Intercriteria Analysis of ACO Performance for Workforce Planning Problem

  • Olympia Roeva
  • Stefka FidanovaEmail author
  • Gabriel Luque
  • Marcin Paprzycki
Part of the Studies in Computational Intelligence book series (SCI, volume 795)


The workforce planning helps organizations to optimize the production process with the aim to minimize the assigning costs. The problem is to select a set of employees from a set of available workers and to assign this staff to the jobs to be performed. A workforce planning problem is very complex and requires special algorithms to be solved. The complexity of this problem does not allow the application of exact methods for instances of realistic size. Therefore, we will apply Ant Colony Optimization (ACO) algorithm, which is a stochastic method for solving combinatorial optimization problems. The ACO algorithm is tested on a set of 20 workforce planning problem instances. The obtained solutions are compared with other methods, as scatter search and genetic algorithm. The results show that ACO algorithm performs better than other the two algorithms. Further, we focus on the influence of the number of ants and the number of iterations on ACO algorithm performance. The tests are done on 16 different problem instances – ten structured and six unstructured problems. The results from ACO optimization procedures are discussed. In order to evaluate the influence of considered ACO parameters additional investigation is done. InterCriteria Analysis is performed on the ACO results for the regarded 16 problems. The results show that for the considered here workforce planning problem the best performance is achieved by the ACO algorithm with five ants in population.


Workforce planning Ant colony optimization Metaheuristics InterCriteria analysis 



Work presented here is partially supported by the National Scientific Fund of Bulgaria under grants DFNI-DN 02/10 “New Instruments for Knowledge Discovery from Data, and their Modelling” and DFNI-DN 12/5 “Efficient Stochastic Methods and Algorithms for Large Scale Problems”.


  1. 1.
    Alba, E., Luque, G., Luna, F.: Parallel metaheuristics for workforce planning. J. Math. Model. Algorithms 6(3), 509–528 (2007)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Angelova, M., Roeva, O., Pencheva, T.: InterCriteria analysis of crossover and mutation rates relations in simple genetic algorithm. In: Proceedings of the 2015 Federated Conference on Computer Science and Information Systems, vol. 5, pp. 419–424 (2015)Google Scholar
  3. 3.
    Atanassov, K.: Index Matrices: Towards an Augmented Matrix Calculus. Springer, Switzerland (2014)zbMATHGoogle Scholar
  4. 4.
    Atanassov, K.: Intuitionistic fuzzy sets. VII ITKR session, Sofia, 20–23 June 1983. Int. J. Bioautom. 20(S1), S1–S6 (2016)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Atanassov, K.: Generalized index matrices. Comptes rendus de l’Academie bulgare des Sciences 40(11), 15–18 (1987)MathSciNetzbMATHGoogle Scholar
  6. 6.
    Atanassov, K.: On Intuitionistic Fuzzy Sets Theory. Springer, Berlin (2012)CrossRefGoogle Scholar
  7. 7.
    Atanassov, K.: On index matrices, Part 1: standard cases. Adv. Stud. Contemp. Math. 20(2), 291–302 (2010)MathSciNetzbMATHGoogle Scholar
  8. 8.
    Atanassov, K.: On index matrices, Part 2: intuitionistic fuzzy case. Proc. Jangjeon Math. Soc. 13(2), 121–126 (2010)MathSciNetzbMATHGoogle Scholar
  9. 9.
    Atanassov, K.: On index matrices. Part 5: 3-dimensional index matrices. Adv. Stud. Contemp. Math. 24(4), 423–432 (2014)Google Scholar
  10. 10.
    Atanassov, K.: Review and new results on intuitionistic fuzzy sets, mathematical foundations of artificial intelligence seminar, Sofia, 1988, Preprint IM-MFAIS-1-88. Int. J. Bioautom. 20(S1), S7–S16 (2016)Google Scholar
  11. 11.
    Atanassov, K., Mavrov, D., Atanassova, V.: Intercriteria decision making: a new approach for multicriteria decision making, based on index matrices and intuitionistic fuzzy sets. Issues in on Intuitionistic Fuzzy Sets and Generalized Nets 11, 1–8 (2014)Google Scholar
  12. 12.
    Atanassov, K., Szmidt, E., Kacprzyk, J.: On intuitionistic fuzzy pairs. Notes Intuitionistic Fuzzy Sets 19(3), 1–13 (2013)zbMATHGoogle Scholar
  13. 13.
    Atanassov, K., Atanassova, V., Gluhchev, G.: InterCriteria analysis: ideas and problems. Notes on Intuitionistic Fuzzy Sets 21(1), 81–88 (2015)Google Scholar
  14. 14.
    Atanassova, V.: Interpretation in the intuitionistic fuzzy triangle of the results, obtained by the InterCriteria analysis. In: Proceedings of the 9th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT), pp. 1369–1374 (2015)Google Scholar
  15. 15.
    Atanassova, V., Mavrov, D., Doukovska, L., Atanassov, K.: Discussion on the threshold values in the InterCriteria decision making approach. Notes on Intuitionistic Fuzzy Sets 20(2), 94–99 (2014)Google Scholar
  16. 16.
    Atanassova, V., Doukovska, L., Atanassov, K., Mavrov, D.: Intercriteria decision making approach to EU member states competitiveness analysis. In: Proceedings of the International Symposium on Business Modeling and Software Design - BMSD’14, pp. 289–294 (2014)Google Scholar
  17. 17.
    Atanassova, V., Doukovska, L., Karastoyanov, D., Capkovic, F.: InterCriteria decision making approach to EU member states competitiveness analysis: trend analysis. In: Intelligent Systems’2014, Advances in Intelligent Systems and Computing, vol. 322, pp. 107–115 (2014)Google Scholar
  18. 18.
    Bonabeau, E., Dorigo, M., Theraulaz, G.: Swarm Intelligence: From Natural to Artificial Systems. Oxford University Press, New York (1999)zbMATHGoogle Scholar
  19. 19.
    Campbell, G.: A two-stage stochastic program for scheduling and allocating cross-trained workers. J. Oper. Res. Soc. 62(6), 1038–1047 (2011)CrossRefGoogle Scholar
  20. 20.
    Dorigo, M., Stutzle, T.: Ant Colony Optimization. MIT Press, Cambridge (2004)zbMATHGoogle Scholar
  21. 21.
    Easton, F.: Service completion estimates for cross-trained workforce schedules under uncertain attendance and demand. Prod. Oper. Manage. 23(4), 660–675 (2014)CrossRefGoogle Scholar
  22. 22.
    Fidanova, S., Roeva, O., Paprzycki, M.: InterCriteria analysis of ACO start strategies. In: Proceedings of the 2016 Federated Conference on Computer Science and Information Systems, vol. 8, pp. 547–550 (2016)Google Scholar
  23. 23.
    Fidanova, S., Roeva, O., Paprzycki, M., Gepner, P.: InterCriteria analysis of ACO start startegies. In: Proceedings of the 2016 Federated Conference on Computer Science and Information Systems, pp. 547–550 (2016)Google Scholar
  24. 24.
    Glover, F., Kochenberger, G., Laguna, M., Wubbena, T.: Selection and assignment of a skilled workforce to meet job requirements in a fixed planning period. In: MAEB04, pp. 636–641 (2004)Google Scholar
  25. 25.
    Grzybowska, K., Kovcs, G.: Sustainable supply chain—Supporting tools. In: Proceedings of the 2014 Federated Conference on Computer Science and Information Systems, vol. 2, pp. 1321–1329 (2014)Google Scholar
  26. 26.
    Hewitt, M., Chacosky, A., Grasman, S., Thomas, B.: Integer programming techniques for solving non-linear workforce planning models with learning. Eur. J. Oper. Res. 242(3), 942–950 (2015)MathSciNetCrossRefGoogle Scholar
  27. 27.
    Hu, K., Zhang, X., Gen, M., Jo, J.: A new model for single machine scheduling with uncertain processing time. J. Intell. Manufact. 28(3), 717–725 (2015)CrossRefGoogle Scholar
  28. 28.
    Ikonomov, N., Vassilev, P., Roeva, O.: ICrAData software for InterCriteria analysis. Int. J. Bioautom. 22(2) (2018) (in press)Google Scholar
  29. 29.
    Li, G., Jiang, H., He, T.: A genetic algorithm-based decomposition approach to solve an integrated equipment-workforce-service planning problem. Omega 50, 1–17 (2015)CrossRefGoogle Scholar
  30. 30.
    Li, R., Liu, G.: An uncertain goal programming model for machine scheduling problem. J. Intell. Manufact. 28(3), 689–694 (2014)CrossRefGoogle Scholar
  31. 31.
    Ning, Y., Liu, J., Yan, L.: Uncertain aggregate production planning. Soft Comput. 17(4), 617–624 (2013)CrossRefGoogle Scholar
  32. 32.
    Othman, M., Bhuiyan, N., Gouw, G.: Integrating workers’ differences into workforce planning. Comput. Ind. Eng. 63(4), 1096–1106 (2012)CrossRefGoogle Scholar
  33. 33.
    Parisio, A., Jones, C.N.: A two-stage stochastic programming approach to employee scheduling in retail outlets with uncertain demand. Omega 53, 97–103 (2015)CrossRefGoogle Scholar
  34. 34.
    Roeva, O., Vassilev, P., Angelova, M., Su, J., Pencheva, T.: Comparison of different algorithms for InterCriteria relations calculation. In: 2016 IEEE 8th International Conference on Intelligent Systems, pp. 567–572 (2016)Google Scholar
  35. 35.
    Roeva, O., Fidanova, S., Paprzycki, M.: InterCriteria analysis of ACO and GA hybrid algorithms. Stud. Comput. Intell. 610, 107–126 (2016)MathSciNetGoogle Scholar
  36. 36.
    Roeva, O., Fidanova, S., Vassilev, P., Gepner, P.: InterCriteria analysis of a model parameters identification using genetic algorithm. Proceedings of the Federated Conference on Computer Science and Information Systems 5, 501–506 (2015)CrossRefGoogle Scholar
  37. 37.
    Soukour, A., Devendeville, L., Lucet, C., Moukrim, A.: A Memetic algorithm for staff scheduling problem in airport security service. Expert Syst. Appl. 40(18), 7504–7512 (2013)CrossRefGoogle Scholar
  38. 38.
    Todinova, S., Mavrov, D., Krumova, S., Marinov, P., Atanassova, V., Atanassov, K., Taneva, S.G.: Blood plasma thermograms dataset analysis by means of InterCriteria and correlation analyses for the case of colorectal cancer. Int. J. Bioautom. 20(1), 115–124 (2016)Google Scholar
  39. 39.
    Yang, G., Tang, W., Zhao, R.: An uncertain workforce planning problem with job satisfaction. Int. J. Mach. Learn. Cybern. (2016). Scholar
  40. 40.
    Zaharieva, B., Doukovska, L., Ribagin, S., Radeva, I.: InterCriteria decision making approach for Behterev’s disease analysis. Int. J. Bioautom. 22(2) (2018) (in press)Google Scholar
  41. 41.
    Zhou, C., Tang, W., Zhao, R.: An uncertain search model for recruitment problem with enterprise performance. J. Intell. Manufact. 28(3), 295–704 (2014)Google Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Olympia Roeva
    • 1
  • Stefka Fidanova
    • 2
    Email author
  • Gabriel Luque
    • 3
  • Marcin Paprzycki
    • 4
  1. 1.Institute of Biophysics and Biomedical EngineeringBulgarian Academy of SciencesSofiaBulgaria
  2. 2.Institute of Information and Communication TechnologyBulgarian Academy of SciencesSofiaBulgaria
  3. 3.Department of Languages and Computer ScienceUniversity of MlagaMlagaSpain
  4. 4.System Research InstitutePolish Academy of Sciences, Warsaw and Management AcademyWarsawPoland

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