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Volumn 15, Issue 2, 2002, Pages 165-192

Single machine scheduling with release dates

Author keywords

Approximation algorithm; LP relaxation; On line algorithm; Scheduling

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; COMPUTATIONAL COMPLEXITY; LINEAR PROGRAMMING; PROBLEM SOLVING; THEOREM PROVING;

EID: 0036487488     PISSN: 08954801     EISSN: None     Source Type: Journal    
DOI: 10.1137/S089548019936223X     Document Type: Article
Times cited : (108)

References (39)
  • 3
    • 0022135711 scopus 로고
    • On the facial structure of scheduling polyhedra
    • E. Balas, On the facial structure of scheduling polyhedra, Math. Programming Stud., 24 (1985), pp. 179-218.
    • (1985) Math. Programming Stud. , vol.24 , pp. 179-218
    • Balas, E.1
  • 4
    • 38249011510 scopus 로고
    • Scheduling with release dates on a single machine to minimize total weighted completion time
    • H. Belouadah, M. E. Posner, and C. N. Potts, Scheduling with release dates on a single machine to minimize total weighted completion time, Discrete Appl. Math., 36 (1992), pp. 213-231.
    • (1992) Discrete Appl. Math. , vol.36 , pp. 213-231
    • Belouadah, H.1    Posner, M.E.2    Potts, C.N.3
  • 6
    • 0036213040 scopus 로고    scopus 로고
    • Approximation techniques for average completion time scheduling
    • C. Chekuri, R. Motwani, B. Natarajan, and C. Stein, Approximation techniques for average completion time scheduling, SIAM J. Comput., 31 (2001), pp. 146-166.
    • (2001) SIAM J. Comput. , vol.31 , pp. 146-166
    • Chekuri, C.1    Motwani, R.2    Natarajan, B.3    Stein, C.4
  • 7
    • 84947273794 scopus 로고    scopus 로고
    • The asymptotic performance ratio of an on-line algorithm for uniform parallel machine scheduling with release dates
    • K. Aardal and B. Gerards, eds., Springer, Berlin
    • C.-F. Chou, M. Queyranne, and D. Simchi-Levi, The asymptotic performance ratio of an on-line algorithm for uniform parallel machine scheduling with release dates, in Integer Programming and Combinatorial Optimization, Lecture-Notes in Comput. Sci. 2081, K. Aardal and B. Gerards, eds., Springer, Berlin, 2001, pp. 45-59.
    • (2001) Integer Programming and Combinatorial Optimization, Lecture-Notes in Comput. Sci. , vol.2081 , pp. 45-59
    • Chou, C.-F.1    Queyranne, M.2    Simchi-Levi, D.3
  • 9
    • 0001559895 scopus 로고
    • Formulating the single machine sequencing problem with release dates as a mixed integer program
    • M. E. Dyer and L. A. Wolsey, Formulating the single machine sequencing problem with release dates as a mixed integer program, Discrete Appl. Math., 26 (1990), pp. 255-270.
    • (1990) Discrete Appl. Math. , vol.26 , pp. 255-270
    • Dyer, M.E.1    Wolsey, L.A.2
  • 10
    • 84947944584 scopus 로고    scopus 로고
    • A supermodular relaxation for scheduling with release dates
    • W. H. Cunningham, S. T. McCormick, and M. Queyranne, eds., Springer, Berlin
    • M. X. Goemans, A supermodular relaxation for scheduling with release dates, in Integer Programming and Combinatorial Optimization, Lecture Notes in Comput. Sci. 1084, W. H. Cunningham, S. T. McCormick, and M. Queyranne, eds., Springer, Berlin, 1996, pp. 288-300.
    • (1996) Integer Programming and Combinatorial Optimization, Lecture Notes in Comput. Sci. , vol.1084 , pp. 288-300
    • Goemans, M.X.1
  • 12
    • 74849101820 scopus 로고
    • Optimization and approximation in deterministic sequencing and scheduling: A survey
    • R. L. Graham, E. L. Lawler, J. K. Lenstra, and A. H. G. Rinnooy Kan, Optimization and approximation in deterministic sequencing and scheduling: A survey, Ann. Discrete Math., 5 (1979), pp. 287-326.
    • (1979) Ann. Discrete Math. , vol.5 , pp. 287-326
    • Graham, R.L.1    Lawler, E.L.2    Lenstra, J.K.3    Rinnooy Kan, A.H.G.4
  • 13
    • 0031207982 scopus 로고    scopus 로고
    • Scheduling to minimize average completion time: Off-line and on-line approximation algorithms
    • L. A. Hall, A. S. Schulz, D. B. Shmoys, and J. Wein, Scheduling to minimize average completion time: Off-line and on-line approximation algorithms, Math. Oper. Res., 22 (1997), pp. 513-544.
    • (1997) Math. Oper. Res. , vol.22 , pp. 513-544
    • Hall, L.A.1    Schulz, A.S.2    Shmoys, D.B.3    Wein, J.4
  • 15
    • 84947903026 scopus 로고    scopus 로고
    • Optimal on-line algorithms for single-machine scheduling
    • W. H. Cunningham, S. T. McCormick, and M. Queyranne, eds., Springer, Berlin
    • J. A. Hoogeveen, and A. P. A. Vestjens, Optimal on-line algorithms for single-machine scheduling, in Integer Programming and Combinatorial Optimization, Lecture Notes in Comput. Sci. 1084, W. H. Cunningham, S. T. McCormick, and M. Queyranne, eds., Springer, Berlin, 1996, pp. 404-414.
    • (1996) Integer Programming and Combinatorial Optimization, Lecture Notes in Comput. Sci. , vol.1084 , pp. 404-414
    • Hoogeveen, J.A.1    Vestjens, A.P.A.2
  • 16
    • 0002087256 scopus 로고
    • Preemptive scheduling of uniform machines subject to release dates
    • W. R. Pulleyblank, ed., Academic Press, New York
    • J. Labetoulle, E. L. Lawler, J. K. Lenstra, and A. H. G. Rinnooy Kan, Preemptive scheduling of uniform machines subject to release dates, in Progress in Combinatorial Optimization, W. R. Pulleyblank, ed., Academic Press, New York, 1984, pp. 245-261.
    • (1984) Progress in Combinatorial Optimization , pp. 245-261
    • Labetoulle, J.1    Lawler, E.L.2    Lenstra, J.K.3    Rinnooy Kan, A.H.G.4
  • 18
    • 0004168557 scopus 로고
    • Randomized Algorithms
    • Cambridge University Press, Cambridge, UK
    • R. Motwani and P. Raghavan, Randomized Algorithms, Cambridge University Press, Cambridge, UK, 1995.
    • (1995)
    • Motwani, R.1    Raghavan, P.2
  • 19
    • 84958753582 scopus 로고    scopus 로고
    • Approximation bounds for a general class of precedence constrained parallel machine scheduling problems
    • R. E. Bixby, E. A. Boyd, and R. Z. Ríos-Mercado, eds., Springer, Berlin; SIAM J. Comput., to appear
    • A. Munier, M. Queyranne, and A. S. Schulz, Approximation bounds for a general class of precedence constrained parallel machine scheduling problems, in Integer Programming and Combinatorial Optimization, Lecture Notes in Comput. Sci. 1412, R. E. Bixby, E. A. Boyd, and R. Z. Ríos-Mercado, eds., Springer, Berlin, 1998, pp. 367-382, SIAM J. Comput., to appear.
    • (1998) Integer Programming and Combinatorial Optimization, Lecture Notes in Comput. Sci. , vol.1412 , pp. 367-382
    • Munier, A.1    Queyranne, M.2    Schulz, A.S.3
  • 20
    • 0000095809 scopus 로고
    • An analysis of approximations for maximizing submodular set functions. I
    • G. L. Nemhauser, L. A. Wolsey, and M. L. Fisher, An analysis of approximations for maximizing submodular set functions. I, Math. Programming, 14 (1978), pp. 265-294.
    • (1978) Math. Programming , vol.14 , pp. 265-294
    • Nemhauser, G.L.1    Wolsey, L.A.2    Fisher, M.L.3
  • 21
    • 0041541787 scopus 로고    scopus 로고
    • Minimizing average completion time in the presence of release dates
    • C. Phillips, C. Stein, and J. Wein, Minimizing average completion time in the presence of release dates, Math. Programming, 82 (1998), pp. 199-223.
    • (1998) Math. Programming , vol.82 , pp. 199-223
    • Phillips, C.1    Stein, C.2    Wein, J.3
  • 22
    • 0001267667 scopus 로고
    • Structure of a simple scheduling polyhedron
    • M. Queyranne. Structure of a simple scheduling polyhedron, Math. Programming, 58 (1993), pp. 263-285.
    • (1993) Math. Programming , vol.58 , pp. 263-285
    • Queyranne, M.1
  • 23
    • 0003838512 scopus 로고
    • Polyhedral approaches to machine scheduling
    • Preprint 408, Department of Mathematics, Technische Universität Berlin, Germany
    • M. Queyranne and A. S. Schulz, Polyhedral Approaches to Machine Scheduling, Preprint 408, Department of Mathematics, Technische Universität Berlin, Germany, 1994.
    • (1994)
    • Queyranne, M.1    Schulz, A.S.2
  • 26
    • 84947916207 scopus 로고    scopus 로고
    • Scheduling to minimize total weighted completion time: Performance guarantees of LP-based heuristics and lower bounds
    • W. H. Cunningham, S. T. McCormick, and M. Queyranne, eds., Springer, Berlin
    • A. S. Schulz, Scheduling to minimize total weighted completion time: Performance guarantees of LP-based heuristics and lower bounds, in Integer Programming and Combinatorial Optimization, Lecture Notes in Comput. Sci. 1084, W. H. Cunningham, S. T. McCormick, and M. Queyranne, eds., Springer, Berlin, 1996, pp. 301-315.
    • (1996) Integer Programming and Combinatorial Optimization, Lecture Notes in Comput. Sci. , vol.1084 , pp. 301-315
    • Schulz, A.S.1
  • 28
    • 84949204738 scopus 로고    scopus 로고
    • Scheduling-LPs bear probabilities: Randomized approximations for min-sum criteria
    • Springer, Berlin; SIAM J. Discrete Math., to appear under the title "Scheduling unrelated machines by randomized rounding."
    • A. S. Schulz and M. Skutella, Scheduling-LPs bear probabilities: Randomized approximations for min-sum criteria, in Algorithms-ESA '97, Lecture Notes in Comput. Sci. 1284, Springer, Berlin, 1997, pp. 416-429, SIAM J. Discrete Math., to appear under the title "Scheduling unrelated machines by randomized rounding."
    • (1997) Algorithms-ESA '97, Lecture Notes in Comput. Sci. , vol.1284 , pp. 416-429
    • Schulz, A.S.1    Skutella, M.2
  • 29
    • 0003358528 scopus 로고    scopus 로고
    • The power of α-points in preemptive single machine scheduling
    • to appear
    • A. S. Schulz and M. Skutella, The power of α-points in preemptive single machine scheduling, J. Sched., 5 (2002), to appear.
    • (2002) J. Sched. , vol.5
    • Schulz, A.S.1    Skutella, M.2
  • 32
    • 0004194243 scopus 로고    scopus 로고
    • Approximation and randomization in scheduling
    • Ph.D. thesis, Technische Universität Berlin, Germany
    • M. Skutella, Approximation and Randomization in Scheduling, Ph.D. thesis, Technische Universität Berlin, Germany, 1998.
    • (1998)
    • Skutella, M.1
  • 33
    • 0000093702 scopus 로고    scopus 로고
    • Convex quadratic and semidefinite programming relaxations in scheduling
    • M. Skutella, Convex quadratic and semidefinite programming relaxations in scheduling, J. ACM, 48 (2001), pp. 206-242.
    • (2001) J. ACM , vol.48 , pp. 206-242
    • Skutella, M.1
  • 34
    • 0034138331 scopus 로고    scopus 로고
    • A PTAS for minimizing the total weighted completion time on identical parallel machines
    • M. Skutella and G. J. Woeginger, A PTAS for minimizing the total weighted completion time on identical parallel machines, Math. Oper. Res., 25 (2000), pp. 63-75.
    • (2000) Math. Oper. Res. , vol.25 , pp. 63-75
    • Skutella, M.1    Woeginger, G.J.2
  • 35
    • 0002066821 scopus 로고
    • Various optimizers for single-stage production
    • W. E. Smith, Various optimizers for single-stage production, Naval Res. Logist. Quart., 3 (1956), pp. 56-66.
    • (1956) Naval Res. Logist. Quart. , vol.3 , pp. 59-66
    • Smith, W.E.1
  • 36
    • 0011365668 scopus 로고    scopus 로고
    • private communication in [15]
    • L. Stougie, private communication in [15], 1995.
    • Stougie, L.1
  • 37
    • 0036543591 scopus 로고    scopus 로고
    • Randomized algorithms for on-line scheduling problems: How low can't you go?
    • to appear
    • L. Stougie and A. P. A. Vestjens, Randomized algorithms for on-line scheduling problems: How low can't you go? Oper. Res. Lett., to appear.
    • Oper. Res. Lett.
    • Stougie, L.1    Vestjens, A.P.A.2
  • 38
    • 84958758843 scopus 로고    scopus 로고
    • On the relationship between combinatorial and LP-based approaches to NP-hard scheduling problems
    • R. E. Bixby, E. A. Boyd, and R. Z. Ríos-Mercado, eds., Springer, Berlin
    • R. N. Uma and J. M. Wein, On the relationship between combinatorial and LP-based approaches to NP-hard scheduling problems, in Integer Programming and Combinatorial Optimization, Lecture Notes in Comput. Sci. 1412, R. E. Bixby, E. A. Boyd, and R. Z. Ríos-Mercado, eds., Springer, Berlin, 1998, pp. 394-408.
    • (1998) Integer Programming and Combinatorial Optimization, Lecture Notes in Comput. Sci. , vol.1412 , pp. 394-408
    • Uma, R.N.1    Wein, J.M.2
  • 39
    • 0004059194 scopus 로고    scopus 로고
    • On-line machine scheduling
    • Ph. D. thesis, Eindhoven University of Technology, The Netherlands
    • A. P. A. Vestjens, On-Line Machine Scheduling, Ph. D. thesis, Eindhoven University of Technology, The Netherlands, 1997.
    • (1997)
    • Vestjens, A.P.A.1


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