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Continuous Preemption Problems

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Handbook on Project Management and Scheduling Vol.1

Part of the book series: International Handbooks on Information Systems ((INFOSYS))

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Abstract

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.

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References

  • Alfieria A, Toliob T, Urgo M (2011) A project scheduling approach to production planning with feeding precedence relations. Int J Prod Res 49:995–1020

    Article  Google Scholar 

  • Ballestín F, Valls V, Quintanilla S (2008) Pre-emption in resource-constrained project scheduling. Eur J Oper Res 189:1136–1152

    Article  Google Scholar 

  • Ballestín F, Valls V, Quintanilla S (2009) Scheduling projects with limited number of preemptions. Comput Oper Res 36:2913–2925

    Article  Google Scholar 

  • Baptiste P, Demassey S (2004) Tight LP bounds for resource constrained project scheduling. OR Spectr 26:251–262

    Article  Google Scholar 

  • 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 http://www.research.ibm.com/people/s/sviri/papers/structure27.pdf. Cited 8 Feb 2014

  • Baptiste P, Carlier J, Kononov A, Queyranned M, Sevastyanov S, Sviridenko M (2011) Properties of optimal schedules in preemptive shop scheduling. Discrete Appl Math 159:272–280

    Article  Google Scholar 

  • Bianco L, Caramia M, Dell’Olmo P (1999) Solving a preemptive project scheduling problem with coloring techniques. In: WÈ©glarz J (ed) Project scheduling: recent models, algorithms, and applications. Kluwer Academic Publishers, Boston, pp 135–145

    Chapter  Google Scholar 

  • BÅ‚ażewicz J, Ecker KH, Pesch E, Schmidt G, WÈ©glarz J (2007) Handbook on scheduling: from theory to applications. Springer, Berlin

    Google Scholar 

  • Braun O, Schmidt G (2003) Parallel processor scheduling with limited number of preemptions. SIAM J Comput 32:671–680

    Article  Google Scholar 

  • Brucker P, Knust S (2000) A linear programming and constraint propagation-based lower bound for the RCPSP. Eur J Oper Res 127:355–362

    Article  Google Scholar 

  • Buddhakulsomsiri J, Kim DS (2006) Properties of multi-mode resource-constrained project scheduling problems with resource vacations and activity splitting. Eur J Oper Res 175:279–295

    Article  Google Scholar 

  • 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 178:374–390

    Article  Google Scholar 

  • Carlier J (1982) The one-machine sequencing problem. Eur J Oper Res 11:42–47

    Article  Google Scholar 

  • 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 139–147

    Google Scholar 

  • Damay J (2011) Personal communication

    Google Scholar 

  • Damay J, Quilliot A, Sanlaville E (2007) Linear programming based algorithms for preemptive and non-preemptive RCPSP. Eur J Oper Res 182:1012–1022

    Article  Google Scholar 

  • Demeulemeester EL, Herroelen WS (1996) An efficient optimal solution procedure for the preemptive resource-constrained project scheduling problem. Eur J Oper Res 90:334–348

    Article  Google Scholar 

  • Floyd RW (1962) Algorithm 97: shortest path. Commun ACM 5:345

    Article  Google Scholar 

  • 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 19:77–85

    Article  Google Scholar 

  • Franck B, Neumann K, Schwindt C (2001a) Truncated branch-and-bound, schedule-construction, and schedule-improvement procedures for resource-constrained project scheduling. OR Spektrum 23:297–324

    Article  Google Scholar 

  • Franck B, Neumann K, Schwindt C (2001b) Project scheduling with calendars. OR Spektrum 23:325–334

    Article  Google Scholar 

  • Hartmann S, Drexl A (1998) Project scheduling with multiple modes: a comparison of exact algorithms. Networks 32:283–298

    Article  Google Scholar 

  • Heilmann R, Schwindt C (1997) Lower bounds for RCPSP/max. Technical Report WIOR-511, University of Karlsruhe, Germany

    Google Scholar 

  • Kaplan L (1988) Resource-constrained project scheduling with preemption of jobs. Ph.D. dissertation, University of Michigan, Ann Arbor

    Google Scholar 

  • Kis T (2005) A branch-and-cut algorithm for scheduling of projects with variable-intensity activities. Math Program 103:515–539

    Article  Google Scholar 

  • Kolisch R, Sprecher A (1996) PSPLIB: a project scheduling library. Eur J Oper Res 96:205–216

    Article  Google Scholar 

  • 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 869–873

    Google Scholar 

  • 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 44:714–729

    Article  Google Scholar 

  • 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 1:35–39

    Google Scholar 

  • Neumann K, Schwindt C, Zimmermann J (2003) Project scheduling with time windows and scarce resources. Springer, Berlin

    Book  Google Scholar 

  • Nudtasomboon N, Randhawa SU (1997) Resource-constrained project scheduling with renewable and non-renewable resources and time-resource tradeoffs. Comput Ind Eng 32:227–242

    Article  Google Scholar 

  • 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 219:59–72

    Article  Google Scholar 

  • 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 Arbor

    Google Scholar 

  • Schwindt C (2005) Resource allocation in project management. Springer, Berlin

    Google Scholar 

  • SÅ‚owiÅ„ski R (1978) A node ordering heuristic for network scheduling under multiple resource constraints. Found Control Eng 3:19–27

    Google Scholar 

  • SÅ‚owiÅ„ski R (1980) Two approaches to problems of resource allocation among project activities: a comparative study. J Oper Res Soc 31:711–723

    Google Scholar 

  • Vanhoucke M (2008) Setup times and fast tracking in resource-constrained project scheduling. Comput Ind Eng 54:1062–1070

    Article  Google Scholar 

  • Vanhoucke M, Demeulemeester E, Herroelen W (2002) Discrete time/cost tradeoffs in project scheduling with time-switch constraints. J Oper Res Soc 53:741–751

    Article  Google Scholar 

  • 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 201:409–418

    Article  Google Scholar 

  • Wikum ED, Llewellyn DC, Nemhauser GL (1994) One-machine generalized precedence constrained scheduling problems. Oper Res Lett 16:87–99

    Article  Google Scholar 

  • Yang HH, Chen YL (2000) Finding the critical path in an activity network with time-switch constraints. Eur J Oper Res 120:603–613

    Article  Google Scholar 

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Acknowledgements

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

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Authors and Affiliations

  1. Institute of Management and Economics, Clausthal University of Technology, Clausthal-Zellerfeld, Germany

    Christoph Schwindt & Tobias Paetz

Authors
  1. Christoph Schwindt
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  2. Tobias Paetz
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Correspondence to Christoph Schwindt .

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Editors and Affiliations

  1. Institute of Management and Economics, Clausthal University of Technology, Clausthal-Zellerfeld, Germany

    Christoph Schwindt

  2. Institute of Management and Economics, Clausthal University of Technology, Clausthal-Zellerfeld, Germany

    Jürgen Zimmermann

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Schwindt, C., Paetz, T. (2015). Continuous Preemption Problems. In: Schwindt, C., Zimmermann, J. (eds) Handbook on Project Management and Scheduling Vol.1. International Handbooks on Information Systems. Springer, Cham. https://doi.org/10.1007/978-3-319-05443-8_13

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