Hostname: page-component-89b8bd64d-72crv Total loading time: 0 Render date: 2026-05-07T12:06:02.840Z Has data issue: false hasContentIssue false
  • English
  • Français

Dynamic load balancing with flexible workers

Part of: Special processes Operations research and management science

Published online by Cambridge University Press:  01 July 2016

Hyun-Soo Ahn  and
Rhonda Righter
Hyun-Soo Ahn*
Affiliation:
University of Michigan
Rhonda Righter*
Affiliation:
University of California, Berkeley
*
∗ Postal address: Department of Operations and Management Science, Ross School of Business, University of Michigan, 701 Tappan Street, Ann Arbor, MI 48109-1234, USA, Email address: hsahn@umich.edu
∗∗ Postal address: Department of Industrial Engineering and Operations Research, University of California, Berkeley, CA 94720, USA. Email address: rrighter@ieor.berkeley.edu
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

We study the problem of dynamically allocating flexible workers to stations in tandem or serial manufacturing systems. Workers are trained to do a subset of consecutive tasks. We show that the optimal policy is often LBFS (last buffer first-served) or FBFS (first buffer first-served). These results generalize earlier results on the optimality of the pick-and-run, expedite, and bucket brigade-type policies. We also show that, for exponential processing times and general manufacturing networks, the optimal policy will tend to have several workers assigned to the same station.

Keywords

Stochastic schedulingtandem systemsmultiserver queueflexible workerload balancing

MSC classification

Primary: 90B36: Scheduling theory, stochastic
Secondary: 90B22: Queues and service 60K25: Queueing theory

Information

Type
General Applied Probability
Information
Advances in Applied Probability , Volume 38 , Issue 3 , September 2006 , pp. 621 - 642
Copyright
Copyright © Applied Probability Trust 2006 

References

Ahn, H.-S. and Righter, R. (2005). Multi-actor Markov decision processes. J. Appl. Prob. 42, 15–26.Google Scholar
Ahn, H.-S., Duenyas, I. and Lewis, M. E. (2002). The optimal control of a two-stage tandem queueing system with flexible servers. Prob. Eng. Inf. Sci. 16, 453–469.CrossRefGoogle Scholar
Ahn, H.-S., Duenyas, I. and Zhang, R. Q. (1999). Optimal stochastic scheduling of a 2-stage tandem queue with parallel servers. Adv. Appl. Prob. 31, 1095–1117.Google Scholar
Andradöttir, S., Ayhan, H. and Down, D. G. (2001). Server assignment policies for maximizing the steady-state throughput. Manag. Sci. 47, 1421–1439.Google Scholar
Andradöttir, S., Ayhan, H. and Down, D. G. (2003). Dynamic server allocation for queueing networks with flexible servers. Operat. Res. 51, 952–968.Google Scholar
Askin, R. G. and Chen, J. (2006). Dynamic task assignment for throughput maximization with worksharing. Europ. J. Operat. Res. 168, 853–869.CrossRefGoogle Scholar
Askin, R. G. and Chen, J. (2006). Throughput maximization in serial production lines with worksharing. Internat. J. Production Econom. 99, 88–101.Google Scholar
Asmussen, S. and Koole, G. M. (1993). Marked point processes as limits of Markovian arrival streams. J. Appl. Prob. 30, 365–372.CrossRefGoogle Scholar
Bartholdi III, J. J. and Eisenstein, D. D. (1996). A production line that balances itself. Operat. Res. 44, 21–34.Google Scholar
Bartholdi III, J. J., Eisenstein, D. D. and Foley, R. D. (2001). Performance of bucket brigades when work is stochastic. Operat. Res. 49, 710–719.Google Scholar
Bischak, D. P. (1996). Performance of a manufacturing module with moving workers. IIE Trans. 28, 723–733.CrossRefGoogle Scholar
Duenyas, I., Gupta, D. and Olsen, T. L. (1998). Control of a single server tandem queueing system with setups. Operat. Res. 46, 218–230.Google Scholar
Farrar, T. (1993). Optimal use of an extra server in a two station tandem queueing network. IEEE Trans. Automatic Control 38, 1296–1299.CrossRefGoogle Scholar
Gel, E. S., Hopp, W. J. and van Oyen, M. P. (2000). Factors affecting opportunity of worksharing as a dynamic line balancing mechanism. IIE Trans. 34, 847–863.Google Scholar
Gel, E. S., Hopp, W. J. and van Oyen, M. P. (2006). Opportunity of hierarchical cross training in serial production. To appear in IIE Trans.Google Scholar
Grassman, W. K. and Tavakoli, J. (2002). A tandem queue with a movable server: an eigenvalue approach. SIAM J. Matrix Anal. Appl. 24, 465–474.Google Scholar
Hopp, W. J., Tekin, E. and van Oyen, M. P. (2004). Benefits of skill chaining in serial production lines with cross-trained workers. Manag. Sci. 50, 83–98.Google Scholar
Iravani, S. M. R., Posner, M. J. M. and Buzacott, J. A. (1997). Two-stage tandem queue attended by a moving server with holding and switching costs; static and semi-dynamic policy. Queueing Systems 26, 203–228.CrossRefGoogle Scholar
Javidi, T., Song, N.-O. and Teneketzis, D. (2001). Expected makespan minimization on identical machines in two interconnected queues. Prob. Eng. Inf. Sci. 15, 409–444.Google Scholar
Koole, G. and Righter, R. (1998). Optimal control of tandem reentrant queues. Queueing Systems 28, 337–347.Google Scholar
Mandelbaum, A. and Reiman, M. I. (1998). On pooling in queueing networks. Manag. Sci. 44, 971–981.CrossRefGoogle Scholar
McClain, J. O., Thomas, L. J. and Sox, C. (1992). ‘On-the-fly’ line balancing with very little WIP. Internat. J. Production Econom. 27, 283–289.CrossRefGoogle Scholar
Ostolaza, J., McClain, J. and Thomas, J. (1990). The use of dynamic (state-dependent) assembly-line balancing to improve throughput. J. Manufacturing Operat. Manag. 3, 105–133.Google Scholar
Pandelis, D. G. (2006). Optimal use of excess capacity in two interconnected queues. To appear in Z. Operat. Res. Google Scholar
Pandelis, D. G. (2006). Optimal control of flexible servers in two tandem queues with operating costs. Preprint.Google Scholar
Pandelis, D. G. and Teneketzis, A. D. (1994). Optimal multiserver stochastic scheduling of two interconnected priority queues. Adv. Appl. Prob. 26, 258–279.Google Scholar
Sennott, L., van Oyen, M. P. and Iravani, S. M. R. (2006). Optimal dynamic assignment of a flexible worker on an open production line with specialists. Europ. J. Operat. Res. 170, 541–566.Google Scholar
Van Oyen, M. P., Gel, E. G. S. and Hopp, W. J. (2001). Performance opportunity for workforce agility in collaborative and noncollaborative work systems. IIE Trans. 33, 761–777.Google Scholar