mixed integer programming model. Due to that the BAP is NP-hard, two efficient and effective simulated annealing (SA) algorithms are proposed to locate vessels along the quay. The first SA assigns vessels to available positions along the quay from the left to the right, while the second assigns vessels from both sides. Both small and large-scale instances in the literature are tested to evaluate the effectiveness of the proposed SA algorithms using the optimization software Gurobi and heuristic algorithms from the literature. The results indicate that the proposed SAs can provide optimal solutions in small-scale instances and updates the best solutions in large-scale instances. The improvement over other comparing heuristics is statistically significant.


Berth allocation problem Continuous Simulated annealing Container terminal 



The authors are grateful to the Ministry of Science and Technology of the Republic of China (Taiwan) and the Linkou Chang Gung Memorial Hospital for financially supporting this research Grants MOST 105-2410-H-182-009-MY2 and CMRPD3G0011, respectively.


  1. Bierwirth C, Meisel F (2010) A survey of berth allocation and quay crane scheduling problems in container terminals. Eur J Oper Res 202(3):615–627MathSciNetCrossRefMATHGoogle Scholar
  2. Bierwirth C, Meisel F (2015) A follow-up survey of berth allocation and quay crane scheduling problems in container terminals. Eur J Oper Res 244(3):675–689MathSciNetCrossRefMATHGoogle Scholar
  3. Buhrkal K, Zuglian S, Ropke S, Larsen J, Lusby R (2011) Models for the discrete berth allocation problem: a computational comparison. Transp Res Part E 47(4):461–473CrossRefGoogle Scholar
  4. Carlo HJ, Vis IFA, Roodbergen KJ (2015) Seaside operations in container terminals: literature overview, trends, and research directions. Flex Serv Manuf J 27(2):224–262CrossRefMATHGoogle Scholar
  5. Cordeau JF, Laporte G, Legato P, Moccia L (2005) Models and tabu search heuristics for the berth-allocation problem. Transp Sci 39(4):526–538CrossRefGoogle Scholar
  6. Dai J, Lin W, Moorthy R, Teo CP (2008) Berth allocation planning optimization in container terminals. In: Tang CS, Teo CP, Wei KK (eds) Supply chain analysis. International series in operations research & management science, vol 119. Springer, Boston, MA, pp 69–104Google Scholar
  7. de Oliveira RM, Mauri GR, Lorena LAN (2012) Clustering search heuristics for solving a continuous berth allocation problem. Lect Notes Comput Sci 7245:49–62CrossRefMATHGoogle Scholar
  8. Frojan P, Correcher JF, Alvarez-Valdes R, Koulouris G, Tamarit JM (2015) The continuous berth allocation problem in a container terminal with multiple quays. Expert Syst Appl 42(21):7356–7366CrossRefGoogle Scholar
  9. Fugazza M (2015) Maritime connectivity and trade. UNCTAD policy issues in international trade and commodities, Research Study Series No. 70. New York and GenevaGoogle Scholar
  10. Guan Y, Cheung RK (2004) The berth allocation problem: models and solution methods. OR Spectrum 26(1):75–92MathSciNetCrossRefMATHGoogle Scholar
  11. Guan Y, Xiao WQ, Cheung RK, Li CL (2002) A multiprocessor task scheduling model for berth allocation: heuristic and worst-case analysis. Oper Res Lett 30(5):343–350MathSciNetCrossRefMATHGoogle Scholar
  12. Hansen P, Oğuz C (2003) A note on formulation of static and dynamic berth allocation problems. Les Cahiers du GERAD G-2003-30Google Scholar
  13. Hansen P, Oğuz C, Mladenovic N (2008) Variable neighborhood search for minimum cost berth allocation. Eur J Oper Res 191(3):636–649CrossRefMATHGoogle Scholar
  14. Imai A, Nagaiwa K, Chan WT (1997) Efficient planning of berth allocation for container terminals in Asia. J Adv Transp 31(1):75–94CrossRefGoogle Scholar
  15. Imai A, Nishimura E, Papadimitriou S (2001) The dynamic berth allocation problem for a container port. Transp Res Part B 35(4):401–417CrossRefGoogle Scholar
  16. Imai A, Nishimura E, Papadimitriou S (2003) Berth allocation with service priority. Transp Res Part B 37(5):437–457CrossRefGoogle Scholar
  17. Imai A, Sun X, Nishimura E, Papadimitriou S (2005) Berth allocation in a container port: using a continuous location space approach. Transp Res Part B 39(3):199–221CrossRefGoogle Scholar
  18. Imai A, Zhang JT, Nishimura E, Papadimitriou S (2007) The berth allocation problem with service time and delay time objectives. Marit Econ Logist 9:269–290CrossRefGoogle Scholar
  19. Imai A, Nishimura E, Papadimitriou S (2008) Berthing ships at a multi-user container terminal with a limited quay capacity. Transp Res Part E 44(1):136–151CrossRefGoogle Scholar
  20. Kim KH, Moon KC (2003) Berth scheduling by simulated annealing. Transp Res Part B 37(6):541–560CrossRefGoogle Scholar
  21. Kirkpatrick S, Gelatt CD, Vecch MP (1983) Optimization by simulated annealing. Science 220:671–680MathSciNetCrossRefMATHGoogle Scholar
  22. Lalla-Ruiz E, Melián-Batista B, Marcos Moreno-Vega J (2012) Artificial intelligence hybrid heuristic based on tabu search for the dynamic berth allocation problem. Eng Appl Artif Intell 25(6):1132–1141CrossRefGoogle Scholar
  23. Lee Y, Chen CY (2009) An optimization heuristic for the berth scheduling problem. Eur J Oper Res 196(2):500–508MathSciNetCrossRefGoogle Scholar
  24. Lee DH, Chen JH, Cao JX (2010) The continuous berth allocation problem: a greedy randomized adaptive search solution. Transp Res Part E 46(6):1017–1029CrossRefGoogle Scholar
  25. Li CL, Cai X, Lee CY (1998) Scheduling with multiple-job-on-one-processor pattern. IIE Trans 30(5):433–445Google Scholar
  26. Lim A (1998) The berth planning problem. Oper Res Lett 22(2–3):105–110MathSciNetCrossRefMATHGoogle Scholar
  27. Lin SW, Ting CJ (2014) Solving the dynamic berth allocation problem by simulated annealing. Eng Optim 46(3):308–327CrossRefGoogle Scholar
  28. Lin SW, Yu VF (2012) A simulated annealing heuristic for the team orienteering problem with time windows. Eur J Oper Res 217(1):94–107MathSciNetCrossRefMATHGoogle Scholar
  29. Lin SW, Ying KC, Wan SY (2014) Minimization of total service time for the discrete dynamic berth allocation problem by iterated greedy heuristic. Sci World J. doi: 10.1155/2014/218925) Google Scholar
  30. Mauri GR, Oliveira ACM, Lorena LAN (2008) A hybrid column generation approach for the berth allocation problem. Lect Notes Comput Sci 4972:110–122CrossRefGoogle Scholar
  31. Mauri GR, Andrade LN, Lorena LAN (2011) A memetic algorithm for a continuous case of the berth allocation problem. In: 2011 international conference on evolutionary computation theory and applications, Paris, FranceGoogle Scholar
  32. Mauri GR, Ribeiro GM, Lorena LAN, Laporte G (2016) An adaptive large neighborhood search for the discrete and continuous berth allocation problem. Comput Oper Res 70:140–154MathSciNetCrossRefGoogle Scholar
  33. McKendall AR, Shan J, Kuppusamy S (2006) Simulated annealing heuristics for the dynamic facility layout problem. Comput Oper Res 33(8):2431–2444MathSciNetCrossRefMATHGoogle Scholar
  34. Metropolis N, Rosenbluth A, Rosenbluth M, Teller A, Teller E (1953) Equation of state calculations by fast computing machines. J Chem Phys 21(6):1087–1090CrossRefGoogle Scholar
  35. Monaco MF, Sammarra M (2007) The berth allocation problem: a strong formulation solved by a Lagrangian approach. Transp Sci 41(2):265–280CrossRefGoogle Scholar
  36. Moorthy R, Teo CP (2006) Berth management in container terminal: the template design problem. OR Spectrum 28(4):495–518CrossRefMATHGoogle Scholar
  37. Nawaz M, Enscore E, Ham I (1983) A heuristic algorithm for the m-machine, n-job flow-shop sequencing problem. Omega 11(1):91–95CrossRefGoogle Scholar
  38. Nishimura E, Imai A, Papadimitriou S (2001) Berth allocation planning in the public berth system by genetic algorithms. Eur J Oper Res 131(2):282–292CrossRefMATHGoogle Scholar
  39. Park KT, Kim KH (2002) Berth scheduling for container terminals by using a subgradient optimization technique. J Oper Res Soc 53(9):1054–1062CrossRefMATHGoogle Scholar
  40. Seckiner SU, Kurt M (2007) A simulated annealing approach to the solution of job rotation scheduling problems. Appl Math Comput 188(1):31–45MATHGoogle Scholar
  41. Seyedalizadeh Ganji SR, Babazadeh A, Arabshahi N (2010) Analysis of the continuous berth allocation problem in container ports using a genetic algorithm. J Mar Sci Technol 15(4):408–416CrossRefGoogle Scholar
  42. Stahlbock R, Voß S (2008) Operations research at container terminals: a literature update. OR Spectrum 30(1):1–52MathSciNetCrossRefMATHGoogle Scholar
  43. Steenken D, Voß S, Stahlbock R (2004) Container terminal operation and operations research a classification and literature review. OR Spectrum 26(1):3–49CrossRefMATHGoogle Scholar
  44. Ting CJ, Wu KC, Chou H (2014) Particle swarm optimization algorithm for the berth allocation problem. Expert Syst Appl 41(4):1543–1550CrossRefGoogle Scholar
  45. Tong CJ, Lau HC, Lim A (1999) Ant colony optimization for the ship berthing problem. Lect Notes Comput Sci 1742:359–370CrossRefGoogle Scholar
  46. UNCTAD (2016) Review of maritime transportation. In: United Nations conference on trade and developmentGoogle Scholar
  47. Wang F, Lim A (2007) A stochastic beam search for the berth allocation problem. Decis Support Syst 42(4):2186–2196CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Department of Information ManagementChang Gung UniversityTaoyuanTaiwan, ROC
  2. 2.Department of Industrial Engineering and ManagementMing Chi University of TechnologyTaipeiTaiwan, ROC
  3. 3.Department of NeurologyLinkou Chang Gung Memorial HospitalTaoyuanTaiwan, ROC
  4. 4.Department of Industrial Engineering and ManagementYuan Ze UniversityTaoyuanTaiwan, ROC

Personalised recommendations