Skip to main content
Log in

Planning personnel retraining: column generation heuristics

  • Published:
Journal of Combinatorial Optimization Aims and scope Submit manuscript

Abstract

Retraining of staff is a compulsory managerial function in many organisations and often requires planning for a large number of employees. The large scale of this problem and various restrictions on the resultant assignment to classes make this planning challenging. The paper presents a complexity analysis of this problem together with linear and nonlinear mathematical programming formulations. Three different column generation based optimisation procedures and a large neighbourhood search procedure, incorporating column generation, are compared by means of computational experiments. The experiments used data typical to large electricity distributors.

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

Access this article

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

Instant access to the full article PDF.

Fig. 1
Fig. 2

Similar content being viewed by others

References

  • Blte A, Thonemann UW (1996) Optimizing simulated annealing schedules with genetic programming. Eur J Oper Res 92(2):402–416. https://doi.org/10.1016/0377-2217(94)00350-5. http://www.sciencedirect.com/science/article/pii/0377221794003505

  • Caprara A, Pisinger D, Toth P (1999) Exact solution of the quadratic knapsack problem. INFORMS J Comput 11(2):125–137

    Article  MathSciNet  MATH  Google Scholar 

  • Chen Y, Hao JK (2015) Iterated responsive threshold search for the quadratic multiple knapsack problem. Ann Oper Res 226:101–131

    Article  MathSciNet  MATH  Google Scholar 

  • Chen Y, Hao JK, Glover F (2016) An evolutionary path relinking approach for the quadratic multiple knapsack problem. Knowl Based Syst 92:23–34

    Article  Google Scholar 

  • Chopra S, Rao MR (1993) The partition problem. Math Program 59(1–3):87–115

    Article  MathSciNet  MATH  Google Scholar 

  • Cornuéjols G, Nemhauser GL, Wolsey LA (1983) The uncapacitated facility location problem. Carnegie-mellon univ pittsburgh pa management sciences research group, Tech. rep

  • Desrosiers J, Lübbecke ME (2005) A primer in column generation. Springer, Berlin

    Book  MATH  Google Scholar 

  • Drezner Z (2003) A new genetic algorithm for the quadratic assignment problem. INFORMS J Comput 15(3):320–330. https://doi.org/10.1287/ijoc.15.3.320.16076.

    Article  MathSciNet  MATH  Google Scholar 

  • García-Martínez C, Rodriguez F, Lozano M (2014) Tabu-enhanced iterated greedy algorithm: a case study in the quadratic multiple knapsack problem. Eur J Oper Res 232:454–463

    Article  MathSciNet  MATH  Google Scholar 

  • Garey MR, Johnson DS (1979) Computers and intractability: a guide to np-completeness. Freeman, San Francisco

    MATH  Google Scholar 

  • Gintner V, Kliewer N, Suhl L (2005) Solving large multiple-depot multiple-vehicle-type bus scheduling problems in practice. OR Spectr. 27(4):507–523

    Article  MATH  Google Scholar 

  • Goldschmidt O, Hochbaum DS, Levin A, Olinick EV (2003) The sonet edge-partition problem. Networks 41(1):13–23

    Article  MathSciNet  MATH  Google Scholar 

  • Hiley A, Julstrom BA (2006) The quadratic multiple knapsack problem and three heuristic approaches to it. In: Proceedings of the 8th annual conference on genetic and evolutionary computation. ACM, pp 547–552

  • Johnson EL, Mehrotra A, Nemhauser GL (1993) Min-cut clustering. Math program 62(1–3):133–151

    Article  MathSciNet  MATH  Google Scholar 

  • Julstrom BA (2005) Greedy, genetic, and greedy genetic algorithms for the quadratic knapsack problem. In: Proceedings of the 7th annual conference on genetic and evolutionary computation. ACM, pp 607–614

  • Pisinger D, Ropke S (2010) Large neighborhood search. In: Potvin J-Y, Gendreau M (eds) Handbook of metaheuristics. Springer, Boston, pp 399–419

    Chapter  Google Scholar 

  • Pochet Y, Wolsey LA (2006) Production planning by mixed integer programming. Springer, Berlin

    MATH  Google Scholar 

  • Shaw P (1998) Using constraint programming and local search methods to solve vehicle routing problems. In: International conference on principles and practice of constraint programming. Springer, pp 417–431

  • Taşkın ZC, Smith JC, Ahmed S, Schaefer AJ (2009) Cutting plane algorithms for solving a stochastic edge-partition problem. Discrete Optim 6(4):420–435

    Article  MathSciNet  MATH  Google Scholar 

  • Wang H, Kochenberger G, Glover F (2012) A computational study on the quadratic knapsack problem with multiple constraints. Comput Oper Res 39(1):3–11

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Oliver G. Czibula.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Czibula, O.G., Gu, H. & Zinder, Y. Planning personnel retraining: column generation heuristics. J Comb Optim 36, 896–915 (2018). https://doi.org/10.1007/s10878-018-0253-2

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10878-018-0253-2

Keywords

Navigation