Abstract
We consider an uncertain single-machine scheduling problem, in which the processing time of a job can take any real value from a given closed interval. The criterion is to minimize the sum of weighted completion times of the n jobs, a weight being associated with each job. For a job permutation, we study the stability box, which is a subset of the stability region. We derive an O(n logn) algorithm for constructing a job permutation with the largest dimension and volume of a stability box. The efficiency of such a permutation is demonstrated via a simulation on a set of randomly generated instances with 1000 ≤ n ≤ 2000. If several permutations have the largest dimension and volume of a stability box, the developed algorithm selects one of them due to a mid-point heuristic.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Daniels, R., Kouvelis, P.: Robust scheduling to hedge against processing time uncertainty in single stage production. Management Science 41(2), 363–376 (1995)
Kasperski, A.: Minimizing maximal regret in the single machine sequencing problem with maximum lateness criterion. Operations Research Letters 33, 431–436 (2005)
Kasperski, A., Zelinski, P.: A 2-approximation algorithm for interval data minmax regret sequencing problem with total flow time criterion. Operations Research Letters 36, 343–344 (2008)
Lai, T.-C., Sotskov, Y.: Sequencing with uncertain numerical data for makespan minimization. Journal of the Operations Research Society 50, 230–243 (1999)
Lai, T.-C., Sotskov, Y., Sotskova, N., Werner, F.: Optimal makespan scheduling with given bounds of processing times. Mathematical and Computer Modelling 26(3), 67–86 (1997)
Pinedo, M.: Scheduling: Theory, Algorithms, and Systems. Prentice-Hall, Englewood Cliffs (2002)
Sabuncuoglu, I., Goren, S.: Hedging production schedules against uncertainty in manufacturing environment with a review of robustness and stability research. International Journal of Computer Integrated Manufacturing 22(2), 138–157 (2009)
Slowinski, R., Hapke, M.: Scheduling under Fuzziness. Physica-Verlag, Heidelberg (1999)
Smith, W.: Various optimizers for single-stage production. Naval Research Logistics Quarterly 3(1), 59–66 (1956)
Sotskov, Y., Egorova, N., Lai, T.-C.: Minimizing total weighted flow time of a set of jobs with interval processing times. Mathematical and Computer Modelling 50, 556–573 (2009)
Sotskov, Y., Egorova, N., Werner, F.: Minimizing total weighted completion time with uncertain data: A stability approach. Automation and Remote Control 71(10), 2038–2057 (2010)
Sotskov, Y., Lai, T.-C.: Minimizing total weighted flow time under uncertainty using dominance and a stability box. Computers & Operations Research 39, 1271–1289 (2012)
Sotskov, Y., Sotskova, N., Lai, T.-C., Werner, F.: Scheduling under Uncertainty. Theory and Algorithms. Belorusskaya nauka, Minsk (2010)
Sotskov, Y., Wagelmans, A., Werner, F.: On the calculation of the stability radius of an optimal or an approximate schedule. Annals of Operations Research 83, 213–252 (1998)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Sotskov, Y.N., Lai, TC., Werner, F. (2013). The Stability Box for Minimizing Total Weighted Flow Time under Uncertain Data. In: Pina, N., Kacprzyk, J., Filipe, J. (eds) Simulation and Modeling Methodologies, Technologies and Applications. Advances in Intelligent Systems and Computing, vol 197. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34336-0_3
Download citation
DOI: https://doi.org/10.1007/978-3-642-34336-0_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-34335-3
Online ISBN: 978-3-642-34336-0
eBook Packages: EngineeringEngineering (R0)