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Staff Scheduling with Particle Swarm Optimisation and Evolution Strategies

EVO Cop 2009, Tuebingen. Staff Scheduling with Particle Swarm Optimisation and Evolution Strategies. Dipl. Wirt.-Inf. Maik Günther maik.guenther@gmx.de Prof. Dr. Volker Nissen volker.nissen@tu-ilmenau.de TU Ilmenau Department of Commercial Information Technology for Services (WI2).

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Staff Scheduling with Particle Swarm Optimisation and Evolution Strategies

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  1. EVO Cop 2009, Tuebingen Staff Scheduling with Particle Swarm Optimisation and Evolution Strategies Dipl. Wirt.-Inf. Maik Günther maik.guenther@gmx.de Prof. Dr. Volker Nissen volker.nissen@tu-ilmenau.de TU IlmenauDepartment of Commercial Information Technology for Services (WI2)

  2. Structure of Presentation • Sub Daily / Sub Shift Staff Scheduling • Particle Swarm Optimisation • Evolution Strategies • Results and Conclusion

  3. Sub Daily / Sub Shift Staff Scheduling

  4. Requirement Hours worked Personnel Hours Overstaffing Understaffing Time elapsed Introduction I • „Five R‘s“: • right qualified employee • right number of employees • at the right time • at the right place • at the right (optimal) costs • Garey and Johnson demonstrate that even simple versions of staff scheduling problems are NP-hard [8]. • Kragelund and Kabel show the NP-hardness of the general employee timetabling problem [10].

  5. Introduction II • employees spend 27 to 36% of their working time unproductive, depending on the branch[12] • often staff scheduling takes place based on experience or with the aid of spreadsheets [1] • even with staff planning software employees are regularly scheduled for one workstation per day • in many branches the one-employee-one-station concept does not correspond to the actual requirements and sacrifices potential resources • service industry (for instance logistics), commercial trade, etc. • sub-daily (sub-shift) planning should be an integral component of demand driven staff scheduling

  6. Description of the Application Problem • originates from a German logistics service provider which operates in a spatially limited area 7 days a week almost 24 hours a day • nine workstations • 65 employees on duty with different start and end times according to their work-time models • employees are quite flexible in terms of working hours (13 different working time models) • many employees are qualified to work at different workstations • strict regulations e.g. with regard to qualifications (damage, injuries) • personnel demand is given in 15-minute intervals with large variations for individual workstations during the day

  7. Demand for Personnel at the Nine Workstations

  8. Current Planning • monthly staff scheduling is carried out with MS EXCEL • they are not able to make sub-daily workstation-rotations with MS EXCEL • employees are assigned on a full-day basis  large phases of over- and understaffing • floor managers intervene on-site by relocating employees ad hoc (reacting instead of ahead-planning) Demand driven staff scheduling cannot be realised today!

  9. Sub-Daily Staff Scheduling • input • full-day assignment (determines availability of personnel) • demand for personnel at the nine workstations in 15-minute intervals • matrix of qualifications (employees and workstations) • relevant constraints (constraints are penalised with error points) • presence and absence • timesheet balances • qualifications • no unnecessary workstation-rotations • one employee can only assigned to one workstation at a time • ....

  10. Problem Representation for PSO and ES • numbers • 0: employee is not working • 1-9: correspond to workstations • based on two-dimensional matrix (65 rows and 560 columns = 36,400) • time is viewed as discrete

  11. Particle Swarm Optimisation

  12. Overall Outline of PSO Approach • termination of PSO • after 400.000 inspected solutions (to keep results comparable) • initialize the swarm • calculate fitness of initial particles • determine pBest for each particle and gBest • repeat • for i = 1 to number of particles • calculate new position // 4 actions • calculate fitness • new pBest? / new gBest? • next i • until termination criterion holds • output gBest from current run

  13. 4 Actions to Calculate the new Position • for each element (> 0) of the matrix • probability to chose one of the 4 actions • 4 actions • no change • random workstation (no qualification errors) • workstation from pBest at the same position • workstation from gBest at the same position

  14. Evolution Strategies

  15. Overall Outline of Evolutionary Approach • termination of ES • after 400.000 inspected solutions (to keep results comparable) • initialize the population • calculate fitness of initial population • repeat • draw and recombine parent solutions • mutate offspring • calculate fitness for offspring • select the new population • until termination criterion holds • output best solution from current run

  16. Details of the Approach • selection • deterministic, non-elitist comma- and plus-selection • following suggestions in the literature [2] [3], the ratio / is set to 1/5 – 1/7 • (1,5)-, (1+5)-, (10,50)-, (10+50)-, (30,200)- and (30+200)-selection • best solution kept in “golden cage” (not part of population) • recombination • recombination of two parent solutions ((10,50), (10+50), (30,200), (30+200)) • random crossover point for each employee

  17. Mutation of Solutions • self adaptive step size for mutation • mutation creates only valid solutions (no availability and qualification errors) • τ = 0,1 • σ‘ = σ * exp(τ * N(0,1)) • Count = round│N(0,σ‘)│ • if Count < 1 then Count = 1 • for i = 1 to Count • random employee e • random time interval t • random workstation • change value at matrix element (e,t) • next i

  18. Mutation with the Principle of Maximum Entropy [14] • the principle of maximum entropy is used in [14] to construct a mutation distribution for unbounded integer search spaces • the difference (Z) of two independent geometrically distributed random numbers (G1 and G2) is added to each element of the matrix • G1 and G2 have the parameter p which is controlled by the step size • the problem of the logistics service provider is bounded (9 workstations), much more dimensions and special constraints • τ² = 17,07/n instead of τ² = 1/n • no availability and qualification errors • recombination „nr. 5“ instead of uniform crossover • Z was too small  now Z has a greater variance to reach all possible workstations

  19. Results and Conclusion

  20. Results for the Logistic Service Provider Problem Indication of absolute minimum: PSO with repair: 51,521 error points Results averaged over 30 runs each. All tests were conducted on a standard PC.

  21. Conclusion • PSO-approach is the most effective heuristic for this problem • PSO is easy to use (2 important parameters  swarm size and probability to set a random workstation) • exchange of information (gBest and pBest) • make small changes in one interation/generation • future research • create further test problems with the aid of cooperating companies • adapt other heuristics from roughly comparable problems in the literature

  22. References ATOSS Software AG, FH Heidelberg (2006) (ed.) Standort Deutschland 2006. Zukunftssicherung durch intelligentes Personalmanagement. München Bäck T. (2002) (ed.) Handbook of Evolutionary Computation. Institute of Physics Publishing, Bristol Beyer H.-G., Schwefel, H.-P. (2002) Evolution strategies: a comprehensive introduction. Natural Computing 1: 3-52 Blöchlinger I. (2004) Modeling Staff Scheduling Problems. EJOR 158: 533-542 Chu S. C., Chen Y. T., Ho J. H. (2006) Timetable Scheduling Using Particle Swarm Optimization. In: Proceedings of ICICIC Beijing 2006, Vol. 3: 324-327 Brodersen, O., Schumann, M. (2007) Einsatz der Particle Swarm Optimization zur Optimierung universitärer Stundenpläne. Technical Report 05/2007, University of Göttingen Ernst A. T., Jiang H., Krishnamoorthy M., Owens B., Sier D. (2002) An Annotated Bibliography of Personnel Scheduling and Rostering. Annals of OR 127: 21-144 Garey, M.R.; Johnson, D.S. (1979) Computers and Intractability. A Guide to the Theory of NP-Completeness Kennedy J., Eberhart R. C., Shi Y. (2001) Swarm Intelligence. Kaufmann, San Francisco Kragelund, L., Kabel, T. (1998) Employee Timetabling. An Empirical Study, Master's Thesis, University of Aarhus Meisels A., Schaerf A. (2003) Modelling and solving employee timetabling problems. Annals of Mathematics and Artificial Intelligence 39: 41-59 Proudfoot Consulting (2007) Produktivitätsbericht 2007. Company Report ROADEF Challenge (2007) Technicians and Interventions Scheduling for Telecommunications. http://www.g-scop. inpg.fr/ChallengeROADEF2007 (2008-06-22) Rudolph, G. (1994) An evolutionary algorithm for integer programming. PPSN III, Jerusalem, Israel, Proceedings, LNCS, Vol. 866:139-148 Tien, J; Kamiyama, A. (1982) On Manpower Scheduling Algorithms, SIAM Rev. 24(3): 275-287 Vanden Berghe G. (2002) An Advanced Model and Novel Metaheuristic Solution Methods to Personnel Scheduling in Healthcare. Thesis, University of Gent, Belgium

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