Soft Computing

, Volume 23, Issue 21, pp 10837–10852 | Cite as

Invisible consumptions and enlargements of activity floats under generalized precedence relations

  • Zhixiong SuEmail author
Methodologies and Application


Generalized precedence relations (GPRs) between activities widely exist in modern construction projects. Time floats of activities (activity floats) are indispensable to arrange the activities to cope with unstable external conditions. This paper discovers that the GPRs result in new singularities of activity floats—time floats of an activity can be consumed and enlarged imperceptibly even if the activity has not started and all activities don’t consume their time floats. The singularities are called invisible consumptions and enlargements of activity floats. This paper analyzes the singularities and presents algorithms to identify and quantize them. The new singular characteristics of activity floats may weaken current optimization approaches for project scheduling. Inspired by the characteristics, this paper develops an emergency resource leveling with GPRs that focuses on emergency actions for the dynamic and uncertain environment. An illustration demonstrates that the correct solution relies on the invisible consumptions and enlargements of activity floats.


Activity networks Generalized precedence relations Time floats Resource leveling 



The authors would like to acknowledge the China Postdoctoral Science Foundation (Grant Number 2017M620713), and the Natural Science Foundation of Science and Technology Department of Jiangxi Province in China (Grant Number 20171BAA208001). The authors are grateful to the anonymous referee for a careful scrutiny of details and for comments that helped improve this paper.

Compliance with ethical standards

Conflict of interest

Zhixiong Su declares that he has no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by the author.


  1. Alfieri A, Tolio T, Urgo M (2011) A project scheduling approach to production planning with feeding precedence relations. Int J Prod Res 49:995–1020CrossRefGoogle Scholar
  2. Amin F, Fahmi A, Abdullah S, Ali A, Ahmed R, Ghani F (2017) Triangular cubic linguistic hesitant fuzzy aggregation operators and their application in group decision making. J Intell Fuzzy Syst 34:2401–2416CrossRefGoogle Scholar
  3. Bartusch M, Möhring RH, Radermacher FJ (1988) Scheduling project networks with resource constraints and time windows. Ann Oper Res 16:201–240MathSciNetCrossRefGoogle Scholar
  4. Bianco L, Caramia M (2011) A new lower bound for the resource-constrained project scheduling problem with generalized precedence relations. Comput Oper Res 38:14–20MathSciNetCrossRefGoogle Scholar
  5. Bianco L, Caramia M (2012) An exact algorithm to minimize the makespan in project scheduling with scarce resources and generalized precedence relations. Eur J Oper Res 219:73–85MathSciNetCrossRefGoogle Scholar
  6. Bianco L, Caramia M, Giordani S (2016) Resource levelling in project scheduling with generalized precedence relationships and variable execution intensities. OR Spectrum 38:405–425MathSciNetCrossRefGoogle Scholar
  7. Brinkmann K, Neumann K (1996) Heuristic procedures for resource-constrained project scheduling with minimal and maximal time lags: the resource-levelling and minimum projectduration problems. J Decis Syst 5:129–155CrossRefGoogle Scholar
  8. Damci A, Arditi D, Polat G (2013) Resource leveling in line-of-balance scheduling. Comput Aided Civ Infrastruct Eng 28:679–692CrossRefGoogle Scholar
  9. Damci A, Arditi D, Polat G (2016) Impacts of different objective functions on resource leveling in line-of-balance scheduling. KSCE J Civ Eng 20:58–67CrossRefGoogle Scholar
  10. Dorndorf U, Pesch E, Phan-Huy T (2000) A time-oriented branch-and-bound algorithm for resource-constrained project scheduling with generalised precedence constraints. Manag Sci 46:1365–1384CrossRefGoogle Scholar
  11. Easa SM (1989) Resource leveling in construction by optimization. J Constr Eng Manag 115:302–316CrossRefGoogle Scholar
  12. Elmaghraby SE, Kamburowski J (1992) The analysis of activity networks under generalized precedence relations (GPRs). Manag Sci 38:1245–1263CrossRefGoogle Scholar
  13. Fahmi A, Amin F, Abdullah S, Ali A (2018a) Cubic fuzzy Einstein aggregation operators and its application to decision making. Int J Syst Sci 49:2385–2397MathSciNetCrossRefGoogle Scholar
  14. Fahmi A, Abdullah S, Amin F, Ali A, Khan WA (2018b) Some geometric operators with triangular cubic linguistic hesitant fuzzy number and their application in group decision-making. J Intell Fuzzy Syst 35:2485–2499CrossRefGoogle Scholar
  15. Fahmi A, Abdullah S, Amin F, Khan MSA (2018c) Trapezoidal cubic fuzzy number einstein hybrid weighted averaging operators and its application to decision making. Soft Comput 1–31.
  16. Fahmi A, Abdullah S, Amin F, Siddque N, Ali A (2017) Aggregation operators on triangular cubic fuzzy numbers and its application to multi-criteria decision making problems. J Intell Fuzzy Syst 33:3323–3337CrossRefGoogle Scholar
  17. George SJ (1988) Time-the next source of competitive advantage. Harv Bus Rev 66:41–51Google Scholar
  18. José LPT, Eugenio P, Javier BM, Carlos AR (2015) The fuzzy project scheduling problem with minimal generalized precedence relations. Comput Aided Civ Infrastruct Eng 30:872–891CrossRefGoogle Scholar
  19. Li H, Dong X (2018) Multi-mode resource leveling in projects with mode-dependent generalized precedence relations. Expert Syst Appl 97:193–204CrossRefGoogle Scholar
  20. Kaveh KD, Madjid T, Abtahi AR, Francisco JSA (2015) Solving multi-mode time-cost-quality trade-off problems under generalized precedence relations. Optim Methods Softw 30:965–1001MathSciNetCrossRefGoogle Scholar
  21. Mattila KG, Abraham DM (1998) Linear scheduling: past resource efforts and future directions. Eng Constr Archit Manag 5:294–303CrossRefGoogle Scholar
  22. Mubarak SA (2010) Construction project scheduling and control, 2nd edn. Wiley, HobokenCrossRefGoogle Scholar
  23. Neetesh K, Deo V (2016) A model for resource-constrained project scheduling using adaptive PSO. Soft Comput 20:1565–1580CrossRefGoogle Scholar
  24. Neumann K, Zimmermann J (2000) Procedures for resource levelling and net present value problems in project scheduling with general temporal and resource constraints. Eur J Oper Res 127:425–443CrossRefGoogle Scholar
  25. Pawel M, Marek S, Lukasz O, Krzysztof O (2015) Hybrid ant colony optimization in solving multi-skill resource-constrained project scheduling problem. Soft Comput 19:3599–3619CrossRefGoogle Scholar
  26. Peng W, Huang M (2014) A critical chain project scheduling method based on a differential evolution algorithm. Int J Prod Res 52:3940–3949CrossRefGoogle Scholar
  27. Pérez Á, Quintanilla S, Lino P, Valls V (2014) A multi-objective approach for a project scheduling problem with due dates and temporal constraints infeasibilities. Int J Prod Res 52:3950–3965CrossRefGoogle Scholar
  28. Pérez E, Posada M, Lorenzana A (2016) Taking advantage of solving the resource constrained multi-project scheduling problems using multi-modal genetic algorithms. Soft Comput 20:1879–1896CrossRefGoogle Scholar
  29. Qi J, Su Z (2014) Analysis of an anomaly: the increase in time float following consumption. Sci World J 2014:415870-1–415870-12Google Scholar
  30. Quintanilla S, Pérez Á, Lino P, Valls V (2012) Time and work generalised precedence relationships in project scheduling with pre-emption: an application to the management of service centres. Eur J Oper Res 219:59–72MathSciNetCrossRefGoogle Scholar
  31. Ranjbar M (2013) A path-relinking metaheuristic for the resource levelling problem. J Oper Res Soc 64:1071–1078CrossRefGoogle Scholar
  32. Rieck J, Zimmermann J, Gather T (2012) Mixed-integer linear programming for resource leveling problems. Eur J Oper Res 221:27–37MathSciNetCrossRefGoogle Scholar
  33. Roy B (1962) Graphes et ordonnancements. Rev Fr Rech Oper 25:323–326Google Scholar
  34. Schnell A, Hartl R (2016) On the efficient modeling and solution of the multi-mode resource-constrained project scheduling problem with generalized precedence relations. OR Spectrum 38:283–303MathSciNetCrossRefGoogle Scholar
  35. Shen S, Smith JC, Ahmed S (2010) Expectation and chance-constrained models and algorithms for insuring critical paths. Manag Sci 56:1794–1814CrossRefGoogle Scholar
  36. Su Z, Qi J, Kan Z (2015) Simplifying activity networks under generalized precedence relations to extended CPM networks. Int Trans Oper Res 23:1141–1161MathSciNetCrossRefGoogle Scholar
  37. Tang Y, Liu R, Sun Q (2014) Two-stage scheduling model for resource leveling of linear projects. J Constr Eng Manag 140:04014022CrossRefGoogle Scholar
  38. Váncza J, Kis T, Kovcs A (2004) Aggregation: the key to integrating production planning and scheduling. Ann CIRP 53:374–376CrossRefGoogle Scholar
  39. Wiest JD (1981) Precedence diagramming method: some unusual characteristics and their implications for project managers. J Oper Manag 1:121–130CrossRefGoogle Scholar
  40. Zhang L, Pan C, Zou X (2013) Criticality comparison between repetitive scheduling method and network model. J Constr Eng Manag 139:06013004CrossRefGoogle Scholar
  41. Zhang L, Zou X, Kan Z (2014) Improved strategy for resource allocation in repetitive projects considering the learning effect. J Constr Eng Manag 140:04014053CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Economics and ManagementNorth China Electric Power UniversityBeijingChina
  2. 2.Business Administration College, Nanchang Institute of TechnologyNanchangChina

Personalised recommendations