Flexible Services and Manufacturing Journal

, Volume 29, Issue 1, pp 97–124 | Cite as

A cooperative quay crane-based stochastic model to estimate vessel handling time

  • Vibhuti Dhingra
  • Debjit RoyEmail author
  • René B. M. de Koster


Having a good estimate of a vessel’s handling time is essential for planning and scheduling container terminal resources, such as berth positions, quay cranes (QCs) and transport vehicles. However, estimating the expected vessel handling time is not straightforward , because it depends on vessel characteristics, resource allocation decisions, and uncertainties in terminal processes. To estimate the expected vessel handling time, we propose a two-level stochastic model. The higher level model consists of a continuous-time Markov chain (CTMC) that captures the effect of QC assignment and scheduling on vessel handling time . The lower level model is a multi-class closed queuing network that models the dynamic interactions among the terminal resources and provides an estimate of the transition rate input parameters to the higher level CTMC model. We estimate the expected vessel handling times for several container load and unload profiles and discuss the effect of terminal layout parameters and crane service time variabilities on vessel handling times. From numerical experiments, we find that by having QCs cooperate, the vessel handling times are reduced by up to 15 %. The vessel handling time is strongly dependent on the variation in the QC service time and on the vehicle travel path topology.


Vessel sojourn time Cooperating QCs Markov chain  Closed queuing network 



We are thankful to the Research and Publications Office at Indian Institute of Management Ahmedabad and Erasmus Smartport for supporting this research. We are thankful to the referees for the comments in improving the exposition of this paper.


  1. Bierwirth C, Meisel F (2010) A survey of berth allocation and quay crane scheduling problems in container terminals. Eur J Oper Res 202:615–627CrossRefzbMATHGoogle Scholar
  2. Canonaco P, Legato P, Mazza R, Musmanno R (2008) A queuing network model for the management of berth crane operations. Comput Oper Res 35(8):2432–2446CrossRefzbMATHGoogle Scholar
  3. Chen J, Lee D, Cao J (2011) Heuristics for quay crane scheduling at indented berth. Transp Res Part E 47:1005–1020CrossRefGoogle Scholar
  4. Chung S, Chan F (2013) A workload balancing genetic algorithm for the quay crane scheduling problem. Int J Prod Res 51:4820–4834CrossRefGoogle Scholar
  5. Daganzo C (1989) The crane scheduling problem. Transp Res Part B 23:159–179MathSciNetCrossRefGoogle Scholar
  6. Easa SM (1987) Approximate queueing models for analyzing harbor terminal operations. Transp Res Part B Methodol 21(4):269–286CrossRefGoogle Scholar
  7. Gharehgozli AH, Roy D, De Koster R (2015) Sea container terminals: new technologies and OR models. Marit Econ Logist. doi: 10.1057/mel.2015.3 Google Scholar
  8. Guan Y, Yang K, Zhou Z (2013) The crane scheduling problem: models and solution approaches. Annals of Oper Res 203:119–139MathSciNetCrossRefzbMATHGoogle Scholar
  9. Han X, Lu Z, Xi L (2010) A proactive approach for simultaneous berth and quay crane scheduling problem with stochastic arrival and handling time. Eur J Oper Res 207:1327–1340CrossRefzbMATHGoogle Scholar
  10. Hoshino S, Ota J, Shinozaki A, Hashimoto H (2007) Optimal design methodology for an AGV transportation system by using the queuing network theory. In: Alami R, Chatila R, Asama H (eds) Distributed autonomous robotic systems, vol 6. Springer, Japan, pp 411–420Google Scholar
  11. Kang S, Medina J, Ouyang C (2008) Optimal operations of transportation fleet for unloading activities at container ports. Transp Res Part B Methodol 42(10):970–984CrossRefGoogle Scholar
  12. Kim K, Park Y (2004) A crane scheduling method for port container terminals. Eur J Oper Res 156:752–768CrossRefzbMATHGoogle Scholar
  13. Koenigsberg E, Lam R (1976) Cyclic queue models of fleet operations. Oper Res 24(3):516–529CrossRefzbMATHGoogle Scholar
  14. Le-Anh T, De Koster R (2005) On-line dispatching rules for vehicle based internal transport systems. Int J Prod Res 43:1711–1728CrossRefGoogle Scholar
  15. Lee D, Wang H, Miao L (2008) Quay crane scheduling with non-interference constraints in port container terminals. Transp Res Part E 44:124–135CrossRefGoogle Scholar
  16. Legato P, Mazza R, Trunfio R (2010) Simulation based optimization for discharge/loading operations at a maritime container terminal. OR Spectr 32:543–567CrossRefzbMATHGoogle Scholar
  17. Legato P, Trunfio R, Meisel F (2012) Modeling and solving rich quay crane scheduling problem. Comput Oper Res 39:2063–2078MathSciNetCrossRefzbMATHGoogle Scholar
  18. Lim A, Rodrigues B, Xiao F, Zhu Y (2004) Crane scheduling with spatial constraints. Nav Res Logistics 51:386–406MathSciNetCrossRefzbMATHGoogle Scholar
  19. Liu Z, Han X, Xi L, Erera A (2012) A heuristic for the quay crane scheduling problem based on contiguous bay crane operations. Comput Oper Res 39:2915–2928MathSciNetCrossRefzbMATHGoogle Scholar
  20. Meisel F (2011) The quay crane scheduling problem with time windows. Nav Res Logistics 58:619–636MathSciNetCrossRefzbMATHGoogle Scholar
  21. Meisel F, Bierwirth C (2011) A unified approach for the evaluation of quay crane scheduling models and algorithms. Compu Oper Res 38:683–693CrossRefGoogle Scholar
  22. Meisel F, Bierwirth C (2013) A framework for integrated berth allocation and crane operations planning in seaport container terminals. Transp Sci 47(2):131–147CrossRefGoogle Scholar
  23. Mennis E, Platis A, Lagoudis I, Nikitakos N (2008) Improving port container terminal efficiency with the use of markov theory. Marit Econ Logistics 10(3):243–257CrossRefGoogle Scholar
  24. Nguyen S, Zhang M, Johnston M, Tan K (2013) Hybrid evolutionary computation methods for quay crane scheduling problems. Comput Oper Res 40:2083–2093CrossRefzbMATHGoogle Scholar
  25. Park Y, Kim K (2003) A scheduling method for berth and quay cranes. OR Spectr 25:1–23MathSciNetCrossRefzbMATHGoogle Scholar
  26. Peterkofsky R, Dazango C (1990) A branch and bound solution method for the crane scheduling problem. Transp Res Part B 24:159–172CrossRefGoogle Scholar
  27. Reiser M, Lavenberg S (1980) Mean-value analysis of closed multichain queuing networks. J Assoc Comput Mach 27:313–322MathSciNetCrossRefzbMATHGoogle Scholar
  28. Roy D, De Koster R. (2012) Optimal design of container terminal layout. In: Proceedings of 12th international material handling research colloquium, Gardanne, FranceGoogle Scholar
  29. Roy D, De Koster R (2014) Modeling and design of container terminal operations. Technical report ERIM report series reference no. ERS-2014-008-LIS, RotterdamGoogle Scholar
  30. Roy D, Gupta A, De Koster R (2015) A non-linear traffic flow-based queuing model to estimate container terminal throughput with AGVs. Int J Prod Res. doi: 10.1080/00207543.2015.1056321 Google Scholar
  31. Unsal O, Oguz C (2013) Constraint programming approach to quay crane scheduling problem. Transp Res Part E 59:108–122CrossRefGoogle Scholar
  32. Vis I, Anholt R (2010) Performance analysis of berth configurations at container terminals. OR Spectr 32:453–476CrossRefGoogle Scholar
  33. Viswanadham N, Narahari Y (1992) Performance modeling of automated manufacturing systems, 1st edn. Prentice-Hall, Upper Saddle RiverzbMATHGoogle Scholar
  34. Zhu Y, Lim A (2006) Crane scheduling with non-crossing constraint. J Oper Res Soc 57:1464–1471CrossRefzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Vibhuti Dhingra
    • 1
  • Debjit Roy
    • 2
    Email author
  • René B. M. de Koster
    • 3
  1. 1.Sauder School of BusinessUniversity of British ColumbiaVancouverCanada
  2. 2.Indian Institute of ManagementVastrapurIndia
  3. 3.Rotterdam School of ManagementErasmus UniversityRotterdamThe Netherlands

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