Abstract
We consider reoptimization problems arising in production planning. Due to unexpected changes in the environment (out-of-order or new machines, modified jobs’ processing requirements, etc.), the production schedule needs to be modified. That is, jobs might be migrated from their current machine to a different one. Migrations are associated with a cost – due to relocation overhead and machine set-up times. The goal is to find a good modified schedule, which is as close as possible to the initial one. We consider the objective of minimizing the total flow time, denoted in standard scheduling notation by P || ∑ C j .
We study two different problems: (i) achieving an optimal solution using the minimal possible transition cost, and (ii) achieving the best possible schedule using a given limited budget for the transition. We present optimal algorithms for the first problem and for several classes of instances for the second problem.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Amato, G., Cattaneo, G., Italiano, G.F.: Experimental analysis of dynamic minimum spanning tree algorithms. In: Proc. of 8th SODA (1997)
Archetti, C., Bertazzi, L., Speranza, M.G.: Reoptimizing the 0-1 knapsack problem. Discrete Applied Mathematics 158(17) (2010)
Ausiello, G., Bonifaci, V., Escoffier, B.: Complexity and approximation in reoptimization. In: Cooper, B., Sorbi, A. (eds.) Computability in Context: Computation and Logic in the Real World. Imperial College Press/World Scientific (2011)
Ausiello, G., Escoffier, B., Monnot, J., Paschos, V.T.: Reoptimization of minimum and maximum traveling salesmans tours. J. of Discrete Algorithms 7(4), 453–463 (2009)
Baram, G., Tamir, T.: Reoptimization of the minimum total flow-time scheduling problem (full version), http://www.faculty.idc.ac.il/tami/Papers/BTfull.pdf
Böckenhauer, H.J., Forlizzi, L., Hromkovič, J., Kneis, J., Kupke, J., Proietti, G., Widmayer, P.: On the approximability of TSP on local modifications of optimally solved instances. Algorithmic Operations Research 2(2) (2007)
Bruno, J.L., Coffman, E.G., Sethi, R.: Scheduling independent tasks to reduce mean finishing time. Communications of the ACM 17, 382–387 (1974)
Chandrasekaran, R., Kaboadi, S.N., Murty, K.G.: Some NP-complete problems in linear programming. Operations Research Letters 1, 101–104 (1982)
Conway, R.W., Maxwell, W.L., Miller, L.W.: Theory of Scheduling. AddisonWesley (1967)
Eppstein, D., Galil, Z., Italiano, G.F.: Dynamic graph algorithms. In: Atallah, M.J. (ed.) CRC Handbook of Algorithms and Theory of Computation, ch. 8 (1999)
Escoffier, B., Milanič, M., Paschos, V.T: Simple and fast reoptimizations for the Steiner tree problem. DIMACS Technical Report 2007-01
Graham, R.L., Lawler, E.L., Lenstra, J.K., Rinnooy Kan, A.H.G.: Optimization and approximation in deterministic sequencing and scheduling: A survey. Annals of Discrete Math. 5, 287–326 (1979)
Grandoni, F., Zenklusen, R.: Optimization with more than one budget. In: Proc. of ESA (2010)
Horn, W.: Minimizing average flow-time with parallel machines. Operations Research 21, 846–847 (1973)
Karzanov, A.V.: Maximum matching of given weight in complete and complete bipartite graphs. Kibernetika 1, 7–11 (1987); English translation in CYBNAW 23, 8–13
Mattox, D.: Handbook of Physical Vapor Deposition (PVD) Processing, 2nd edn. Elsevier (2010)
Nardelli, E., Proietti, G., Widmayer, P.: Swapping a failing edge of a single source shortest paths tree is good and fast. Algorithmica 35 (2003)
Pallottino, S., Scutella, M.G.: A new algorithm for reoptimizing shortest paths when the arc costs change. Operations Research Letters 31 (2003)
Ravi, R., Goemans, M.X.: The Constrained Minimum Spanning Tree Problem. In: Karlsson, R., Lingas, A. (eds.) SWAT 1996. LNCS, vol. 1097, pp. 66–75. Springer, Heidelberg (1996)
Shachnai, H., Tamir, G., Tamir, T.: Minimal Cost Reconfiguration of Data Placement in Storage Area Network. In: Bampis, E., Jansen, K. (eds.) WAOA 2009. LNCS, vol. 5893, pp. 229–241. Springer, Heidelberg (2010)
Shachnai, H., Tamir, G., Tamir, T.: A Theory and Algorithms for Combinatorial Reoptimization. In: Fernández-Baca, D. (ed.) LATIN 2012. LNCS, vol. 7256, pp. 618–630. Springer, Heidelberg (2012)
Sitters, R.A.: Two NP-Hardness Results for Preemptive Minsum Scheduling of Unrelated Parallel Machines. In: Aardal, K., Gerards, B. (eds.) IPCO 2001. LNCS, vol. 2081, pp. 396–405. Springer, Heidelberg (2001)
Smith, W.E.: Various optimizers for single-stage production. Naval Research Logistics Quarterly 3, 59–66 (1956)
Thorup, M., Karger, D.R.: Dynamic Graph Algorithms with Applications. In: Halldórsson, M.M. (ed.) SWAT 2000. LNCS, vol. 1851, pp. 1–9. Springer, Heidelberg (2000)
Yi, T., Murty, K.G., Spera, C.: Matchings in colored bipartite networks. Discrete Applied Mathematics 121, 261–277 (2002)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Baram, G., Tamir, T. (2012). Reoptimization of the Minimum Total Flow-Time Scheduling Problem. In: Even, G., Rawitz, D. (eds) Design and Analysis of Algorithms. MedAlg 2012. Lecture Notes in Computer Science, vol 7659. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34862-4_4
Download citation
DOI: https://doi.org/10.1007/978-3-642-34862-4_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-34861-7
Online ISBN: 978-3-642-34862-4
eBook Packages: Computer ScienceComputer Science (R0)