MedAlg 2012: Design and Analysis of Algorithms pp 52-66 | Cite as
Reoptimization of the Minimum Total Flow-Time Scheduling Problem
Conference paper
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.
Keywords
Bipartite Graph Optimal Schedule Complete Bipartite Graph Short Processing Time Migration Cost
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Preview
Unable to display preview. Download preview PDF.
References
- 1.Amato, G., Cattaneo, G., Italiano, G.F.: Experimental analysis of dynamic minimum spanning tree algorithms. In: Proc. of 8th SODA (1997)Google Scholar
- 2.Archetti, C., Bertazzi, L., Speranza, M.G.: Reoptimizing the 0-1 knapsack problem. Discrete Applied Mathematics 158(17) (2010)Google Scholar
- 3.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)Google Scholar
- 4.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)MathSciNetMATHCrossRefGoogle Scholar
- 5.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
- 6.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)Google Scholar
- 7.Bruno, J.L., Coffman, E.G., Sethi, R.: Scheduling independent tasks to reduce mean finishing time. Communications of the ACM 17, 382–387 (1974)MathSciNetMATHCrossRefGoogle Scholar
- 8.Chandrasekaran, R., Kaboadi, S.N., Murty, K.G.: Some NP-complete problems in linear programming. Operations Research Letters 1, 101–104 (1982)MATHCrossRefGoogle Scholar
- 9.Conway, R.W., Maxwell, W.L., Miller, L.W.: Theory of Scheduling. AddisonWesley (1967)Google Scholar
- 10.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)Google Scholar
- 11.Escoffier, B., Milanič, M., Paschos, V.T: Simple and fast reoptimizations for the Steiner tree problem. DIMACS Technical Report 2007-01Google Scholar
- 12.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)MathSciNetMATHCrossRefGoogle Scholar
- 13.Grandoni, F., Zenklusen, R.: Optimization with more than one budget. In: Proc. of ESA (2010)Google Scholar
- 14.Horn, W.: Minimizing average flow-time with parallel machines. Operations Research 21, 846–847 (1973)MATHCrossRefGoogle Scholar
- 15.Karzanov, A.V.: Maximum matching of given weight in complete and complete bipartite graphs. Kibernetika 1, 7–11 (1987); English translation in CYBNAW 23, 8–13Google Scholar
- 16.Mattox, D.: Handbook of Physical Vapor Deposition (PVD) Processing, 2nd edn. Elsevier (2010)Google Scholar
- 17.Nardelli, E., Proietti, G., Widmayer, P.: Swapping a failing edge of a single source shortest paths tree is good and fast. Algorithmica 35 (2003)Google Scholar
- 18.Pallottino, S., Scutella, M.G.: A new algorithm for reoptimizing shortest paths when the arc costs change. Operations Research Letters 31 (2003)Google Scholar
- 19.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)CrossRefGoogle Scholar
- 20.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)CrossRefGoogle Scholar
- 21.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)CrossRefGoogle Scholar
- 22.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)CrossRefGoogle Scholar
- 23.Smith, W.E.: Various optimizers for single-stage production. Naval Research Logistics Quarterly 3, 59–66 (1956)MathSciNetCrossRefGoogle Scholar
- 24.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)CrossRefGoogle Scholar
- 25.Yi, T., Murty, K.G., Spera, C.: Matchings in colored bipartite networks. Discrete Applied Mathematics 121, 261–277 (2002)MathSciNetMATHCrossRefGoogle Scholar
Copyright information
© Springer-Verlag Berlin Heidelberg 2012