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Volumn 30, Issue 4, 2005, Pages 1005-1021

Single-machine scheduling with precedence constraints

Author keywords

Approximation algorithm; Integer programming formulation; Linear ordering; Linear programming relaxation; Partial order; Scheduling; Vertex cover

Indexed keywords

APPROXIMATION ALGORITHM; INTEGER PROGRAMMING FORMULATION; LINEAR ORDERING; LINEAR PROGRAMMING RELAXATION; PARTIAL ORDER; VERTEX COVER;

EID: 31144479402     PISSN: 0364765X     EISSN: 15265471     Source Type: Journal    
DOI: 10.1287/moor.1050.0158     Document Type: Article
Times cited : (64)

References (36)
  • 1
    • 0022135711 scopus 로고
    • On the facial structure of scheduling polyhedra
    • Balas, E. 1985. On the facial structure of scheduling polyhedra. Math. Programming Stud. 24 179-218.
    • (1985) Math. Programming Stud. , vol.24 , pp. 179-218
    • Balas, E.1
  • 2
    • 0000190029 scopus 로고
    • On a selection problem
    • Balinski, M. 1970. On a selection problem. Management Sci. 17 230-231.
    • (1970) Management Sci. , vol.17 , pp. 230-231
    • Balinski, M.1
  • 3
    • 0004659229 scopus 로고
    • The poset scheduling problem
    • Chang, G. J., J. Edmonds. 1985. The poset scheduling problem. Order 2 113-118.
    • (1985) Order , vol.2 , pp. 113-118
    • Chang, G.J.1    Edmonds, J.2
  • 4
    • 0001808449 scopus 로고    scopus 로고
    • Precedence constrained scheduling to minimize sum of weighted completion time on a single machine
    • Chekuri, C., R. Motwani. 1999. Precedence constrained scheduling to minimize sum of weighted completion time on a single machine. Discrete Appl. Math. 98 29-38.
    • (1999) Discrete Appl. Math. , vol.98 , pp. 29-38
    • Chekuri, C.1    Motwani, R.2
  • 5
    • 0033358135 scopus 로고    scopus 로고
    • A half-integral linear programming relaxation for scheduling precedence-constrained jobs on a single machine
    • Chudak, F. A., D. S. Hochbaum. 1999. A half-integral linear programming relaxation for scheduling precedence-constrained jobs on a single machine. Oper. Res. Lett. 25 199-204.
    • (1999) Oper. Res. Lett. , vol.25 , pp. 199-204
    • Chudak, F.A.1    Hochbaum, D.S.2
  • 7
    • 0001559895 scopus 로고
    • Formulating the single machine sequencing problem with release dates as a mixed integer program
    • Dyer, M. E., L. A. Wolsey. 1990. Formulating the single machine sequencing problem with release dates as a mixed integer program. Discrete Appl. Math. 26 255-270.
    • (1990) Discrete Appl. Math. , vol.26 , pp. 255-270
    • Dyer, M.E.1    Wolsey, L.A.2
  • 8
    • 0000552246 scopus 로고
    • Bounds for the optimal scheduling of n jobs on m processors
    • Eastman, W. L., S. Even, I. Isaacs. 1964. Bounds for the optimal scheduling of n jobs on m processors. Management Sci. 11 268-279.
    • (1964) Management Sci. , vol.11 , pp. 268-279
    • Eastman, W.L.1    Even, S.2    Isaacs, I.3
  • 9
    • 0041480788 scopus 로고    scopus 로고
    • Two-dimensional Gantt charts and a scheduling algorithm of Lawler
    • Goemans, M. X., D. P. Williamson. 2000. Two-dimensional Gantt charts and a scheduling algorithm of Lawler. SIAM J. Discrete Math. 13 281-294.
    • (2000) SIAM J. Discrete Math. , vol.13 , pp. 281-294
    • Goemans, M.X.1    Williamson, D.P.2
  • 10
    • 74849101820 scopus 로고
    • Optimization and approximation in deterministic sequencing and scheduling: A survey
    • Graham, R. L., E. L. Lawler, J. K. Lenstra, A. H. G. Rinnooy Kan. 1979. Optimization and approximation in deterministic sequencing and scheduling: A survey. Ann. Discrete Math. 5 287-326.
    • (1979) Ann. Discrete Math. , vol.5 , pp. 287-326
    • Graham, R.L.1    Lawler, E.L.2    Lenstra, J.K.3    Kan, A.H.G.R.4
  • 11
    • 84983439747 scopus 로고    scopus 로고
    • Scheduling to minimize average completion time: Off-line and on-line algorithms
    • Atlanta, GA. SIAM, Philadelphia, PA
    • Hall, L. A., D. B. Shmoys, J. Wein. 1996. Scheduling to minimize average completion time: Off-line and on-line algorithms. Proc. 7th Annual ACM-SIAM Sympos. on Discrete Algorithms, Atlanta, GA. SIAM, Philadelphia, PA, 142-151.
    • (1996) Proc. 7th Annual ACM-SIAM Sympos. on Discrete Algorithms , pp. 142-151
    • Hall, L.A.1    Shmoys, D.B.2    Wein, J.3
  • 12
    • 0031207982 scopus 로고    scopus 로고
    • Scheduling to minimize average completion time: Off-line and on-line approximation algorithms
    • Hall, L. A., A. S. Schulz, D. B. Shmoys, J. Wein. 1997. Scheduling to minimize average completion time: Off-line and on-line approximation algorithms. Math. Oper. Res. 22 513-544.
    • (1997) Math. Oper. Res. , vol.22 , pp. 513-544
    • Hall, L.A.1    Schulz, A.S.2    Shmoys, D.B.3    Wein, J.4
  • 13
    • 0020822226 scopus 로고
    • Efficient bounds for the stable set, vertex cover and set packing problems
    • Hochbaum, D. S. 1983. Efficient bounds for the stable set, vertex cover and set packing problems. Discrete Appl. Math. 6 243-254.
    • (1983) Discrete Appl. Math. , vol.6 , pp. 243-254
    • Hochbaum, D.S.1
  • 14
    • 84938098905 scopus 로고    scopus 로고
    • Partially-ordered knapsack and applications to scheduling
    • R. H. Möhring, R. Raman, eds. Algorithms-ESA 2002. Springer, Heidelberg, Germany
    • Kolliopoulos, S. G., G. Steiner. 2002. Partially-ordered knapsack and applications to scheduling. R. H. Möhring, R. Raman, eds. Algorithms-ESA 2002, Vol. 2461. Lecture Notes in Computer Science. Springer, Heidelberg, Germany, 612-624.
    • (2002) Lecture Notes in Computer Science , vol.2461 , pp. 612-624
    • Kolliopoulos, S.G.1    Steiner, G.2
  • 15
    • 77951587888 scopus 로고
    • Sequencing jobs to minimize total weighted completion time subject to precedence constraints
    • Lawler, E. L. 1978. Sequencing jobs to minimize total weighted completion time subject to precedence constraints. Ann. Discrete. Math. 2 75-90.
    • (1978) Ann. Discrete. Math. , vol.2 , pp. 75-90
    • Lawler, E.L.1
  • 16
    • 0017924416 scopus 로고
    • Complexity of scheduling under precedence constraints
    • Lenstra, J. K., A. H. G. Rinnooy Kan. 1978. Complexity of scheduling under precedence constraints. Oper. Res. 26 22-35.
    • (1978) Oper. Res. , vol.26 , pp. 22-35
    • Lenstra, J.K.1    Kan, A.H.G.R.2
  • 17
    • 4344662655 scopus 로고    scopus 로고
    • Decompositions, network flows, and a precedence constrained single-machine scheduling problem
    • Margot, F., M. Queyranne, Y. Wang. 2003. Decompositions, network flows, and a precedence constrained single-machine scheduling problem. Oper. Res. 51 981-992.
    • (2003) Oper. Res. , vol.51 , pp. 981-992
    • Margot, F.1    Queyranne, M.2    Wang, Y.3
  • 18
    • 0000515937 scopus 로고
    • Computationally tractable classes of ordered sets
    • I. Rival, ed. Kluwer Academic, Dordrecht, The Netherlands
    • Möhring, R. H. 1989. Computationally tractable classes of ordered sets. I. Rival, ed. Algorithms and Order, Kluwer Academic, Dordrecht, The Netherlands, 105-193.
    • (1989) Algorithms and Order , pp. 105-193
    • Möhring, R.H.1
  • 19
    • 0016028005 scopus 로고
    • Properties of vertex packing and independence system polyhedra
    • Nemhauser, G. L., L. E. Trotter, Jr. 1974. Properties of vertex packing and independence system polyhedra. Math. Programming 6 48-61.
    • (1974) Math. Programming , vol.6 , pp. 48-61
    • Nemhauser, G.L.1    Trotter Jr., L.E.2
  • 20
    • 34250404286 scopus 로고
    • Vertex packing: Structural properties and algorithms
    • Nemhauser, G. L., L. E. Trotter, Jr. 1975. Vertex packing: Structural properties and algorithms. Math. Programming 8 232-248.
    • (1975) Math. Programming , vol.8 , pp. 232-248
    • Nemhauser, G.L.1    Trotter Jr., L.E.2
  • 21
    • 31144451826 scopus 로고
    • Colloquium Publications. American Mathematical Society, Providence, RI
    • Ore, O. 1962. Theory of Graphs, Vol. XXXVIII, Colloquium Publications. American Mathematical Society, Providence, RI.
    • (1962) Theory of Graphs , vol.38
    • Ore, O.1
  • 22
    • 0016972463 scopus 로고
    • Maximal closure of a graph and applications to combinatorial problems
    • Picard, J.-C. 1976. Maximal closure of a graph and applications to combinatorial problems. Management Sci. 22 1268-1272.
    • (1976) Management Sci. , vol.22 , pp. 1268-1272
    • Picard, J.-C.1
  • 23
    • 0002694122 scopus 로고
    • On the structure of all minimum cuts in a network and applications
    • Picard, J.-C., M. Queyranne. 1980. On the structure of all minimum cuts in a network and applications. Math. Programming Stud. 13 8-16.
    • (1980) Math. Programming Stud. , vol.13 , pp. 8-16
    • Picard, J.-C.1    Queyranne, M.2
  • 24
    • 0013141214 scopus 로고
    • Transitive orientation of graphs and identification of permutation graphs
    • Pnueli, A., A. Lempel, S. Even. 1971. Transitive orientation of graphs and identification of permutation graphs. Canadian J. Math. 23 160-175.
    • (1971) Canadian J. Math. , vol.23 , pp. 160-175
    • Pnueli, A.1    Lempel, A.2    Even, S.3
  • 25
    • 0042983555 scopus 로고
    • An algorithm for the single machine sequencing problem with precedence constraints
    • Potts, C. N. 1980. An algorithm for the single machine sequencing problem with precedence constraints. Math. Programming Stud. 13 78-87.
    • (1980) Math. Programming Stud. , vol.13 , pp. 78-87
    • Potts, C.N.1
  • 26
    • 0001267667 scopus 로고
    • Structure of a simple scheduling polyhedron
    • Queyranne, M. 1993. Structure of a simple scheduling polyhedron. Math. Programming 58 263-285.
    • (1993) Math. Programming , vol.58 , pp. 263-285
    • Queyranne, M.1
  • 27
    • 0003838512 scopus 로고
    • Polyhedral approaches to machine scheduling
    • Department of Mathematics, Technische Universität Berlin, Berlin, Germany
    • Queyranne, M., A. S. Schulz. 1994. Polyhedral approaches to machine scheduling. Technical report 408/1994, Department of Mathematics, Technische Universität Berlin, Berlin, Germany.
    • (1994) Technical Report , vol.408 , Issue.1994
    • Queyranne, M.1    Schulz, A.S.2
  • 28
    • 0041456171 scopus 로고
    • Single-machine scheduling polyhedra with precedence constraints
    • Queyranne, M., Y. Wang. 1991. Single-machine scheduling polyhedra with precedence constraints. Math. Oper. Res. 16 1-20.
    • (1991) Math. Oper. Res. , vol.16 , pp. 1-20
    • Queyranne, M.1    Wang, Y.2
  • 29
    • 0014869124 scopus 로고
    • A selection problem of shared fixed costs and network flows
    • Rhys, J. M. W. 1970. A selection problem of shared fixed costs and network flows. Management Sci. 17 200-207.
    • (1970) Management Sci. , vol.17 , pp. 200-207
    • Rhys, J.M.W.1
  • 30
    • 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, M. Queyranne, eds. Integer Programming and Combinatorial Optimization, Springer, Heidelberg, Germany
    • Schulz, A. S. 1996. Scheduling to minimize total weighted completion time: Performance guarantees of LP-based heuristics and lower bounds. W. H. Cunningham, S. T. McCormick, M. Queyranne, eds. Integer Programming and Combinatorial Optimization, Vol. 1084. Lecture Notes in Computer Science, Springer, Heidelberg, Germany, 301-315.
    • (1996) Lecture Notes in Computer Science , vol.1084 , pp. 301-315
    • Schulz, A.S.1
  • 31
    • 84957662347 scopus 로고    scopus 로고
    • Random-based scheduling: New approximations and LP lower bounds
    • J. D. P. Rolim, ed. Randomization and Approximation Techniques in Computer Science, Springer, Heidelberg, Germany
    • Schulz, A. S., M. Skutella. 1997. Random-based scheduling: New approximations and LP lower bounds. J. D. P. Rolim, ed. Randomization and Approximation Techniques in Computer Science, Vol. 1269. Lecture Notes in Computer Science, Springer, Heidelberg, Germany, 119-133.
    • (1997) Lecture Notes in Computer Science , vol.1269 , pp. 119-133
    • Schulz, A.S.1    Skutella, M.2
  • 32
    • 0016483826 scopus 로고
    • Decomposition algorithms for single machine scheduling with precedence relations and deferral costs
    • Sidney, J. B. 1975. Decomposition algorithms for single machine scheduling with precedence relations and deferral costs. Oper: Res. 23 283-298.
    • (1975) Oper: Res. , vol.23 , pp. 283-298
    • Sidney, J.B.1
  • 33
    • 0002066821 scopus 로고
    • Various optimizers for single-stage production
    • Smith, W. E. 1956. Various optimizers for single-stage production. Naval Res. Logist. Quart. 3 59-66.
    • (1956) Naval Res. Logist. Quart. , vol.3 , pp. 59-66
    • Smith, W.E.1
  • 34
    • 0042863253 scopus 로고    scopus 로고
    • On the approximability of average completion time scheduling under precedence constraints
    • Woeginger, G. J. 2003. On the approximability of average completion time scheduling under precedence constraints. Discrete Appl. Math. 131 237-252.
    • (2003) Discrete Appl. Math. , vol.131 , pp. 237-252
    • Woeginger, G.J.1
  • 35
    • 6244271807 scopus 로고
    • Mixed integer programming formulations for production planning and scheduling problems
    • MIT, Cambridge, MA
    • Wolsey, L. A. 1985. Mixed integer programming formulations for production planning and scheduling problems. Invited talk at the 12th Internat. Sympos. Math. Programming, MIT, Cambridge, MA.
    • (1985) Invited Talk at the 12th Internat. Sympos. Math. Programming
    • Wolsey, L.A.1
  • 36
    • 0343107232 scopus 로고
    • Formulating single machine scheduling problems with precedence constraints
    • J. J. Gabszewicz, J. F. Richard, L. A. Wolsey, eds. North-Holland, Amsterdam, The Netherlands
    • Wolsey, L. A. 1990. Formulating single machine scheduling problems with precedence constraints. J. J. Gabszewicz, J. F. Richard, L. A. Wolsey, eds. Economic Decision-Making: Games, Econometrics and Optimisation, North-Holland, Amsterdam, The Netherlands, 473-484.
    • (1990) Economic Decision-making: Games, Econometrics and Optimisation , pp. 473-484
    • Wolsey, L.A.1


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