Lower Bounds and Exact Solution Approaches

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

Abstract

Generalized precedence relations are temporal constraints in which the starting/finishing times of a pair of activities have to be separated by at least or at most an amount of time denoted as time lag (minimum time lag and maximum time lag, respectively). This chapter is devoted to project scheduling with generalized precedence relations with and without resource constraints. Attention is focused on lower bounds and exact algorithms. In presenting existing results on these topics, we concentrate on recent results obtained by ourselves. The mathematical models and the algorithms presented here are supported by extensive computational results.

Keywords

Generalized precedence relations Makespan minimization Project scheduling Resource constraints 
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References

  1. Ahuja RK, Magnanti T, Orlin J (1993) Network flows. Prentice Hall, New YorkGoogle Scholar
  2. Bartusch M, Möhring RH, Radermacher FJ (1988) Scheduling project networks with resource constraints and time windows. Ann Oper Res 16(1):201–240CrossRefGoogle Scholar
  3. Bianco L, Caramia M (2010) A new formulation of the resource-unconstrained project scheduling problem with generalized precedence relations to minimize the completion time. Networks 56(4):263–271CrossRefGoogle Scholar
  4. Bianco L, Caramia M (2011a) A new lower bound for the resource-constrained project scheduling problem with generalized precedence relations. Comput Oper Res 38(1):14–20CrossRefGoogle Scholar
  5. Bianco L, Caramia M (2011b) Minimizing the completion time of a project under resource constraints and feeding precedence relations: a Lagrangian relaxation based lower bound. 4OR-Q J Oper Res 9(4):371–389CrossRefGoogle Scholar
  6. 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(1):73–85CrossRefGoogle Scholar
  7. Demeulemeester EL, Herroelen WS (1997a) New benchmark results for the resource-constrained project scheduling problem. Manage Sci 43(11):1485–1492CrossRefGoogle Scholar
  8. Demeulemeester EL, Herroelen WS (1997b) A branch-and-bound procedure for the generalized resource-constrained project scheduling problem. Oper Res 45(2):201–212CrossRefGoogle Scholar
  9. Demeulemeester EL, Herroelen WS (2002) Project scheduling: a research handbook. Kluwer, BostonGoogle Scholar
  10. De Reyck B (1998) Scheduling projects with generalized precedence relations: exact and heuristic approaches. Ph.D. dissertation, Department of Applied Economics, Katholieke Universiteit Leuven, LeuvenGoogle Scholar
  11. De Reyck B, Herroelen W (1998) A branch-and-bound procedure for the resource-constrained project scheduling problem with generalized precedence relations. Eur J Oper Res 111(1):152–174CrossRefGoogle Scholar
  12. Dorndorf U (2002) Project scheduling with time windows. Physica, HeidelbergCrossRefGoogle Scholar
  13. Dorndorf U, Pesch E, Phan-Huy T (2000) A time-oriented branch-and-bound algorithm for resource-constrained project scheduling with generalised precedence constraints. Manage Sci 46(10):1365–1384CrossRefGoogle Scholar
  14. Elmaghraby SEE, Kamburowski J (1992) The analysis of activity networks under generalized precedence relations (GPRs). Manage Sci 38(9):1245–1263CrossRefGoogle Scholar
  15. Fest A, Möhring RH, Stork F, Uetz M (1999) Resource-constrained project scheduling with time windows: a branching scheme based on dynamic release dates. Technical Report 596, Technical University of Berlin, BerlinGoogle Scholar
  16. Held M, Karp RM (1970) The traveling-salesman problem and minimum spanning trees. Oper Res 18(6):1138–1162CrossRefGoogle Scholar
  17. Hochbaum D, Naor J (1994) Simple and fast algorithms for linear and integer programs with two variables per inequality. SIAM J Comput 23(6):1179–1192CrossRefGoogle Scholar
  18. Kelley JE (1963) The critical path method: resource planning and scheduling. In: Muth JF, Thompson GL (eds) Industrial scheduling. Prentice-Hall Inc., Englewood Cliffs, pp 347–365Google Scholar
  19. Klein R, Scholl A (1999) Computing lower bounds by destructive improvement: an application to resource-constrained project scheduling. Eur J Oper Res 112(2):322–346CrossRefGoogle Scholar
  20. Kolisch R, Sprecher A, Drexl A (1995) Characterization and generation of a general class of resource-constrained project scheduling problems. Manage Sci 41(10):1693–1703CrossRefGoogle Scholar
  21. Moder JJ, Philips CR, Davis EW (1983) Project management with CPM, PERT and precedence diagramming, 3rd edn. Van Nostrand Reinhold Company, New YorkGoogle Scholar
  22. Möhring RH, Schulz AS, Stork F, Uetz M (1999) Resource-constrained project scheduling: computing lower bounds by solving minimum cut problems. Lecture notes in computer science, vol 1643. Springer, Berlin, pp 139–150Google Scholar
  23. Möhring RH, Schulz AS, Stork F, Uetz M (2003) Solving project scheduling problems by minimum cut computations. Manage Sci 49(3):330–350CrossRefGoogle Scholar
  24. Neumann K, Schwindt C, Zimmerman J (2003) Project scheduling with time windows and scarce resources, 2nd edn. LNEMS, vol 508. Springer, BerlinGoogle Scholar
  25. Radermacher FJ (1985) Scheduling of project networks. Ann Oper Res 4(1):227–252CrossRefGoogle Scholar
  26. Schwindt C (1996) ProGen/Max: generation of resource-constrained scheduling problems with minimal and maximal time lags. Technical Report WIOR-489, University of Karlsruhe, KarlsruheGoogle Scholar
  27. Schwindt C (1998) Verfahren zur Lösung des ressourcenbeschränkten Projektdauerminimierungsproblems mit planungsabhängigen Zeitfenstern. Shaker, AachenGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of Enterprise EngineeringUniversity of Rome “Tor Vergata”RomaItaly

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