An exact algorithm for single-machine scheduling without machine idle time

Journal of Scheduling

Volumn 12, Issue 6, 2009, Pages 575-593

  Tanaka, Shunji ^a   Fujikuma, Shuji ^a   Araki, Mituhiko ^b  

^a KYOTO UNIVERSITY   (Japan)

^b MATSUE NATIONAL COLLEGE OF TECHNOLOGY   (Japan)

Author keywords

Exact algorithm; Lagrangian relaxation; Single machine scheduling; Successive sublimation dynamic programming method; Time indexed formulation

Indexed keywords

COMPUTATIONAL EFFORT; DYNAMIC PROGRAMMING METHODS; EXACT ALGORITHMS; JOB COMPLETION; LAGRANGIAN RELAXATION; MACHINE IDLE; MEMORY USAGE; NUMERICAL EXPERIMENTS; SINGLE-MACHINE SCHEDULING; TOTAL-WEIGHTED TARDINESS; WEIGHTED EARLINESS;

DYNAMIC PROGRAMMING; LAGRANGE MULTIPLIERS; MACHINERY; SUBLIMATION; SYSTEMS ENGINEERING; WIRELESS TELECOMMUNICATION SYSTEMS;

ALGORITHMS;

EID: 72249099711     PISSN: 10946136     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10951-008-0093-5     Document Type: Conference Paper

References (21)

1. T. S. Abdul-Razaq C. N. Potts 1988 Dynamic programming state-space relaxation for single-machine scheduling Journal of the Operational Research Society 39 141 152 10.1057/jors.1988.26
2. N. Christofides A. Mingozzi P. Toth 1981 State-space relaxation procedures for the computation of bounds to routing problems Networks 11 145 164 10.1002/net.3230110207
3. R. K. Congram C. N. Potts S. L. van de Velde 2002 An iterated dynasearch algorithm for the single-machine total weighted tardiness scheduling problem INFORMS Journal on Computing 14 52 67 10.1287/ijoc.14.1.52.7712
4. H. A. J. Crauwels C. N. Potts L. N. Van Wassenhove 1998 Local search heuristics for the single machine total weighted tardiness scheduling problem INFORMS Journal on Computing 10 341 350 10.1287/ijoc.10.3.341
5. M. E. Dyer L. A. Wolsey 1990 Formulating the single-machine sequencing problem with release dates as a mixed integer problem Discrete Applied Mathematics 26 255 270 10.1016/0166-218X(90)90104-K
6. M. L. Fisher 1973 Optimal solution of scheduling problems using Lagrange multipliers: part I Operations Research 21 1114 1127 10.1287/opre.21.5.1114
7. M. L. Fisher 1985 An applications oriented guide to Lagrangian relaxation Interfaces 15 10 21 10.1287/inte.15.2.10
8. A. Grosso F. Della Croce R. Tadei 2004 An enhanced dynasearch neighborhood for the single-machine total weighted tardiness scheduling problem Operations Research Letters 32 68 72 10.1016/S0167-6377(03)00064-6
9. Ibaraki, T. (1987). Enumerative approaches to combinatorial optimization. Annals of Operations Research, 10-11.
10. T. Ibaraki Y. Nakamura 1994 A dynamic programming method for single machine scheduling European Journal of Operational Research 76 72 82 10.1016/0377-2217(94)90007-8
11. C.-F. Liaw 1999 A branch-and-bound algorithm for the single machine earliness and tardiness scheduling problem Computers & Operations Research 26 679 693 10.1016/S0305-0548(98)00081-1 (Pubitemid 29346445)
12. Y. Pan L. Shi 2007 On the equivalence of the max-min transportation lower bound and the time-indexed lower bound for single-machine scheduling problems Mathematical Programming, Series A 110 543 559 10.1007/s10107-006-0013-4 (Pubitemid 46862320)
13. L. Péridy É. Pinson D. Rivreau 2003 Using short-term memory to minimize the weighted number of late jobs on a single machine European Journal of Operational Research 148 591 603 10.1016/S0377-2217(02)00438-1
14. C. N. Potts L. N. Van Wassenhove 1985 A branch and bound algorithm for the total weighted tardiness problem Operations Research 33 363 377 10.1287/opre.33.2.363
15. A. A. B. Pritsker L. J. Watters P. M. Wolfe 1969 Multiproject scheduling with limited resources: a zero-one programming approach Management Science 16 93 108 10.1287/mnsc.16.1.93
16. Sourd, F. (2006). A reinforced Lagrangean relaxation for non-preemptive single machine problem. In Proceedings of tenth international workshop on project management and scheduling, Poznań, Poland, 26-28 April 2006.
17. Sourd, F. (2008). New exact algorithms for one-machine earliness-tardiness scheduling. INFORMS Journal on Computing. doi: 10.1287/ijoc.1080.0287
18. J. P. Sousa L. A. Wolsey 1992 A time indexed formulation of non-preemptive single machine scheduling problems Mathematical Programming 54 353 367 10.1007/BF01586059
19. Tanaka, S., Fujikuma, S., & Araki, M. (2006). A branch-and-bound algorithm based on Lagrangian relaxation for single-machine scheduling. In Proceedings of international symposium on scheduling 2006 (pp. 148-153), Tokyo, Japan, 18-20 July 2006.
20. J. M. van den Akker C. P. M. van Hoesel M. W. P. Savelsbergh 1999 A polyhedral approach to single-machine scheduling problems Mathematical Programming 85 541 572 10.1007/s101070050071
21. J. M. van den Akker C. A. J. Hurkens M. W. P. Savelsbergh 2000 Time-indexed formulations for machine scheduling problems: Column generation INFORMS Journal on Computing 12 111 124 10.1287/ijoc.12.2.111.11896