Efficient Lagrangian relaxation algorithms for industry size job-shop scheduling problems

IIE Transactions (Institute of Industrial Engineers)

Volumn 30, Issue 11, 1998, Pages 1085-1097

  Kaskavelis, Christos A ^b,c   Caramanis, Michael C ^a  

^a BOSTON UNIVERSITY   (United States)

^b TCA Inc   (United States)

^c CIMPLEST ^*

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; ASYMPTOTIC STABILITY; COSTS; INTEGER PROGRAMMING; LAGRANGE MULTIPLIERS; MANUFACTURE; OPERATIONS RESEARCH;

DUAL COST FUNCTION; INDUSTRY SIZE JOB SHOP SCHEDULING PROBLEMS; LAGRANGIAN RELAXATION ALGORITHMS;

SCHEDULING;

EID: 0032256280     PISSN: 0740817X     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1007515931780     Document Type: Article

References (22)

1. Fisher, M.L. (1971) Optimal solution of scheduling problems using Lagrange multipliers, part I. Operations Research, 21, 1114-1127.
2. Graves, S.C. (1981) A review of production scheduling. Operations Research, 18, 841-852.
3. Everett, III, H. (1963) Generalized Lagrange multiplier method for solving problems of optimum allocation of resources. Operations Research, 11, 399-4171.
4. Hoitomt, D.J., Luh, P.B., Max, E. and Pattipati, K.R. (1990) Scheduling jobs with simple precedence constraints on parallel machines. Control Systems Magazine, 10, 34-40.
5. Hoitomt, D.J., Luh, P.B., Pattipati, K.R. (1993) A practical approach to job shop scheduling problems. IEEE Transactions on Robotics and Automation, 9, 1-13.
6. Wang, J., Luh, P.B. and Zhao, X. (1997) "An optimization-based algorithm for job shop scheduling", SADHANA, a Journal of Indian Academy of Sciences, a Special issue on competitive manufacturing systems, Vol. 22, Part 2, April 1997, pp. 241-256.
7. Wang, J. and Luh, P.B. (1996) Scheduling of a machining center. Mathematical and Computer Modeling, 24, (11/12), 203-214.
8. Brooks, R. and Geoffrion, A. (1966) Finding Everett's Lagrange multipliers by linear programming. Operations Research, 17, 1149-1153.
9. Chen, H., Chu, C. and Proth J.M. (1995) A more efficient Lagrangian relaxation approach to job shop scheduling problems, in Proceedings of IEEE International Conference on Robotics and Automation, pp. 496-501.
10. Polyak, B.T. (1969) Minimization of unsmooth functionals. USSR Computational Mathematics and Mathematical Physics, 9, 14-29.
11. Held, M., Wolfe, P. and Crowder H.P. (1974) Validation of subgradient optimization. Mathematical Programming, 6, 62-68.
12. Goffin, J.L. (1977) On convergence rates of subgradient optimization methods. Mathematical Programming, 13, 329-347.
13. Tomastik, R.N. and Luh, P.B. (1993) The facet ascending algorithm for integer programming problems, in Proceedings of the 32nd IEEE Conference on Decision and Control, San Antonio, TX, pp. 2280-2884. Dec. 1993.
14. Tomastik, R.N., Luh, P.B. and Liu, G. (1996) Scheduling flexibly manufacturing systems for apparel production. IEEE Transactions on Robotics and Automation, 12, 789-799.
15. Kaskavelis, C.A. and Caramanis, M.C. (1994a) A Lagrangian relaxation based algorithm for scheduling multiple-part-type-production-systems: industrial implementation practice, in Proceedings of the 1994 Japan-USA Symposium on Flexible Automation, Kobe, Japan, pp. 173-180, SCI.
16. Kaskavelis, C.A. and Caramanis, M.C. (1994b) Application of a Lagrangian relaxation based scheduling algorithm to a semiconductor testing facility, in Proceedings of the 4th International Conference on Computer Integrated Manufacturing and Automation Technology, RPI, October 10-12, 94, IEEE Computer Society Press, Troy, NY, pp. 106-112.
17. Fisher, M.L. (1981) The Lagrangian relaxation method for solving integer programming problems. Management Science, 27, 1-18.
18. Goffin, J.L., Haurie, A. and Vial, J.P. (1992) Decomposition and the nondifierentiable optimization with the projective algorithm. Management Science, 38, No. 2, 284-302.
19. Kaskavelis, C.A. (1994) The Lagrangian relaxation scheduling algorithm: theoretical issues and applications to industry. Masters Thesis, Dept. of Manufacturing Engineering, Boston University, Boston MA.
20. Bertsekas, D.P. (1995) Non-linear Programming, Athena Scientific, Belmont, MA.
21. Kushner, H.J. and Yin, G. (1987) Stochastic approximation algorithms for parallel and distributed processing. Stochastics, 22, 219-250.
22. Vazquez-Abad, F.J., Cassandras, C.G. and Julka, V. (1998) Centralized and decentralized asynchronous optimization of stochastic discrete event systems. IEEE Transactions on Automatic Control, AC-43, 5, pp. 631-655.