Browse > Article

A rounding algorithm for alternate machine scheduling  

Hwang, Hark-Chin (조선대학교 산업공학과)
Publication Information
Korean Management Science Review / v.24, no.2, 2007 , pp. 33-42 More about this Journal
Abstract
In this paper we consider an alternate m machine scheduling problem in which each job having at most two eligible machines should be assigned with the objective of makespan minimization. For this problem. we propose a $O(m2^m)$ time rounding algorithm with performance ratio at most 1.5. For a little general problem where each job can be processed in at most three machines, we prove that a polynomial time algorithm does not exist with performance ratio less than 1.5.
Keywords
Parallel machine scheduling; Approximation algorithm; Performance ratio; NP-Complete;
Citations & Related Records
연도 인용수 순위
  • Reference
1 Chang S.Y. and H.-C. Hwang, The worstcase analysis of the MULTIFIT algorithm for scheduling nonsimultaneous parallel machines, Discrete Applied Mathematics, Vol. 92(1999), pp.135-147   DOI   ScienceOn
2 Garey M.R. and D.S. Johnson, Computers and Intractability：A Guide to the theory of NP-Completeness, Freeman, San Francisco, 1979
3 Hwang H.-C. and G. Kim, 2-Approximation Algorithm for Parallel Machine Scheduling with Consecutive Eligibility, KIIE, Vol.29(2003), pp.190-196
4 Hwang H.-C, S.Y. Chang, and Y. Hong, The Posterior Competitiveness for List Scheduling Algorithm on Machines with Eligibility Constraints, Asia-Pacific Journal of Operational Research, Vol.1(2004), pp.1-9
5 Kellerer H., U. Pferschy, A New Fully Polynomial Approximation Scheme for the Knapsack Problem, Journal of Combinatorial Optimization, Vol.3(1999), pp.59-71   DOI
6 Vairaktarakis, G.L. and X. Cai, The Value of Processing Flexibility in Multipurpose Machines, IIE Transactions, Vol.35(2003), pp.763-774   DOI
7 Hochbaum D.S. and D. Shmoys, Using dual approximation algorithms for scheduling problems： Theoretical and practical results, J. ACM, Vol.34(1987), pp.144-162   DOI   ScienceOn
8 Hwang H.-C, K. Lee, and S.Y. Chang, Parallel machine scheduling under a grade of service provision, Computers & Operations Research, Vol.31(2004), pp.2055-2061   DOI   ScienceOn
9 Azar, Y., J. Naor, and R. Rom, The competitiveness of On-Line Assignments, J. Algorithms, Vol.18(1995), pp.221-237   DOI   ScienceOn
10 Kaplan R.S. and R. Cooper, Cost & Effect, Havard Business School Press, Boston, Massachusetts, 1997
11 Hochbaum D.S., Approximation Algorithms for NP-Hard Problems, PWS PUBLISHING COMPANY, Boston, (1997), 370-371
12 Shchepinal E.V. and N. Vakhania, An optimal rounding gives a better approximation for scheduling unrelated machines, Operations Research Letters, Vol.33(2005), pp. 127-133   DOI   ScienceOn
13 M. Yue, On the exact upper bound for the MULTIFIT processor scheduling algorithm, in Operations Research in China, M. Yue (ed.), of Annals of Operations Research, Baltzer, Basel, Switzerland, Vol.24(1990), pp. 233-259   DOI
14 Hwang H.-C. and S.Y. Chang, Parallel machines scheduling with machine shutdowns, Computers and Mathematics with Applications, Vol.36(1998), pp.21-31
15 He Y., H. Kellerer, and V. Kotov, Linear Compound Algorithms for the Partitioning Problem, Naval Research Logistics, Vol.47 (2000), pp.593-601   DOI   ScienceOn
16 Potts C.N., Analysis of a linear programming euristic for scheduling unrelated parallel machines, Discrete Appl. Math. Vol. 10(1985), pp.155-164   DOI
17 Yu, L., Scheduling of unrelated parallel machines： an application to PWB manufacturing, IIE Transactions, Vol.34(2003), pp. 921-931
18 Coffman Jr E.G., M.R. Garey, and D.S. Johnson, An application of bin-packing to multiprocessor scheduling, SIAM J. Comput., Vol.7(1978), pp.1-17   DOI
19 Graham R.L., Bounds on multiprocessor timing anomalies, SIAM J. Appl. Math., Vol. 17(1969), pp.263-269
20 Graham, R.L., E.L. Lawler, J.K. Lenstra, and A.H.G. Rinnooy Kan, Optimization and Approximation in Deterministic Machine Scheduling： A Survey, Annals of Discrete Mathematics, Vol.5(1979), pp.287-326   DOI
21 Friesen D.K., Tighter bounds for the multi processor scheduling algorithm, SIAM J. of Comput., Vol.13(1984), pp.35-59
22 Hwang H.-C, LPT Scheduling for Multipurpose Machines, IE Interfaces, Vol.16(2003), pp.132-137
23 Ibarra O.H. and C.E. Kim, Fast approximation algorithms for the knapsack and sum of subset problems, J. ACM, Vol.22 (1975), pp.463-468   DOI   ScienceOn
24 Lenstra J.K., D.B. Shmoys, and E. Tardos, Approximation Algorithms for Scheduling Unrelated Parallel Machines, Mathematical Programming, Vol.46(1990), pp.259-271   DOI
25 Hwang H.-C, A PTAS for nonsimultaneous parallel machine scheduling, Journal of the Korean Society of Maintenance Management, Vol.3(2003), pp.181-193