Journal of the Operational Research Society

, Volume 68, Issue 8, pp 952–972 | Cite as

Real-world flexible resource profile scheduling with multiple criteria: learning scalarization functions for MIP and heuristic approaches



This article addresses a scheduling problem for a chemical research laboratory. Activities with potentially variable, non-rectangular resource allocation profiles must be scheduled on discrete renewable resources. A mixed-integer programming (MIP) formulation for the problem includes maximum time lags, custom resource allocation constraints, and multiple nonstandard objectives. We present a list scheduling heuristic that mimics the human decision maker and thus provides reference solutions. These solutions are the basis for an automated learning-based determination of coefficients for the convex combination of objectives used by the MIP and a dedicated variable neighborhood search (VNS) approach. The development of the VNS also involves the design of new neighborhood structures that prove particularly effective for the custom objectives under consideration. Relative improvements of up to 60% are achievable for isolated objectives, as demonstrated by the final computational study based on a broad spectrum of randomly generated instances of different sizes and real-world data from the company’s live system.


scheduling integer programming heuristics machine learning 


  1. Ballestin F and Blanco R (2011). Theoretical and practical fundamentals for multi-objective optimisation in resource-constrained project scheduling problems. Computers & Operations Research 38(1):51–62.CrossRefGoogle Scholar
  2. Bianco L and Caramia M (2013). A new formulation for the project scheduling problem under limited resources. Flexible Services and Manufacturing Journal 25(1–2):6–24.CrossRefGoogle Scholar
  3. Blazewicz J, Kovalyov M, Machowiak M, Trystram D and Weglarz J (2006). Preemptable malleable task scheduling problem. IEEE Transactions on Computers 55(4):486–490.Google Scholar
  4. Branke J and Mattfeld DC (2005). Anticipation and flexibility in dynamic scheduling. International Journal of Production Research 43(15):3103–3129.CrossRefGoogle Scholar
  5. Brucker P (2004). Scheduling Algorithms, 4 edn. Berlin: Springer.Google Scholar
  6. Brucker P, Drexl A, Möhring R, Neumann K and Pesch E (1999). Resource-constrained project-scheduling: notation, classification, models and methods. European Journal of Operational Research 112(1):3–41.CrossRefGoogle Scholar
  7. Dubois-Lacoste J, López-Ibáñez M and Stützle T (2011). Automatic configuration of state-of-the-art multi-objective optimizers using the tp+pls framework. In Proceedings of the Genetic and Evolutionary Computation Conference, GECCO 2011. New York: ACM Press, pp. 2019–2026.Google Scholar
  8. Ehrgott M (2000a). Multicriteria Optimization. Lecture Notes in Economics and Mathematical Systems. Berlin: Springer.Google Scholar
  9. Ehrgott M (2000b). A survey and annotated bibliography of multiobjective combinatorial optimization. OR Spektrum 22(4):425–460.CrossRefGoogle Scholar
  10. Fündeling C-U (2006). Ressourcenbeschränkte Projektplanung bei vorgegebenen Arbeitsvolumina. Wiesbaden: Deutscher Universität-Verlag.Google Scholar
  11. Fündeling C-U and Trautmann N (2010). A priority-rule method for project scheduling with work-content constraints. European Journal of Operational Research 203(3):568–574.CrossRefGoogle Scholar
  12. Garey MR, Johnson DS and Sethi R (1976). The complexity of flow shop and job shop scheduling. Mathematics of Operations Research 1(2):117–129.CrossRefGoogle Scholar
  13. Gomes HC, de Assis das Neves F and Souza MJF (2014). Multi-objective metaheuristic algorithms for the resource-constrained project scheduling problem with precedence relations. Computers & Operations Research 44(April):92–104.CrossRefGoogle Scholar
  14. Gonçalves JF, Mendes JJM and Resende MGC (2008). A genetic algorithm for the resource constrained multi-project scheduling problem. European Journal of Operational Research 189(3):1171–1190.CrossRefGoogle Scholar
  15. Hans E, Herroelen W, Leus R and Wullink G (2007). A hierarchical approach to multi-project planning under uncertainty. Omega 35(5):563–577.CrossRefGoogle Scholar
  16. Hartmann S and Briskorn D (2010). A survey of variants and extensions of the resource-constrained project scheduling problem. European Journal of Operational Research 207(1):1–14.CrossRefGoogle Scholar
  17. Kis T (2005). A branch-and-cut algorithm for scheduling of projects with variable-intensity activities. Mathematical Programming Series A 103(3):515–539.CrossRefGoogle Scholar
  18. Klein R (2000). Scheduling of Resource-Constrained Projects, volume 10 of Operations Research/Computer Science Interface Series. New York: Springer.Google Scholar
  19. Kogan K and Shtub A (1999). Scheduling projects with variable-intensity activities: the case of dynamic earliness and tardiness costs. European Journal of Operational Research 118(1):65–80.CrossRefGoogle Scholar
  20. Kolisch R and Hartmann S (1999). Heuristic algorithms for solving the resource-constrained project scheduling problem: classification and computational analysis. In Weglarz J, (Ed.) Handbook on Recent Advances in Project Scheduling, Chapter 7. Dordrecht: Kluwer/Academic Publishers, pp. 147–178.Google Scholar
  21. Kolisch R and Meyer K (2006). Selection and scheduling of pharmaceutical research projects. In Jozefowska J and Weglarz J (Eds.) Perspectives in Modern Project Scheduling, volume 92 of International Series in Operations Research & Management Science. New York: Springer, pp. 321–344.Google Scholar
  22. Kolisch R, Meyer K, Mohr R, Schwindt C and Urmann M (2003). Ablaufplanung für die Leitstrukturoptimierung in der Pharmaforschung. Zeitschrift für Betriebswirtschaft 73:825–848.Google Scholar
  23. Leachman R (1990). Resource-constrained scheduling of projects with variable intensity activities. IIE Transactions 2(1):31–39.CrossRefGoogle Scholar
  24. López-Ibáñez M, Dubois-Lacoste J, Stützle T and Birattari M (2011). The irace Package, Iterated Race for Automatic Algorithm Configuration. Technical Report TR/IRIDIA/2011-004, IRIDIA, Université libre de Bruxelles, Belgium.Google Scholar
  25. Mladenović N and Hansen P (1997). Variable neighborhood search. Computers and Operations Research 24(11):1097–1100.CrossRefGoogle Scholar
  26. Naber A and Kolisch R (2014). MIP models for resource-constrained project scheduling with flexible resource profiles. European Journal of Operational Research 239(2):335–348.CrossRefGoogle Scholar
  27. Nabrzyski J and Weglarz J (1999). Knowledge-based multiobjective project scheduling problems. In Weglarz J (Ed.) Project Scheduling: Recent Models, Algorithms and Applications. Dordrecht: Kluwer, pp. 383–411.Google Scholar
  28. Neumann K and Zimmermann J (2000). Procedures for resource leveling and net present value problems in project scheduling with general temporal and resource constraints. European Journal of Operational Research 127(2):425–443.CrossRefGoogle Scholar
  29. Perez A, Quintanilla S, Lino P and Valls V (2014). A multi-objective approach for a project scheduling problem with due dates and temporal constraints infeasibilities. International Journal of Production Research 52(13):3950–3965.CrossRefGoogle Scholar
  30. Ranjbar M and Kianfar F (2010). Resource-constrained project scheduling problem with flexible work profiles: a genetic algorithm approach. Transaction E: Industrial Engineering 17(1):25–35.Google Scholar
  31. Shabtay D, Gaspar N and Kaspi M (2013). A survey on offline scheduling with rejection. Journal of Scheduling 16(1):3–28.CrossRefGoogle Scholar
  32. T’kindt V and Billaut J-C (2002). Multicriteria Scheduling. Berlin: Springer.Google Scholar
  33. Weglarz J, Jozefowska J, Mika M and Waligora G (2011). Project scheduling with finite or infinite number of activity processing modes—a survey. European Journal of Operational Research 208(3):177–205.CrossRefGoogle Scholar
  34. Zitzler E, Knowles J and Thiele L (2008). Quality assessment of Pareto set approximations. In Branke J et al (Eds.) Multiobjective Optimization, volume 5252 of LNCS. Berlin: Springer, pp. 373–404.Google Scholar
  35. Zitzler E, Thiele L, Laumanns M, Fonseca CM and da Fonseca VG (2003). Performance assessment of multiobjective optimizers: an analysis and review. IEEE Transactions on Evolutionary Computation 7(2):117–132.CrossRefGoogle Scholar

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© The Operational Research Society 2017

Authors and Affiliations

  1. 1.Department of Business AdministrationUniversity of ViennaViennaAustria

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