Continuous Preemption Problems

  • Christoph SchwindtEmail author
  • Tobias Paetz
Part of the International Handbooks on Information Systems book series (INFOSYS)


In this chapter we are concerned with project scheduling problems involving preemption of activities at arbitrary points in time. We survey the literature on preemptive project scheduling and propose a classification scheme for these problems. We then consider a project scheduling problem under continuous preemption, flexible resource allocation, and generalized feeding precedence relations between the activities. After providing a formal problem statement we reduce the problem to a canonical form only containing nonpositive completion-to-start time lags and investigate structural issues like necessary feasibility conditions and preemption gains. Next, we develop an MILP formulation that encodes a schedule as a sequence of slices containing sets of activities that are simultaneously in progress. Moreover, feasibility tests, preprocessing methods, and a column-generated based lower bound on the minimum project duration are presented. Finally, we report on the results of an experimental performance analysis of the MILP model for the project duration problem.


Column generation Continuous preemption Makespan minimization Mixed-integer linear programming formulation Project scheduling Resource constraints 



The authors are indebted to Dr. Jean Damay for providing the benchmark results of the KSD-30 instances.


  1. Alfieria A, Toliob T, Urgo M (2011) A project scheduling approach to production planning with feeding precedence relations. Int J Prod Res 49:995–1020CrossRefGoogle Scholar
  2. Ballestín F, Valls V, Quintanilla S (2008) Pre-emption in resource-constrained project scheduling. Eur J Oper Res 189:1136–1152CrossRefGoogle Scholar
  3. Ballestín F, Valls V, Quintanilla S (2009) Scheduling projects with limited number of preemptions. Comput Oper Res 36:2913–2925CrossRefGoogle Scholar
  4. Baptiste P, Demassey S (2004) Tight LP bounds for resource constrained project scheduling. OR Spectr 26:251–262CrossRefGoogle Scholar
  5. Baptiste P, Carlier J, Kononov A, Queyranned M, Sevastyanov S, Sviridenko M (2004) Structural properties of preemptive schedules. IBM Research Report, IBM T.J. Watson Research Center, Yorktown Heigths. Available at Cited 8 Feb 2014
  6. Baptiste P, Carlier J, Kononov A, Queyranned M, Sevastyanov S, Sviridenko M (2011) Properties of optimal schedules in preemptive shop scheduling. Discrete Appl Math 159:272–280CrossRefGoogle Scholar
  7. Bianco L, Caramia M, Dell’Olmo P (1999) Solving a preemptive project scheduling problem with coloring techniques. In: Wȩglarz J (ed) Project scheduling: recent models, algorithms, and applications. Kluwer Academic Publishers, Boston, pp 135–145CrossRefGoogle Scholar
  8. Błażewicz J, Ecker KH, Pesch E, Schmidt G, Wȩglarz J (2007) Handbook on scheduling: from theory to applications. Springer, BerlinGoogle Scholar
  9. Braun O, Schmidt G (2003) Parallel processor scheduling with limited number of preemptions. SIAM J Comput 32:671–680CrossRefGoogle Scholar
  10. Brucker P, Knust S (2000) A linear programming and constraint propagation-based lower bound for the RCPSP. Eur J Oper Res 127:355–362CrossRefGoogle Scholar
  11. Buddhakulsomsiri J, Kim DS (2006) Properties of multi-mode resource-constrained project scheduling problems with resource vacations and activity splitting. Eur J Oper Res 175:279–295CrossRefGoogle Scholar
  12. Buddhakulsomsiri J, Kim DS (2007) Priority rule-based heuristic for multi-mode resource-constrained project scheduling problems with resource vacations and activity splitting. Eur J Oper Res 178:374–390CrossRefGoogle Scholar
  13. Carlier J (1982) The one-machine sequencing problem. Eur J Oper Res 11:42–47CrossRefGoogle Scholar
  14. Damay J (2008) Preemptive activities. In: Artigues C, Demassey S, Néron E (eds) Resource-constrained project scheduling: models, algorithms, extensions and applications. Wiley, Hoboken, pp 139–147Google Scholar
  15. Damay J (2011) Personal communicationGoogle Scholar
  16. Damay J, Quilliot A, Sanlaville E (2007) Linear programming based algorithms for preemptive and non-preemptive RCPSP. Eur J Oper Res 182:1012–1022CrossRefGoogle Scholar
  17. Demeulemeester EL, Herroelen WS (1996) An efficient optimal solution procedure for the preemptive resource-constrained project scheduling problem. Eur J Oper Res 90:334–348CrossRefGoogle Scholar
  18. Floyd RW (1962) Algorithm 97: shortest path. Commun ACM 5:345CrossRefGoogle Scholar
  19. Franck B, Neumann K, Schwindt C (1997) A capacity-oriented hierarchical approach to single-item and small-batch production planning using project-scheduling methods. OR Spektrum 19:77–85CrossRefGoogle Scholar
  20. Franck B, Neumann K, Schwindt C (2001a) Truncated branch-and-bound, schedule-construction, and schedule-improvement procedures for resource-constrained project scheduling. OR Spektrum 23:297–324CrossRefGoogle Scholar
  21. Franck B, Neumann K, Schwindt C (2001b) Project scheduling with calendars. OR Spektrum 23:325–334CrossRefGoogle Scholar
  22. Hartmann S, Drexl A (1998) Project scheduling with multiple modes: a comparison of exact algorithms. Networks 32:283–298CrossRefGoogle Scholar
  23. Heilmann R, Schwindt C (1997) Lower bounds for RCPSP/max. Technical Report WIOR-511, University of Karlsruhe, GermanyGoogle Scholar
  24. Kaplan L (1988) Resource-constrained project scheduling with preemption of jobs. Ph.D. dissertation, University of Michigan, Ann ArborGoogle Scholar
  25. Kis T (2005) A branch-and-cut algorithm for scheduling of projects with variable-intensity activities. Math Program 103:515–539CrossRefGoogle Scholar
  26. Kolisch R, Sprecher A (1996) PSPLIB: a project scheduling library. Eur J Oper Res 96:205–216CrossRefGoogle Scholar
  27. Li F, Lai C, Shou Y (2011) Particle swarm optimization for preemptive project scheduling with resource constraints. In: Proceedings of the 2011 IEEE international conference on industrial engineering and engineering management (IEEM), Singapore, pp 869–873Google Scholar
  28. Mingozzi A, Maniezzo V, Ricciardelly S, Bianco L (1998) An exact algorithm for the resource-constrained project scheduling based on a new mathematical formulation. Manage Sci 44:714–729CrossRefGoogle Scholar
  29. Nadjafi BA, Shadrokh S (2008) The preemptive resource-constrained project scheduling problem subject to due dates and preemption penalties: an integer programming approach. J Ind Eng 1:35–39Google Scholar
  30. Neumann K, Schwindt C, Zimmermann J (2003) Project scheduling with time windows and scarce resources. Springer, BerlinCrossRefGoogle Scholar
  31. Nudtasomboon N, Randhawa SU (1997) Resource-constrained project scheduling with renewable and non-renewable resources and time-resource tradeoffs. Comput Ind Eng 32:227–242CrossRefGoogle Scholar
  32. Quintanilla S, Pérez A, Lino P, Valls V (2012) Time and work generalised precedence relatioships in project scheduling with pre-emption: an application to the management of Service Centres. Eur J Oper Res 219:59–72CrossRefGoogle Scholar
  33. Richter LK, Yano CA (1986) A comparison of heuristics for preemptive resource-constrained project scheduling. Technical Report 86–39, Department of Industrial and Operations Engineering, University of Michigan, Ann ArborGoogle Scholar
  34. Schwindt C (2005) Resource allocation in project management. Springer, BerlinGoogle Scholar
  35. Słowiński R (1978) A node ordering heuristic for network scheduling under multiple resource constraints. Found Control Eng 3:19–27Google Scholar
  36. Słowiński R (1980) Two approaches to problems of resource allocation among project activities: a comparative study. J Oper Res Soc 31:711–723Google Scholar
  37. Vanhoucke M (2008) Setup times and fast tracking in resource-constrained project scheduling. Comput Ind Eng 54:1062–1070CrossRefGoogle Scholar
  38. Vanhoucke M, Demeulemeester E, Herroelen W (2002) Discrete time/cost tradeoffs in project scheduling with time-switch constraints. J Oper Res Soc 53:741–751CrossRefGoogle Scholar
  39. Van Peteghem V, Vanhoucke M (2010) A genetic algorithm for the preemptive and non-preemptive multi-mode resource-constrained project scheduling problem. Eur J Oper Res 201:409–418CrossRefGoogle Scholar
  40. Wikum ED, Llewellyn DC, Nemhauser GL (1994) One-machine generalized precedence constrained scheduling problems. Oper Res Lett 16:87–99CrossRefGoogle Scholar
  41. Yang HH, Chen YL (2000) Finding the critical path in an activity network with time-switch constraints. Eur J Oper Res 120:603–613CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Institute of Management and EconomicsClausthal University of TechnologyClausthal-ZellerfeldGermany

Personalised recommendations