Optimization and Approximation in Deterministic Sequencing and Scheduling: a Survey

The theory of deterministic sequencing and scheduling has expanded rapidly during the past years. In this paper we survey the state of the art with respect to optimization and approximation algorithms and interpret these in terms of computational complexity theory. Special cases considered are single machine scheduling, identical, uniform and unrelated parallel machine scheduling, and open shop, flow shop and job shop scheduling. We indicate some problems for future research and include a selective bibliography.

[1]  Marc T. Kaufman Anomalies in scheduling unit-time tasks. , 1972 .

[2]  Ronald L. Graham,et al.  Performance Guarantees for Scheduling Algorithms , 1978, Oper. Res..

[3]  Edward G. Coffman,et al.  Optimal Preemptive Scheduling on Two-Processor Systems , 1969, IEEE Transactions on Computers.

[4]  J. Piehler,et al.  Ein Beitrag zum Reihenfolgeproblem , 1960, Unternehmensforschung.

[5]  L. G. Mitten Sequencing n Jobs on Two Machines with Arbitrary Time Lags , 1959 .

[6]  M. T. Kaufman,et al.  An Almost-Optimal Algorithm for the Assembly Line Scheduling Problem , 1974, IEEE Transactions on Computers.

[7]  Jane W.-S. Liu,et al.  Bounds on Scheduling Algorithms for Heterogeneous Comnputing Systems , 1974, IFIP Congress.

[8]  Kenneth R. Baker,et al.  Sequencing with due-dates and early start times to minimize maximum tardiness , 1974 .

[9]  Edward W. Davis,et al.  Project Scheduling under Resource Constraints—Historical Review and Categorization of Procedures , 1973 .

[10]  W. Szwarc Elimination methods in the m × n sequencing problem , 1971 .

[11]  Edward G. Coffman,et al.  Preemptive Scheduling of Real-Time Tasks on Multiprocessor Systems , 1970, JACM.

[12]  E. Lawler A “Pseudopolynomial” Algorithm for Sequencing Jobs to Minimize Total Tardiness , 1977 .

[13]  Edward G. Coffman,et al.  An Application of Bin-Packing to Multiprocessor Scheduling , 1978, SIAM J. Comput..

[14]  Ellis Horowitz,et al.  Exact and Approximate Algorithms for Scheduling Nonidentical Processors , 1976, JACM.

[15]  R. Gomory,et al.  Sequencing a One State-Variable Machine: A Solvable Case of the Traveling Salesman Problem , 1964 .

[16]  Wayne E. Smith Various optimizers for single‐stage production , 1956 .

[17]  Linus Schrage,et al.  Finding an Optimal Sequence by Dynamic Programming: An Extension to Precedence-Related Tasks , 1978, Oper. Res..

[18]  David S. Johnson,et al.  Scheduling Equal-Length Tasks Under Treelike Precedence Constraints to Minimize Maximum Lateness , 1977, Math. Oper. Res..

[19]  Oscar H. Ibarra,et al.  On Two—Processor Scheduling of One— or Two—Unit Time Tasks with Precedence Constraints , 1975 .

[20]  David S. Johnson,et al.  Fast Algorithms for Bin Packing , 1974, J. Comput. Syst. Sci..

[21]  John M. Charlton,et al.  A Generalized Machine-Scheduling Algorithm , 1970 .

[22]  Ravi Sethi,et al.  On the Complexity of Mean Flow Time Scheduling , 1977, Math. Oper. Res..

[23]  S. M. Johnson,et al.  Optimal two- and three-stage production schedules with setup times included , 1954 .

[24]  Dennis G. Kafura,et al.  An Algorithm to Design the Memory Configuration of a Computer Network , 1978, JACM.

[25]  S. S. Panwalkar,et al.  A Survey of Scheduling Rules , 1977, Oper. Res..

[26]  J. M. Moore An n Job, One Machine Sequencing Algorithm for Minimizing the Number of Late Jobs , 1968 .

[27]  Alfred V. Aho,et al.  The Transitive Reduction of a Directed Graph , 1972, SIAM J. Comput..

[28]  Andrew Chi-Chih Yao,et al.  Resource Constrained Scheduling as Generalized Bin Packing , 1976, J. Comb. Theory A.

[29]  Jan Karel Lenstra,et al.  Some Simple Applications of the Travelling Salesman Problem , 1975 .

[30]  T. C. Hu Parallel Sequencing and Assembly Line Problems , 1961 .

[31]  Robert McNaughton,et al.  Scheduling with Deadlines and Loss Functions , 1959 .

[32]  Eugene L. Lawler,et al.  Preemptive scheduling of uniform machines subject to release dates : (preprint) , 1979 .

[33]  David S. Johnson,et al.  Complexity Results for Multiprocessor Scheduling under Resource Constraints , 1975, SIAM J. Comput..

[34]  Toshihide Ibaraki,et al.  A Solvable Case of the One-Machine Scheduling Problem with Ready and Due Times , 1978, Oper. Res..

[35]  B. J. Lageweg,et al.  Minimizing Total Costs in One-Machine Scheduling , 1975, Oper. Res..

[36]  Shimon Even,et al.  Bounds for the Optimal Scheduling of n Jobs on m Processors , 1964 .

[37]  Jeffrey D. Ullman,et al.  NP-Complete Scheduling Problems , 1975, J. Comput. Syst. Sci..

[38]  Wlodzimierz Szwarc Optimal Elimination Methods in the m × n Flow-Shop Scheduling Problem , 1973, Oper. Res..

[39]  Pierre N. Robillard,et al.  Scheduling with earliest start and due date constraints on multiple machines , 1975 .

[40]  K. R. Baker,et al.  Minimizing Mean Flowtime in the Flow Shop with No Intermediate Queues , 1974 .

[41]  Jan Karel Lenstra,et al.  Complexity of machine scheduling problems , 1975 .

[42]  B. J. Lageweg,et al.  A General Bounding Scheme for the Permutation Flow-Shop Problem , 1978, Oper. Res..

[43]  W. A. Horn Technical Note - Minimizing Average Flow Time with Parallel Machines , 1973, Oper. Res..

[44]  E. Ignall,et al.  Application of the Branch and Bound Technique to Some Flow-Shop Scheduling Problems , 1965 .

[45]  David S. Johnson,et al.  Near-optimal bin packing algorithms , 1973 .

[46]  Jan Karel Lenstra,et al.  Complexity of Scheduling under Precedence Constraints , 1978, Oper. Res..

[47]  Kenneth R. Baker,et al.  Scheduling with parallel processors and linear delay costs , 1973 .

[48]  Edward G. Coffman,et al.  Scheduling independent tasks to reduce mean finishing time , 1974, CACM.

[49]  Oscar H. Ibarra,et al.  Heuristic Algorithms for Scheduling Independent Tasks on Nonidentical Processors , 1977, JACM.

[50]  Michael H. Rothkopf,et al.  Scheduling Independent Tasks on Parallel Processors , 1966 .

[51]  G. Thompson,et al.  Algorithms for Solving Production-Scheduling Problems , 1960 .

[52]  D. Adolphson Optimal linear-ordering. , 1973 .

[53]  J. Lenstra,et al.  Job-Shop Scheduling by Implicit Enumeration , 1977 .

[54]  Sartaj Sahni,et al.  Algorithms for Scheduling Independent Tasks , 1976, J. ACM.

[55]  James E. Day,et al.  Review of sequencing research , 1970 .

[56]  Peter J. Denning,et al.  A note on sub-expression ordering in the execution of arithmetic expressions , 1973, CACM.

[57]  J. M. Moore,et al.  A Functional Equation and its Application to Resource Allocation and Sequencing Problems , 1969 .

[58]  Graham McMahon,et al.  On Scheduling with Ready Times and Due Dates to Minimize Maximum Lateness , 1975, Oper. Res..

[59]  W. A. Horn Some simple scheduling algorithms , 1974 .

[60]  Teofilo F. Gonzalez,et al.  Open Shop Scheduling to Minimize Finish Time , 1976, JACM.

[61]  Donald L. Adolphson,et al.  Single Machine Job Sequencing with Precedence Constraints , 1977, SIAM J. Comput..

[62]  Shui Lam,et al.  A Level Algorithm for Preemptive Scheduling , 1977, J. ACM.

[63]  Clyde L. Monma,et al.  A general algorithm for optimal job sequencing with series-parallel precedence constraints , 1977 .

[64]  Ludo Gelders,et al.  Coordinating Aggregate and Detailed Scheduling in the One-Machine Job Shop: II - Computation and Structure , 1975, Oper. Res..

[65]  Richard M. Karp,et al.  On the Computational Complexity of Combinatorial Problems , 1975, Networks.

[66]  Oscar H. Ibarra,et al.  Bounds for LPT Schedules on Uniform Processors , 1977, SIAM J. Comput..

[67]  M. Fujii,et al.  Optimal Sequencing of Two Equivalent Processors , 1969 .

[68]  L. Gelders,et al.  Coordinating Aggregate and Detailed Scheduling Decisions in the One-Machine Job Shop: Part I. Theory , 2015, Oper. Res..

[69]  David S. Johnson,et al.  Two-Processor Scheduling with Start-Times and Deadlines , 1977, SIAM J. Comput..

[70]  Marshall L. Fisher,et al.  Optimal Solution of Scheduling Problems Using Lagrange Multipliers: Part I , 1973, Oper. Res..

[71]  Ravi Sethi,et al.  Scheduling Graphs on Two Processors , 1976, SIAM J. Comput..

[72]  W. A. Horn Single-Machine Job Sequencing with Treelike Precedence Ordering and Linear Delay Penalties , 1972 .

[73]  David S. Johnson,et al.  Approximation algorithms for combinatorial problems: an annotated bibliography , 1976 .

[74]  C. V. Ramamoorthy,et al.  On the Flow-Shop Sequencing Problem with No Wait in Process † , 1972 .

[75]  Chak-Kuen Wong,et al.  Worst-Case Analysis of a Placement Algorithm Related to Storage Allocation , 1975, SIAM J. Comput..

[76]  J. K. Lenstra,et al.  Computational complexity of discrete optimization problems , 1977 .

[77]  Teofilo F. Gonzalez,et al.  Preemptive Scheduling of Uniform Processor Systems , 1978, JACM.

[78]  C. L. Liu,et al.  Optimal Scheduling on Multi-Processor Computing Systems , 1972, SWAT.

[79]  Marshall L. Fisher,et al.  A dual algorithm for the one-machine scheduling problem , 1976, Math. Program..

[80]  Herb Schwetman,et al.  Analysis of Several Task-Scheduling Algorithms for a Model of Multiprogramming Computer Systems , 1975, JACM.

[81]  N. Hsu Elementary proof of Hu’s theorem on isotone mappings , 1966 .

[82]  William S. Gere Heuristics in Job Shop Scheduling , 1966 .

[83]  W. Townsend A Branch-and-Bound Method for Sequencing Problems with Linear and Exponential Penalty Functions , 1977 .

[84]  E. Lawler Sequencing Jobs to Minimize Total Weighted Completion Time Subject to Precedence Constraints , 1978 .

[85]  J. J. Brennan,et al.  An Improved Algorithm for Scheduling Jobs on Identical Machines , 1977 .

[86]  W. Townsend Note---Sequencing n Jobs on m Machines to Minimise Maximum Tardiness: A Branch-and-Bound Solution , 1977 .

[87]  Ronald L. Graham,et al.  Bounds for certain multiprocessing anomalies , 1966 .

[88]  Selmer Martin Johnson,et al.  Discussion: Sequencing n Jobs on Two Machines with Arbitrary Time Lags , 1959 .

[89]  James R. Jackson,et al.  An extension of Johnson's results on job IDT scheduling , 1956 .

[90]  Ravi Sethi,et al.  The Complexity of Flowshop and Jobshop Scheduling , 1976, Math. Oper. Res..

[91]  B. J. Lageweg,et al.  Minimizing maximum lateness on one machine : Computational experience and some applications , 1976 .

[92]  David S. Johnson,et al.  Scheduling Tasks with Nonuniform Deadlines on Two Processors , 1976, J. ACM.

[93]  Salah E. Elmaghraby,et al.  On the Scheduling of Jobs on a Number of Identical Machines. , 1972 .

[94]  D. G. KAFURA,et al.  Task Scheduling on a Multiprocessor System with Independent Memories , 1977, SIAM J. Comput..

[95]  Teofilo F. Gonzalez,et al.  A Note on Open Shop Preemptive Schedules , 1979, IEEE Transactions on Computers.

[96]  Ronald L. Graham,et al.  Bounds on Multiprocessing Timing Anomalies , 1969, SIAM Journal of Applied Mathematics.

[97]  Shui Lam,et al.  Worst Case Analysis of Two Scheduling Algorithms , 1977, SIAM J. Comput..

[98]  Eugene L. Lawler,et al.  Optimal Sequencing of a Single Machine Subject to Precedence Constraints , 1973 .

[99]  D. A. Wismer,et al.  Solution of the Flowshop-Scheduling Problem with No Intermediate Queues , 1972, Oper. Res..

[100]  Yoichi Muraoka,et al.  Parallelism exposure and exploitation in programs , 1971 .

[101]  Jeffrey D. Ullman,et al.  Worst-Case Performance Bounds for Simple One-Dimensional Packing Algorithms , 1974, SIAM J. Comput..

[102]  Teofilo F. Gonzalez,et al.  Flowshop and Jobshop Schedules: Complexity and Approximation , 1978, Oper. Res..

[103]  Jeffrey B. Sidney,et al.  Decomposition Algorithms for Single-Machine Sequencing with Precedence Relations and Deferral Costs , 1975, Oper. Res..

[104]  Eugene L. Lawler,et al.  On Preemptive Scheduling of Unrelated Parallel Processors by Linear Programming , 1978, JACM.

[105]  Wlodzimierz Szwarc Technical Note - Dominance Conditions for the Three-Machine Flow-Shop Problem , 1978, Oper. Res..

[106]  Jatinder N. D. Gupta,et al.  Technical Note - Improved Dominance Conditions for the Three-Machine Flowshop Scheduling Problem , 1978, Oper. Res..

[107]  Ronald L. Graham,et al.  Bounds for Multiprocessor Scheduling with Resource Constraints , 1975, SIAM J. Comput..

[108]  Wlodzimierz Szwarc On some sequencing problems , 1968 .

[109]  C. L. Liu,et al.  On a Class of Scheduling Algorithms for Multiprocessors Computing Systems , 1974, Sagamore Computer Conference.