On the asymptotic optimality of the SPT rule for the flow shop average completion time problem

Operations Research

Volumn 48, Issue 4, 2000, Pages 615-622

  Xia, Cathy H ^a   Shanthikumar, J George ^b   Glynn, Peter W ^c  

^a IBM T J WATSON RESEARCH CENTER   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

^c STANFORD UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGEBRA; ASYMPTOTIC STABILITY; CRITICAL PATH ANALYSIS; MACHINE SHOPS; QUEUEING THEORY; RECURSIVE FUNCTIONS; STATISTICAL METHODS; TOTAL QUALITY MANAGEMENT;

AVERAGE COMPLETION TIME; FLOW SHOP; PERMUTATION SCHEDULE; SHORTEST PROCESSING TIME RULE; TOTAL SERVICE REQUIREMENT;

SCHEDULING;

EID: 0034223270     PISSN: 0030364X     EISSN: None     Source Type: Journal    
DOI: 10.1287/opre.48.4.615.12423     Document Type: Article

References (19)

1. Burkholder, D., D. Davis, R. Gundy. 1972. Integral inequalities for convex functions of operators on martingales. Proc. Sixth Berkeley Sympos. Math. Statist. Probab., Vol. 2. Univ. of California Press, Berkeley, CA, 223-240.
2. Buzacott, J., J.G. Shanthikumar. 1993. Stochastic Models of Manufacturing Systems. Prentice Hall, Englewood Cliffs, NJ.
3. Chung, K. L. 1974. A Course in Probability Theory. Academic Press, New York.
4. Conway, R. W., W. L. Maxwell, L. W. Miller. 1967. Theory of Scheduling. Addison-Wesley, Reading, MA.
5. Garey, M. R., D. S. Johnson, R. Sethi. 1976. The complexity of flowshop and jobshop scheduling. Math. Oper. Res. 1 117-129.
6. Glynn, P. W., W. Whitt. 1991. Departures from many queues in series. Ann. Appl. Probab. 4 546-572.
7. Hillier, F. S., R. M. Boling. 1979. On the optimal allocation of work in symmetric balanced production line systems with variable operation times. Management Sci. 25 721-728.
8. Kaminsky, P., D. Simchi-Levi. 1996a. Probabilistic analysis and practical algorithms for the flow shop weighted completion time problem. Oper. Res. 46 872-882.
9. _,_. 1996b. The asymptotic optimality of the SPT rule for the flow shop mean completion lime problem. To appear in Oper. Res.
10. Krone, M. J., K. Steiglitz. 1974. Heuristic programming solutions of a flowshop scheduling problem. Oper. Res. 22 629-638.
11. Muth, E. J. 1979. The reversibility property of production lines. Management Sci. 25 152-158.
12. Pinedo, M. 1995a. Minimizing the expected makespan in stochastic flow shops. Oper. Res. 30 148-162.
13. _. 1995b. Scheduling: Theory, Algorithms and Systems. Prentice Hall, Englewood Cliffs, NJ.
14. Shanthikumar, J. G., S. Xu. 1997. Asymptotically optimal routing and service rate allocation in a multi-server queueing system. Oper. Res. 45 464-469.
15. Van de Velde, S. L. 1990. Minimizing the sum of the job completion times in the two-machine flow shop by Lagrangean relaxation. Ann. Oper. Res. 26 257-268.
16. Weber, R. R. 1992. The interchangeability of tandem queues with heterogeneous customers and dependent service times. Adv. Appl. Prob. 24 727-737.
17. Williams, D. 1991. Probability with Martingales. University Press, Cambridge, UK.
18. Xia, C. H. 1999. Dynamic scheduling of queuing systems with applications to computer networks and flexible manufacturing. Ph.D. Thesis. Stanford University.
19. Xia, C. H., J. G. Shanthikumar, 1998. Optimal and asymptotically optimal scheduling - an extension of the cμ rule, Working Paper, Stanford University.