Comparison of mixed integer linear programming models for the resource-constrained project scheduling problem with consumption and production of resources

  • Oumar Koné
  • Christian Artigues
  • Pierre Lopez
  • Marcel Mongeau


This paper addresses an extension of the resource-constrained project scheduling problem that takes into account storage resources which may be produced or consumed by activities. To solve this problem, we propose the generalization of two existing mixed integer linear programming models for the classical resource-constrained project scheduling problem, as well as one novel formulation based on the concept of event. Computational results are reported to compare these formulations with each other, as well as with a reference method from the literature. Conclusions are drawn on the merits and drawbacks of each model according to the instance characteristics.


Resource-constrained project scheduling Mixed integer linear programming Consumption and production of resources Event-based on/off formulation 



This project was partially funded by the CNRS Energy Interdisciplinary Program (PIE), GIMEP project 2008–2010, and partially supported by French National Research Agency (ANR) through COSINUS program (project ID4CS no ANR-09-COSI-005). The authors are grateful to Philippe Laborie who kindly provided his code for our computational comparisons and to Emmanuel Hébrard for help in conducting some experiments. We also wish to thank the anonymous referees for their numerous constructive remarks. This research was initiated while the first author was with CIRRELT, Université de Montréal, Canada.


  1. Agha MH, Thery R, Hetreux G, Haït A, Le Lann J-M (2010) Integrated production and utility system approach for optimizing industrial unit operations. Energy 35(2):611–627CrossRefGoogle Scholar
  2. Alvarez-Valdès R, Tamarit JM (1993) The project scheduling polyhedron: dimension, facets and lifting theorems. Eur J Oper Res 67(2):204–220MATHCrossRefGoogle Scholar
  3. Applegate D, Cook W (1991) A computational study of job-shop scheduling. ORSA J Comput 3(2):149–156MATHCrossRefGoogle Scholar
  4. Artigues C, Michelon P, Reusser S (2003) Insertion techniques for static and dynamic resource-constrained project scheduling. Eur J Oper Res 149(2):249–267MathSciNetMATHCrossRefGoogle Scholar
  5. Artigues C, Koné O, Lopez P, Mongeau M, Néron E, Rivreau D (2008) Computational experiments. In: Artigues C, Demassey S, Néron E (eds) Resource-constrained project scheduling: Models, algorithms, extensions and applications, ISTE/Wiley, pp 98–102Google Scholar
  6. Balas E (1970) Project scheduling with resource constraints. In: Beale EML (ed) Applications of mathematical programming techniques. American Elsevier, Amsterdam, pp 187–200Google Scholar
  7. Baptiste P, Le Pape C (2000) Constraint propagation and decomposition techniques for highly disjunctive and highly cumulative project scheduling problems. Constraints 5(1–2):119–139MathSciNetMATHCrossRefGoogle Scholar
  8. Blazewicz J, Lenstra J, Rinnooy Kan AHG (1983) Scheduling subject to resource constraints: classification and complexity. Discrete Appl Math 5(1):11–24MathSciNetMATHCrossRefGoogle Scholar
  9. Bouly H, Carlier J, Moukrim A, Russo M (2005) Solving RCPSP with resources production possibility by tasks. In: MHOSI’2005, 24–26 AprilGoogle Scholar
  10. Bowman EH (1959) The schedule-sequencing problem. Oper Res 7:621–624CrossRefGoogle Scholar
  11. Carlier J, Néron E (2003) On linear lower bounds for resource constrained project scheduling problem. Eur J Oper Res 149:314–324MATHCrossRefGoogle Scholar
  12. Carlier J, Moukrim A, Xu H (2009) The project scheduling problem with production and consumption of resources: a list-scheduling based algorithm. Discrete Appl Math 157(17):3631–3642MathSciNetMATHCrossRefGoogle Scholar
  13. Castro PM, Grossmann E (2006) An efficient MILP model for the short-term scheduling of single stage batch plants. Comput Chem Eng 30:1003–1018CrossRefGoogle Scholar
  14. Christofides N, Alvarez-Valdès R, Tamarit JM (1987) Project scheduling with resource constraints: a branch and bound approach. Eur J Oper Res 29(3):262–273MATHCrossRefGoogle Scholar
  15. Dauzère-Pérès S, Lasserre JB (1995) A new mixed-integer formulation of the flow-shop sequencing problem. In: 2nd Workshop on models and algorithms for planning and scheduling problems, Wernigerode, GermanyGoogle Scholar
  16. Demassey S, Artigues C, Michelon P (2005) Constraint propagation based cutting planes: an application to the resource-constrained project scheduling problem. INFORMS J Comput 17(1):52–65MathSciNetMATHCrossRefGoogle Scholar
  17. Floudas CA, Lin X (2005) Mixed integer linear programming in process scheduling: modeling, algorithms, and applications. Ann Oper Res 139:131–162MathSciNetMATHCrossRefGoogle Scholar
  18. Herroelen W, De Reyck B, Demeulemeester E (1998) Resource-constrained project scheduling: a survey of recent developments. Comput Oper Res 25:279–302MathSciNetMATHCrossRefGoogle Scholar
  19. High-duration RCPSP instances with consumption and production of resources.
  20. Kolisch R (1996) Serial and parallel resource-constrained project scheduling methods revisited: theory and computation. Eur J Oper Res 90(2):320–333MATHCrossRefGoogle Scholar
  21. Kolisch R, Sprecher A (1997) PSPLIB—a project scheduling problem library. Eur J Oper Res 96(1):205–216Google Scholar
  22. Koné O, Artigues C, Lopez P, Mongeau M (2011) Event-based MILP models for resource-constrained project scheduling problems. Comput Oper Res 38(1):3–13MathSciNetMATHCrossRefGoogle Scholar
  23. Laborie P (2003) Algorithms for propagating resource constraints in a planning and scheduling: existing approaches and new results. Artif Intell 143:151–188MathSciNetMATHCrossRefGoogle Scholar
  24. Lasserre JB, Queyranne M (1992) Generic scheduling polyhedra and a new mixed-integer formulation for single-machine scheduling. In: Proceedings of the 2nd integer programming and combinatorial optimization conference, IPCO, pp 136–149Google Scholar
  25. Neumann K, Schwindt C (2002) Project scheduling with inventory constraints. Math Methods Oper Res 56:513–533MathSciNetMATHCrossRefGoogle Scholar
  26. Neumann K, Schwindt C, Trautmann N (2002) Advanced production scheduling for batch plants in process industries. OR Spectrum 24:251–279MathSciNetMATHCrossRefGoogle Scholar
  27. Neumann K, Schwindt C, Zimmermann J (2003) Project scheduling with time windows and scarce resources. Springer, BerlinMATHCrossRefGoogle Scholar
  28. Pfund ME, Mason SJ, Fowler JW (2006) Semiconductor manufacturing scheduling and dispatching. State of the art and survey of needs. In: Handbook of Production Scheduling. International Series in Operations Research & Management Science. Springer, Berlin, vol 89, pp 213–241Google Scholar
  29. Pinto JM, Grossmann IE (1995) A continuous time mixed integer linear programming model for short term scheduling of multistage batch plants. Ind Eng Chem Res 34(9):3037–3051CrossRefGoogle Scholar
  30. Pritsker A, Watters L, Wolfe P (1969) Multi-project scheduling with limited resources: a zero-one programming approach. Manage Sci 16:93–108CrossRefGoogle Scholar
  31. Schwindt C, Trautmann N (2000) Batch scheduling in process industries: an application of resource-constrained project scheduling. OR Spektrum 22:501–524MathSciNetMATHCrossRefGoogle Scholar
  32. Uetz M (2001) Algorithms for deterministic and stochastic scheduling, PhD thesis, Technische Universität Berlin, 2001Google Scholar
  33. Zapata JC, Hodge BM, Reklaitis GV (2008) The multimode resource constrained multiproject scheduling problem: alternative formulations. AIChE J 54(8):2101–2119CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Oumar Koné
    • 1
  • Christian Artigues
    • 2
    • 3
  • Pierre Lopez
    • 2
    • 3
  • Marcel Mongeau
    • 4
  1. 1.Laboratoire de Mathématiques et InformatiqueUFR-SFA, Université d’Abobo, AdjaméAbidjanIvory Coast
  2. 2.CNRS, LAASToulouseFrance
  3. 3.Univ de Toulouse, LAASToulouseFrance
  4. 4.École Nationale de l’Aviation CivileToulouse cedex 4France

Personalised recommendations