Gawiejnowicz Time-Dependent Scheduling

1. Auflage 2008
ISBN: 978-3-540-69446-5
Verlag: Springer Berlin Heidelberg
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 380 Seiten

Reihe: Monographs in Theoretical Computer Science. An EATCS Series

hebookpresentedtothereaderisdevotedtotime-dependentscheduling. TScheduling problems, in general, consist in the allocation of resources over time in order to perform a set of jobs. Any allocation that meets all requirements concerning the jobs and resources is called a feasible schedule. The quality of a schedule is measured by a criterion function. The aim of scheduling is to ?nd, among all feasible schedules, a schedule that optimizes the criterion function. A solution to an arbitrary scheduling problem consists in giving a polynomial-time algorithm generating either an optimal schedule or a schedule that is close to the optimal one, if the given scheduling problem has been proved to be computationally intractable. The scheduling problems are subject of interest of the scheduling theory, originated in mid-?fties of the twentieth century. The theory has been developing dynamically and new research areas constantly come into existence. The subject of this book, ti- dependent scheduling, is one of such areas. In time-dependent scheduling, the processing time of a job is variable and depends on the starting time of the job. This crucial assumption allows us to apply the scheduling theory to a broader spectrum of problems. For example, in the framework of the time-dependent scheduling theory we may consider the problems of repayment of multiple loans, ?re ?ghting and maintenance assignments. In this book, we will discuss algorithms and complexity issues concerning various time-dependent scheduling problems.

Autoren/Hrsg.

Gawiejnowicz, Stanislaw

Inhaltsverzeichnis

1;Preface;6
2;Contents;9
3;Part I FUNDAMENTALS;15
3.1;1 Preliminaries;16
3.1.1;1.1 Mathematical notation;16
3.1.2;1.2 Basic definitions and results;19
3.1.3;1.3 Bibliographic notes;26
3.2;2 Problems and algorithms;27
3.2.1;2.1 Decision and optimization problems;27
3.2.2;2.2 Basic concepts related to algorithms;29
3.2.3;2.3 Bibliographic notes;38
3.3;3 NP- complete problems;39
3.3.1;3.1 Basic definitions and results;39
3.3.2;3.2 Examples of NP- complete problems;43
3.3.3;3.3 Bibliographic notes;45
3.4;4 Basics of the scheduling theory;46
3.4.1;4.1 Parameters of the scheduling problem;46
3.4.2;4.2 The notion of schedule;50
3.4.3;4.3 The criteria of schedule optimality;54
3.4.4;4.4 Notation of scheduling problems;56
3.4.5;4.5 Bibliographic notes;57
3.5;5 Basics of time-dependent scheduling;58
3.5.1;5.1 The scheduling theory vs. time-dependent scheduling;58
3.5.2;5.2 Formulation of time-dependent scheduling problems;60
3.5.3;5.3 Terminology and notation;62
3.5.4;5.4 Applications of time-dependent scheduling;64
3.5.5;5.5 Bibliographic notes;67
4;Part II COMPLEXITY;68
4.1;6 Single-machine time-dependent scheduling;69
4.1.1;6.1 Minimizing the maximum completion time;69
4.1.2;6.2 Minimizing the total completion time;113
4.1.3;6.3 Minimizing the maximum lateness;128
4.1.4;6.4 Other criteria;133
4.1.5;6.5 Summary and tables;157
4.2;7 Parallel-machine time-dependent scheduling;164
4.2.1;7.1 Minimizing the maximum completion time;164
4.2.2;7.2 Minimizing the total completion time;169
4.2.3;7.3 Other criteria;173
4.2.4;7.4 Summary and tables;176
4.3;8 Dedicated-machine time-dependent scheduling;179
4.3.1;8.1 Minimizing the maximum completion time;179
4.3.2;8.2 Minimizing the total completion time;194
4.3.3;8.3 Minimizing the maximum lateness;200
4.3.4;8.4 Other criteria;202
4.3.5;8.5 Summary and tables;204
5;Part III ALGORITHMS;209
5.1;9 Approximation and heuristic algorithms;210
5.1.1;9.1 Minimizing the maximum completion time;210
5.1.2;9.2 Minimizing the total completion time;233
5.1.3;9.3 Minimizing the maximum lateness;241
5.1.4;9.4 Other criteria;243
5.1.5;9.5 Concluding remarks;247
5.2;10 Greedy algorithms based on signatures;252
5.2.1;10.1 Preliminaries;252
5.2.2;10.2 Basic properties of signatures;254
5.2.3;10.3 A greedy algorithm;258
5.2.4;10.4 Signatures of regular sequences;261
5.2.5;10.5 Concluding remarks;272
5.3;11 Local search algorithms;273
5.3.1;11.1 Preliminaries;273
5.3.2;11.2 Selected types of local search algorithms;275
5.3.3;11.3 Local search time-dependent scheduling algorithms;279
5.3.4;11.4 Concluding remarks;288
6;Part IV ADVANCED TOPICS;289
6.1;12 Matrix methods in time-dependent scheduling;290
6.1.1;12.1 Preliminaries;290
6.1.2;12.2 A matrix approach;291
6.1.3;12.3 The lp norm criterion;294
6.1.4;12.4 Equivalent problems;297
6.1.5;12.5 Concluding remarks and open problems;303
6.2;13 Scheduling dependent deteriorating jobs;304
6.2.1;13.1 Preliminaries;304
6.2.2;13.2 Chain precedence constraints;309
6.2.3;13.3 Tree and forest precedence constraints;312
6.2.4;13.4 Series-parallel constraints;317
6.2.5;13.5 General precedence constraints;320
6.2.6;13.6 Concluding remarks and open problems;323
6.3;14 Time-dependent scheduling with two criteria;325
6.3.1;14.1 Preliminaries;325
6.3.2;14.2 Pareto optimality;328
6.3.3;14.3 Scalar optimality;332
6.3.4;14.4 Computational experiments;339
6.3.5;14.5 Concluding remarks and open problems;341
7;Afterword;342
8;References;344
9;List of Figures;360
10;List of Tables;361
11;Author Index;364
12;Subject Index;368
13;Symbol Index;375