Theory of Scheduling
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Theory of Scheduling

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This comprehensive text explores the mathematical models underlying the theory of scheduling. Organized according to scheduling problem type, it examines three solution techniques: algebraic, probabilistic, and Monte Carlo simulation by computer. Topics include problems of sequence, measures for schedule evaluation, finite sequencing for a single machine, and further problems with one operation per job. Additional chapters cover flow-shop scheduling, the general n/m job-shop problem, general network problems related to scheduling, selection disciplines in a single-server queuing system, single-server queuing systems with setup classes, multiple-server queuing models, and experimental investigation of the continuous job-shop process. 1967 edition.
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Product details

  • Paperback | 304 pages
  • 156 x 226 x 15mm | 395g
  • New York, United States
  • English
  • Reprint
  • Illustrations, unspecified
  • 0486428176
  • 9780486428178
  • 1,308,770

Table of contents

Chapter 1
Problems of Sequence
1-1 "Questions of "pure" sequence"
1-2 The job-shop process
1-3 A classification of scheduling probems
Chapter 2
Measures for Schedule Evaluation
2-1 Variables that define a scheduling problem
2-2 Variables that describe the solution to a scheduling problem
2-3 Performance measures for the shop
2-4 The relationship between flow-time and inventory
2-5 Costs associated with scheudling decisions
Chapter 3
Finite Sequencing for a Single Machine
3-1 Permutation schedules
3-2 Sequencing according to processing-time
3-3 Sequencing according to due date
3-4 Random sequencing
3-5 Properties of antithetical rules
3-6 SPT sequencing with incomplete information
3-7 Sequencing against weighted measures of performance
3-8 Sequencing with multiple classes
Chapter 4
Further Problems with One Operation per Job
4-1 Sequence-dependent setup-times
4-1.1 "A "branch-and-bound" algorithm for the traveling-salesman problem"
4-1.2 Solution of the traveling-salesman problem by dynamic programming
4-1.3 "The "closest-unvisited-city" algorithm for the traveling-salesman problem"
4-2 Intermittent job arrivals
4-3 Required precedence among jobs
4-3.1 Required strings of jobs
4-3.2 General precedence constraints
4-4 Parallel machines
Chapter 5
Flow-Shop Scheduling
5-1 Permutation schedules
5-2 Minimizing maximum flow-time in a two-machine flow-shop
5-3 Minimizing mean flow-time in a two-machine flow-shop
5-4 The three-machine flow shop
5-5 Sequencing in large flow-shops
Chapter 6
The General n/m Job-Shop Problem
6-1 A graphical description of the problem
6-2 The two-machine job-shop problem
6-3 The two-job job-shop problem
6-4 Integer programming formulation of the job-shop problem
6-5 Types of schedules
6-6 Generation of schedules
6-7 Branch-and-bound approach to the job-shop problem
6-8 Examples of schedule generation
6-9 Probabilistic dispatching
6-10 Heuristic procedures
Chapter 7
General Network Problems Related to Scheduling
7-1 Critical route analysis
7-2 Shortest route determination
7-3 Assembly-line balancing problems
Chapter 8
Selection Disciplines in a Single-Server Queuing System
8-1 Queues with Poisson arrivals
8-2 System states
8-3 The busy period of a queue with Poisson arrivals
8-4 "The distribution of flow-time under the first-come, first-served discipline"
8-5 Selection disciplines that are independent of processing-times
8-5.1 Distribution of number of jobs in the system
8-5.2 "The last-come, first-served discipline"
8-5.3 The random rule
8-6 Nonpreemptive priority and shortest-processing-time disciplines
8-6.1 Nonpreemptive priority disciplines
8-6.2 The shortest-processing-time discipline
8-6.3 Multiple-level nonpreemptive-priority disciplines
8-7 Preemptive priortity disciplines
8-7.1 Preemptive-resume and preemptive-repeat disciplines
8-7.2 Semi-preemptive priority and shortest-remaining-processing-time disciplines
8-8 The due-date rule and related disciplines
8-9 The effect of processing-time-dependent disciplines on flow-time
8-10 Historical notes
Chapter 9
Single-Server Queuing Systems with Setup Classes
9-1 Preemptive-resume priorities with preemptive-repeat setup-times for each job
9-2 Alternating priority discipline without setup-time
9-3 "First-come, first-served with setup classes"
9-4 Alternating priority disciplines with setup-time
Chapter 10
Multiple-Server Queuing Models
10-1 State-dependent completion rates; multiple-channel queues
10-2 The output of a Poisson-exponential queuing system
10-3 Queues in series
10-4 General queue networks
Chapter 11
Experimental Investigation of the Continuous Job-Shop Process
11-1 Experimental conditions and procedures
11-2 The reduction of mean queue length and work-in-process inventory
11-2.1 Truncation of the shortest-processing-time rule
11-2.2 SPT sequencing with multiple classes
11-2.3 SPT sequencing with incomplete information
11-3 Sequencing against due-dates
11-3.1 Assignment of due-dates
11-3.2 A state-dependent due-date procedure
11-4 Investigations of more complex job-shop models
11-4.1 Flexibility in machine selection
11-4.2 Flexibility in operation sequence
11-4.3 Sequencing in an assembly shop
Bibliography
Appendix A
The Laplace-Stieltjes Transform of a Distribution Function
Appendix B
Experimental Results: n/m Job-Shop Problem
B-1 Mean flow-time
B-2 Maximum flow-time
B-3 Mean machine finish-time
Appendix C
Experimental Results: Continuous-Process Job-Shop Problem
C-1 Notation used in priority rules
C-2 Definition of priority rules for the RAND study
C-3 "Experimental investigation of priority assignment in a simple, symmetric, random-routed job-shop of 9 machines"
C-4 "Experimental results for a state-dependent due-date procedure in a simple, symmetric, random-routed job-shop of 8 machines"
C-5 Flexibility in machine selection in a symmetric random-routed job-shop of 9 machines
C-6 Flexibility in operation sequence in a symmetric random-routed job-shop of 9 machines
C-7 Sequencing in an assembly shop
Index
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