Skip to main content
SpringerLink
Log in

A Forward–Backward Relax-and-Solve Algorithm for the Resource-Constrained Project Scheduling Problem

  • Original Research
  • Published:
SN Computer Science Aims and scope Submit manuscript

Abstract

Scheduling projects under limited resource availability, which is called the resource-constrained project scheduling problem (RCPSP), has a wide range of real-world applications, e.g., in mining, manufacturing and supply chain. The RCPSP is NP-hard, and over the last five decades researchers attempted to propose various solution techniques for this challenging problem. The relax-and-solve (R&S) algorithm is a recently proposed method for solving various scheduling problems, such as job-shop and single and parallel machine scheduling problems. This research contributes to the existing research on the R&S by presenting an easy-to-implement and effective R&S method for solving RCPSP. Our R&S employs CPLEX CP optimizer as an optimization solver to generate and optimize schedules within a heuristic framework. We further improve the algorithm’s performance by employing forward–backward passes. The results of testing the algorithms on 1560 standard instances from the well-known PSPLIB show our heuristic delivers competitive results and outperforms state-of-the-art methods for solving the RCPSP.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1

Similar content being viewed by others

References

  1. Herroelen W, Leus R. Identification and illumination of popular misconceptions about project scheduling and time buffering in a resource-constrained environment. J Oper Res Soc. 2005;56(1):102–9.

    Article  MATH  Google Scholar 

  2. Pritsker A, Waiters LJ, Wolfe P. Multiproject scheduling with limited resources: a zero-one programming approach. Manag Sci. 1969;16:93–108.

    Article  Google Scholar 

  3. Liu J, Lu M. Optimization on Supply-constrained Module Assembly Process. In: IGLC 2017 - Proceedings of the 25th Annual Conference of the International Group for Lean Construction, 2017; 813–820. https://doi.org/10.24928/2017/0104. cited By 2

  4. Alford C, Brazil M, Lee DH. Optimisation in Underground Mining, pp. 561–577. Springer, Boston, MA (2007). https://doi.org/10.1007/978-0-387-71815-6_30.

  5. Demeulemeester E, Herroelen W. A branch-and-bound procedure for the multiple resource-constrained project scheduling problem. Manag Sci. 1992;38(12):1803–18.

    Article  MATH  Google Scholar 

  6. Blazewicz J, Lenstra JK, Kan AHGR. Scheduling subject to resource constraints: classification and complexity. Discrete Appl Math. 1983;5(1):11–24. https://doi.org/10.1016/0166-218X(83)90012-4.

    Article  MathSciNet  MATH  Google Scholar 

  7. Rahman HF, Chakrabortty RK, Ryan MJ. Memetic algorithm for solving resource constrained project scheduling problems. Auto Construction. 2020;111: 103052. https://doi.org/10.1016/j.autcon.2019.103052.

    Article  Google Scholar 

  8. Herroelen W, De Reyck B, Demeulemeester E. Resource-constrained project scheduling: a survey of recent developments. Comput Oper Res. 1998;25(4):279–302. https://doi.org/10.1016/S0305-0548(97)00055-5.

    Article  MathSciNet  MATH  Google Scholar 

  9. Chen H, Ding G, Qin S, Zhang J. A hyper-heuristic based ensemble genetic programming approach for stochastic resource constrained project scheduling problem. Expert Syst Appl. 2021;167: 114174. https://doi.org/10.1016/j.eswa.2020.114174.

    Article  Google Scholar 

  10. Kolisch R, Hartmann S. Experimental investigation of heuristics for resource-constrained project scheduling: an update. Euro J Oper Res. 2006;174(1):23–37. https://doi.org/10.1016/j.ejor.2005.01.065.

    Article  MATH  Google Scholar 

  11. Li KY, Willis RJ. An iterative scheduling technique for resource-constrained project scheduling. European Journal of Operational Research. 1992;56(3):370–9. https://doi.org/10.1016/0377-2217(92)90320-9.

    Article  MATH  Google Scholar 

  12. Pellerin R, Perrier N, Berthaut F. A survey of hybrid metaheuristics for the resource-constrained project scheduling problem. Euro J Oper Res. 2020;280(2):395–416. https://doi.org/10.1016/j.ejor.2019.01.063.

    Article  MathSciNet  MATH  Google Scholar 

  13. Holland JH. Genetic algorithms. Scientific American (1992)

  14. Agarwal A, Colak S, Erenguc S. A neurogenetic approach for the resource-constrained project scheduling problem. Computers & Operations Research 2011;38(1), 44–50. https://doi.org/10.1016/j.cor.2010.01.007. Project Management and Scheduling

  15. Debels D, Vanhoucke M. A decomposition-based genetic algorithm for the resource-constrained project-scheduling problem. Oper Res. 2007;55:457–69. https://doi.org/10.1287/opre.1060.0358.

    Article  MATH  Google Scholar 

  16. Lim A, Ma H, Rodrigues B, Tan S, Xiao F. New meta-heuristics for the resource-constrained project scheduling problem. Flexible Services Manuf J. 2011;25:48–73. https://doi.org/10.1007/s10696-011-9133-0.

    Article  Google Scholar 

  17. Cervantes M, Lova A, Tormos P, Barber F. A dynamic population steady-state genetic algorithm for the resource-constrained project scheduling problem. In: Nguyen NT, Borzemski L, Grzech A, Ali M, editors. New frontiers in applied artificial intelligence. Berlin, Heidelberg: Springer; 2008. p. 611–20.

    Chapter  Google Scholar 

  18. Ismail I, Barghash M. Diversity guided genetic algorithm to solve the resource constrained project scheduling problem. Int J Plann Scheduling. 2012;1:147–70. https://doi.org/10.1504/IJPS.2012.050125.

    Article  Google Scholar 

  19. Alcaraz J, Maroto C, Ruiz R. Improving the performance of genetic algorithms for the rcps problem. Proceedings of the Ninth International Workshop on Project Management and Scheduling, 2004;40–43. Cited By :39

  20. Wang H, Li T, Lin D. Efficient genetic algorithm for resource-constrained project scheduling problem. Trans Tianjin Univ. 2010;16(5):376–82. https://doi.org/10.1007/s12209-010-1495-y.

    Article  Google Scholar 

  21. Zamani R. A competitive magnet-based genetic algorithm for solving the resource-constrained project scheduling problem. Euro J Oper Res. 2013;229(2):552–9. https://doi.org/10.1016/j.ejor.2013.03.005.

    Article  MathSciNet  MATH  Google Scholar 

  22. Valls V, Ballestín F, Quintanilla S. A hybrid genetic algorithm for the resource-constrained project scheduling problem. Euro J Oper Res. 2008;185:495–508. https://doi.org/10.1016/j.ejor.2006.12.033.

    Article  MATH  Google Scholar 

  23. Debels D, Vanhoucke M. A bi-population based genetic algorithm for the resource-constrained project scheduling problem. In: Gervasi O, Gavrilova ML, Kumar V, Laganá A, Lee HP, Mun Y, Taniar D, Tan CJK, editors. Computational science and its applications—ICCSA 2005. Berlin, Heidelberg: Springer; 2005. p. 378–87.

    Chapter  Google Scholar 

  24. Fernando GJ, C RMG, M MJJ. A biased random-key genetic algorithm with forward-backward improvement for the resource constrained project scheduling problem. J Heuristics 2011;17(5), 467–486. https://doi.org/10.1007/s10732-010-9142-2

  25. Chand S, Singh HK, Ray T. A heuristic algorithm for solving resource constrained project scheduling problems. In: 2017 IEEE Congress on Evolutionary Computation (CEC), 2017; 225–232. https://doi.org/10.1109/CEC.2017.7969317

  26. Deng L, Lin V, Chen M. Hybrid ant colony optimization for the resource-constrained project scheduling problem. J Syst Eng Electron. 2010;21(1):67–71. https://doi.org/10.3969/j.issn.1004-4132.2010.01.012.

    Article  Google Scholar 

  27. Dorigo M, Di Caro G, Gambardella LM. Ant algorithms for discrete optimization.” artificial life 5, 137-172. Artificial Life 5, 1999;137–172. https://doi.org/10.1162/106454699568728

  28. Ziarati K, Akbari R, Zeighami V. On the performance of bee algorithms for resource-constrained project scheduling problem. Appl Soft Comput. 2011;11(4):3720–33. https://doi.org/10.1016/j.asoc.2011.02.002.

    Article  Google Scholar 

  29. Pham D, Ghanbarzadeh A, Koç E, Otri S, Rahim S, Zaidi M. The bees algorithm technical note. Manufacturing Engineering Centre, Cardiff University, UK, 2005;1–57

  30. Karaboga D. An idea based on honey bee swarm for numerical optimization, technical report - tr06. Technical Report, Erciyes University (2005)

  31. A novel bee swarm optimization algorithm for numerical function optimization. Communications in Nonlinear Science and Numerical Simulation 15(10), 2010; 3142–3155. https://doi.org/10.1016/j.cnsns.2009.11.003

  32. Berthaut F, Pellerin R, Hajji A, Perrier N. A path relinking-based scatter search for the resource-constrained project scheduling problem. Int J Project Organisation Manag. 2018;10(1):1–36. https://doi.org/10.1504/IJPOM.2018.090372.

    Article  Google Scholar 

  33. Gu H, Schutt A, Stuckey PJ. A lagrangian relaxation based forward-backward improvement heuristic for maximising the net present value of resource-constrained projects. In: Gomes C, Sellmann M, editors. Integration of AI and OR techniques in constraint programming for combinatorial optimization problems. Berlin, Heidelberg: Springer; 2013. p. 340–6.

    Chapter  MATH  Google Scholar 

  34. Laborie P. An Update on the Comparison of MIP, CP and Hybrid Approaches for Mixed Resource Allocation and Scheduling, pp. 403–411. Springer, Cham (2018)

  35. Maleck C, Nieke G, Bock K, Pabst D, Stehli M. A comparison of an cp and mip approach for scheduling jobs in production areas with time constraints and uncertainties. In: 2018 Winter Simulation Conference (WSC), 2018;3526–3537. https://doi.org/10.1109/WSC.2018.8632404

  36. Kelareva E, Brand S, Kilby P, Thiebaux S, Wallace M. Cp and mip methods for ship scheduling with time-varying draft. ICAPS 2012 - Proceedings of the 22nd International Conference on Automated Planning and Scheduling 2012

  37. Liess O, Michelon P. A constraint programming approach for the resource-constrained project scheduling problem. Ann Oper Res. 2008;157(1):25–36.

    Article  MathSciNet  MATH  Google Scholar 

  38. Schutt A, Feydy T, Stuckey P, Wallace M. Explaining the cumulative propagator. Constraints. 2011;16:250–82. https://doi.org/10.1007/s10601-010-9103-2.

    Article  MathSciNet  MATH  Google Scholar 

  39. Schutt A, Feydy T, Stuckey PJ, Wallace MG. A Satisfiability Solving Approach, 2015;135–160. Springer, Cham . https://doi.org/10.1007/978-3-319-05443-8_7.

  40. Kreter S, Schutt A, Stuckey P. Using constraint programming for solving rcpsp/max-cal. Constraints 22 2017. https://doi.org/10.1007/s10601-016-9266-6

  41. Absi N, van den Heuvel W. Worst case analysis of relax and fix heuristics for lot-sizing problems. Euro J Oper Res. 2019;279(2):449–58. https://doi.org/10.1016/j.ejor.2019.06.010.

    Article  MathSciNet  MATH  Google Scholar 

  42. Helber S, Sahling F. A fix-and-optimize approach for the multi-level capacitated lot sizing problem. Int J Prod Econ. 2010;123(2):247–56.

    Article  Google Scholar 

  43. Escudero LF, Romero CP. On solving a large-scale problem on facility location and customer assignment with interaction costs along a time horizon. TOP: An Official Journal of the Spanish Society of Statistics and Operations Research 25(3), 2017;01–622. https://doi.org/10.1007/s11750-017-0461-4

  44. Salehipour A. A heuristic algorithm for the aircraft landing problem. In: 22nd International Congress on Modelling and Simulation (2017). Modelling and Simulation Society of Australia and New Zealand Inc.(MSSANZ)

  45. Salehipour A, Ahmadian M, Oron D. Efficient and simple heuristics for the aircraft landing problem. In: Matheuristic 2018 International Conference (2018)

  46. Ahmadian MM, Salehipour A, Kovalyov M. An efficient relax-and-solve heuristic for open-shop scheduling problem to minimize total weighted earliness-tardiness. Available at SSRN 3601396 (2020)

  47. Ahmadian MM, Salehipour A, Cheng TCE. A meta-heuristic to solve the just-in-time job-shop scheduling problem. Euro J Oper Res. 2021;288(1):14–29.

    Article  MathSciNet  MATH  Google Scholar 

  48. Etminaniesfahani, A, Gu, H, Salehipour, A. An Efficient Relax-and-Solve Algorithm for the Resource-Constrained Project Scheduling Problem. In: Proceedings of the 11th International Conference on Operations Research and Enterprise Systems - ICORES,, pp. 271–277. SciTePress. https://doi.org/10.5220/0010772400003117. INSTICC

  49. Gu H, Schutt A, Stuckey PJ, Wallace MG, Chu G. In: Schwindt, C., Zimmermann, J. (eds.) Exact and Heuristic Methods for the Resource-Constrained Net Present Value Problem, 2015;299–318. Springer, Cham. https://doi.org/10.1007/978-3-319-05443-8_14.

  50. Laurent Perron and Vincent Furnon: OR-Tools version 7.2 (2019-7-19). https://developers.google.com/optimization/

  51. CPLEX II. version 12.8.0. IBM Corp., Armonk, New York, U.S. (2017)

  52. M. Pour S, Drake JH, Ejlertsen LS, Rasmussen KM, Burke EK. A hybrid constraint programming/mixed integer programming framework for the preventive signaling maintenance crew scheduling problem. European Journal of Operational Research 269(1), 2018;41–352. https://doi.org/10.1016/j.ejor.2017.08.033

  53. Bockmayr A, Hooker JN. Constraint programming. In: Aardal, K., Nemhauser, G.L., Weismantel, R. (eds.) Discrete Optimization. Handbooks in Operations Research and Management Science, vol. 12, pp. 559–600. Elsevier. https://doi.org/10.1016/S0927-0507(05)12010-6. https://www.sciencedirect.com/science/article/pii/S0927050705120106

  54. Kolisch R, Hartmann S. Heuristic Algorithms for the Resource-Constrained Project Scheduling Problem: Classification and Computational Analysis, 1999;147–178. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-5533-9_7.

  55. Kolisch R, Sprecher A. Psplib - a project scheduling problem library: Or software - orsep operations research software exchange program. Euro J Oper Res. 1997;96(1):205–16. https://doi.org/10.1016/S0377-2217(96)00170-1.

    Article  MATH  Google Scholar 

  56. Vilím P, Laborie P, Shaw P. Failure-directed search for constraint-based scheduling. In: Michel L, editor. Integration of AI and OR Techniques in Constraint Programming. Cham: Springer; 2015. p. 437–53.

    MATH  Google Scholar 

  57. Feydy T, Stuckey PJ. Lazy clause generation reengineered. In: Gent IP, editor. Principles and practice of constraint programming—CP 2009. Berlin, Heidelberg: Springer; 2009. p. 352–66.

    Chapter  Google Scholar 

  58. Bofill M, Coll J, Suy J, Villaret M. Smt encodings for resource-constrained project scheduling problems. Comput Ind Eng. 2020;149: 106777. https://doi.org/10.1016/j.cie.2020.106777.

    Article  Google Scholar 

  59. Czogalla J, Fink A. Particle Swarm Topologies for Resource Constrained Project Scheduling, 2009;61–73. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03211-0_6.

  60. Muller LF. An adaptive large neighborhood search algorithm for the resource-constrained project scheduling problem. In: Proceedings of the VIII Metaheuristics International Conference (MIC) 2009

  61. Debels D, De Reyck B, Leus R, Vanhoucke M. A hybrid scatter search/electromagnetism meta-heuristic for project scheduling. European Journal of Operational Research. 2006;169(2):638–53. https://doi.org/10.1016/j.ejor.2004.08.020. Feature Cluster on Scatter Search Methods for Optimization.

  62. Fahmy A, Hassan TM, Bassioni H. Improving rcpsp solutions quality with stacking justification—application with particle swarm optimization. Expert Syst Appl. 2014;41(13):5870–81. https://doi.org/10.1016/j.eswa.2014.03.027.

    Article  Google Scholar 

  63. Nasiri MM. A pseudo particle swarm optimization for the rcpsp. Int J Adv Manuf Technol. 2013;65(5):909–18. https://doi.org/10.1007/s00170-012-4227-8.

    Article  Google Scholar 

  64. Liu J, Liu Y, Shi Y, Li J. Solving resource-constrained project scheduling problem via genetic algorithm. J Comput Civ Eng. 2020;34(2):04019055. https://doi.org/10.1061/(ASCE)CP.1943-5487.0000874.

    Article  Google Scholar 

  65. Elsayed S, Sarker R, Ray T, Coello CC. Consolidated optimization algorithm for resource-constrained project scheduling problems. Inform Sci. 2017;418–419:346–62. https://doi.org/10.1016/j.ins.2017.08.023.

    Article  Google Scholar 

  66. Koulinas G, Kotsikas L, Anagnostopoulos K. A particle swarm optimization based hyper-heuristic algorithm for the classic resource constrained project scheduling problem. Inform Sci. 2014;277:680–93. https://doi.org/10.1016/j.ins.2014.02.155.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematical and Physical Sciences, University of Technology Sydney, Broadway, Sydney, 2007, NSW, Australia

    Alireza Etminaniesfahani & Hanyu Gu

  2. School of the Built Environment, University of Technology Sydney, Broadway, Sydney, 2007, NSW, Australia

    Leila Moslemi Naeni

  3. The University of Sydney Business School, Darlington, 2006, NSW, Australia

    Amir Salehipour

Authors
  1. Alireza Etminaniesfahani
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hanyu Gu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Leila Moslemi Naeni
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Amir Salehipour
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Alireza Etminaniesfahani.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This article is part of the topical collection “Advances on Operations Research and Enterprise Systems” guest edited by Marc Demange, Federico Liberatore and Greg H. Parlier.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Etminaniesfahani, A., Gu, H., Naeni, L.M. et al. A Forward–Backward Relax-and-Solve Algorithm for the Resource-Constrained Project Scheduling Problem. SN COMPUT. SCI. 4, 104 (2023). https://doi.org/10.1007/s42979-022-01487-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s42979-022-01487-1

Keywords

Search

Navigation