A branch-and-bound algorithm with Lagrangian relaxation to minimize total tardiness on identical parallel machines

International Journal of Production Economics

Volumn 113, Issue 1, 2008, Pages 446-458

  Tanaka, Shunji ^a   Araki, Mituhiko ^b  

^a KYOTO UNIVERSITY   (Japan)

^b MATSUE NATIONAL COLLEGE OF TECHNOLOGY   (Japan)

Author keywords

Branch and bound algorithm; Identical parallel machines; Lagrangian relaxation; Scheduling; Total tardiness

Indexed keywords

COMPUTATIONAL MECHANICS; LAGRANGE MULTIPLIERS; PARALLEL PROCESSING SYSTEMS; RELAXATION PROCESSES;

BRANCH-AND-BOUND ALGORITHM; IDENTICAL PARALLEL MACHINES; LAGRANGIAN RELAXATION;

ALGORITHMS;

EID: 41549132670     PISSN: 09255273     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijpe.2007.10.006     Document Type: Article

References (18)

1. Azizoglu M., and Kirca O. Tardiness minimization on parallel machines. International Journal of Production Economics 55 (1998) 163-168
2. Babu P., Peridy L., and Pinson E. A branch and bound algorithm to minimize total weighted tardiness on a single processor. Annals of Operations Research 129 (2004) 33-46
3. Barnes J.W., and Brennan J.J. An improved algorithm for scheduling jobs on identical machines. AIIE Transactions 9 (1977) 25-31
4. Elmaghraby S.E., and Park S.H. Scheduling jobs on a number of identical machines. AIIE Transactions 6 (1974) 1-13
5. Emmons H. One-machine sequencing to minimize certain functions of job tardiness. Operations Research 17 (1969) 701-715
6. Fisher M.L. A dual algorithm for the one-machine scheduling problem. Mathematical Programming 11 (1976) 229-251
7. Fisher M.L. The Lagrangian relaxation method for solving integer programming problems. Management Science 27 (1981) 1-18
8. Ho J.C., and Chang Y.-L. Heuristics for minimizing mean tardiness for m parallel machines. Naval Research Logistics 38 (1991) 367-381
9. Koulamas C. The total tardiness problem: Review and extensions. Operations Research 42 (1994) 1025-1041
10. Koulamas C. Polynomially solvable total tardiness problems: Review and extensions. Omega 25 (1997) 235-239
11. Lawler E.L. A "pseudopolynomial" algorithm for sequencing jobs to minimize total tardiness. Annals of Discrete Mathematics 1 (1977) 331-342
12. Liaw C.-F., Lin Y.-K., Cheng C.-Y., and Chen M. Scheduling unrelated parallel machines to minimize total weighted tardiness. Computers & Operations Research 30 (2003) 1777-1789
13. Luh P.B., Hoitomt D.J., Max E., and Pattipati K.R. Schedule generation and reconfiguration for parallel machines. IEEE Transactions on Robotics and Automation 6 (1990) 687-696
14. Root J.G. Scheduling with deadlines and loss functions on k parallel machines. Management Science 11 (1965) 460-475
15. Szwarc W., Croce F.D., and Grosso A. Solution of the single machine total tardiness problem. Journal of Scheduling 2 (1999) 55-71
16. Tansel B.C., Kara B.Y., and Sabuncuoglu I. An efficient algorithm for the single machine total tardiness problem. IIE Transactions 33 (2001) 661-674
17. Wilkerson L.J., and Irwin J.D. An improved method for scheduling independent tasks. AIIE Transactions 3 (1971) 239-245
18. Yalaoui F., and Chu C. Parallel machine scheduling to minimize total tardiness. International Journal of Production Economics 76 (2002) 265-279