Scheduling with Time-Changing Effects and Rate-Modifying Activities
In scheduling theory, the models that have attracted considerable attention during the last two decades allow the processing times to be variable, i.e., to be subjected to various effects that make the actual processing time of a job dependent on its location in a schedule. The impact of these effec...
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| Main Author | |
|---|---|
| Format | eBook Publication |
| Language | English |
| Published |
Cham
Springer Nature
2016
Springer International Publishing AG Springer International Publishing Springer |
| Edition | 1 |
| Series | International Series in Operations Research & Management Science |
| Subjects | |
| Online Access | Get full text |
| ISBN | 9783319395746 3319395742 3319395726 9783319395722 |
| ISSN | 0884-8289 2214-7934 |
| DOI | 10.1007/978-3-319-39574-6 |
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| Abstract | In scheduling theory, the models that have attracted considerable attention during the last two decades allow the processing times to be variable, i.e., to be subjected to various effects that make the actual processing time of a job dependent on its location in a schedule. The impact of these effects includes, but is not limited to, deterioration and learning. Under the first type of effect, the later a job is scheduled, the longer its actual processing time becomes. In the case of learning, delaying a job will result in shorter processing times. Scheduling with Time-Changing Effects and Rate-Modifying Activities covers and advances the state-of-the-art research in this area. The book focuses on single machine and parallel machine scheduling problems to minimize either the maximum completion time or the sum of completion times of all jobs, provided that the processing times are subject to various effects. Models that describe deterioration, learning and general non-monotone effects to be considered include positional, start-time dependent, cumulative and their combinations, which cover most of the traditionally used models. The authors also consider more enhanced models in which the decision-maker may insert certain Rate-Modifying Activities (RMA) on processing machines, such as for example, maintenance or rest periods. In any case, the processing times of jobs are not only dependent on effects mentioned above but also on the place of a job in a schedule relative to an RMA. For most of the enhanced models described in the book, polynomial-time algorithms are presented which are based on similar algorithmic ideas such as reduction to linear assignment problems (in a full form or in a reduced form), discrete convexity, and controlled generation of options |
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| AbstractList | In scheduling theory, the models that have attracted considerable attention during the last two decades allow the processing times to be variable, i.e., to be subjected to various effects that make the actual processing time of a job dependent on its location in a schedule. The impact of these effects includes, but is not limited to, deterioration and learning. Under the first type of effect, the later a job is scheduled, the longer its actual processing time becomes. In the case of learning, delaying a job will result in shorter processing times. Scheduling with Time-Changing Effects and Rate-Modifying Activities covers and advances the state-of-the-art research in this area. The book focuses on single machine and parallel machine scheduling problems to minimize either the maximum completion time or the sum of completion times of all jobs, provided that the processing times are subject to various effects. Models that describe deterioration, learning and general non-monotone effects to be considered include positional, start-time dependent, cumulative and their combinations, which cover most of the traditionally used models. The authors also consider more enhanced models in which the decision-maker may insert certain Rate-Modifying Activities (RMA) on processing machines, such as for example, maintenance or rest periods. In any case, the processing times of jobs are not only dependent on effects mentioned above but also on the place of a job in a schedule relative to an RMA. For most of the enhanced models described in the book, polynomial-time algorithms are presented which are based on similar algorithmic ideas such as reduction to linear assignment problems (in a full form or in a reduced form), discrete convexity, and controlled generation of options The book focuses on single machine and parallel machine scheduling problems to minimize either the maximum completion time or the sum of completion times of all jobs, provided that the processing times are subject to various effects. Models that describe deterioration, learning and general non-monotone effects to be considered include positional, start-time dependent, cumulative and their combinations, which cover most of the traditionally used models. The authors also consider more enhanced models in which the decision-maker may insert certain Rate-Modifying Activities (RMA) on processing machines, such as for example, maintenance or rest periods. In any case, the processing times of jobs are not only dependent on effects mentioned above but also on the place of a job in a schedule relative to an RMA. For most of the enhanced models described in the book, polynomial time algorithms are presented which are based on similar algorithmic ideas such as reduction to linear assignment problems (in a full form or in a reduced form), discrete convexity, and controlled generation of options.In scheduling theory, the models that have attracted considerable attention during the last two decades allow the processing times to be variable, i.e., to be subjected to various effects that make the actual processing time of a job dependent on its location in a schedule. The impact of these effects includes, but is not limited to, deterioration and learning. Under the first type of effect, the later a job is scheduled, the longer its actual processing time becomes. In the case of learning, delaying a job will result in shorter processing times. Scheduling with Time-Changing Effects and Rate-Modifying Activities covers and advances the state-of-the-art research in this area. |
| Author | Strusevich, Vitaly A |
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| RelatedPersons | Zhu, Joe Hillier, Frederick S. Price, Camille C. |
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| Snippet | In scheduling theory, the models that have attracted considerable attention during the last two decades allow the processing times to be variable, i.e., to be... The book focuses on single machine and parallel machine scheduling problems to minimize either the maximum completion time or the sum of completion times of... |
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| SubjectTerms | Business Business and Management Business logistics Decision making Engineering economics Engineering Economics, Organization, Logistics, Marketing Engineering economy General management Logistics Operations research Operations Research/Decision Theory Production scheduling |
| TableOfContents | Intro -- Preface -- Contents -- About the Authors -- List of Figures -- List of Tables -- Part I Models and Methods of Classical Scheduling -- 1 Models and Concepts of Classical Scheduling -- 1.1 Classical Scheduling Models -- 1.1.1 Machine Environment -- 1.1.2 Job Characteristics -- 1.1.3 Optimality Criteria -- 1.2 Three-Field Classification Scheme -- 1.3 Computational Complexity -- 1.3.1 Time Complexity of Algorithms -- 1.3.2 Hard and Easy Problems -- 1.3.3 Implications to Scheduling -- 1.3.4 Approximation Algorithms -- References -- 2 Pairwise Interchange Argument and Priority Rules -- 2.1 Minimizing a Linear Form -- 2.1.1 Minimizing Total Completion Time on a Single Machine -- 2.1.2 Minimizing the Sum of Products -- 2.2 Minimizing Total Weighted Completion Time -- 2.3 Minimizing Total Completion Time on Parallel Machines -- 2.3.1 Uniform Machines -- 2.3.2 Identical Machines -- 2.4 Bibliographic Notes -- References -- 3 Sequencing Under Precedence Constraints -- 3.1 Graphs, Posets, and Other Definitions -- 3.1.1 Reduction Graphs -- 3.1.2 Series-Parallel Graphs -- 3.2 Priority-Generating Functions -- 3.2.1 Minimizing Total Weighted Completion Time -- 3.2.2 Minimizing a Linear Form -- 3.2.3 Minimizing Makespan Versus Total Completion Time -- 3.3 Minimizing Priority-Generating Functions Under Series-Parallel Constraints -- 3.4 Bibliographic Notes -- References -- 4 Relevant Boolean Programming Problems -- 4.1 Linear Assignment Problems -- 4.1.1 Methods for Solving the Rectangular Assignment Problem -- 4.1.2 Minimizing Total Completion Times of Unrelated Machines -- 4.1.3 Linear Assignment Problems with a Product Matrix -- 4.2 Knapsack and Subset-Sum Problems -- 4.3 Half-Product: Approximation and Relaxation -- 4.3.1 Formulation and Approximation -- 4.3.2 Convex Half-Product and Its Continuous Relaxation -- 4.4 Symmetric Quadratic Functions 4.5 Bibliographic Notes -- 4.5.1 Assignment Problem -- 4.5.2 Linear Knapsack Problem -- 4.5.3 Half-Product Problem and Its Variants -- References -- 5 Convex Sequences and Combinatorial Counting -- 5.1 Introduction to Convex and V-Shaped Sequences -- 5.2 Convexity of a Sequence Involving Sums of Functions of Ceilings -- 5.3 Combinatorial Counting -- 5.4 Bibliographic Notes -- References -- Part II Scheduling with Time-Changing Effects -- 6 Introduction to Time-Changing Effects -- 6.1 Positional Effects -- 6.2 Time-Dependent Effects -- 6.3 Cumulative Effects -- References -- 7 Scheduling with Positional Effects -- 7.1 Scheduling Independent Jobs Under Job-Dependent Positional Effect -- 7.2 Scheduling Independent Jobs Under Job-Independent Positional Effect -- 7.2.1 Minimizing Makespan -- 7.2.2 Minimizing Total Flow Time -- 7.3 Scheduling with Series-Parallel Precedence Constraints Under Positional Effects -- 7.3.1 Exponential Positional Effect -- 7.3.2 Polynomial Positional Effect -- 7.4 Bibliographic Notes -- References -- 8 Scheduling with Pure and Combined Additive Start-Time-Dependent Effects -- 8.1 Scheduling Independent Jobs -- 8.1.1 Combined Effects -- 8.1.2 Job-Dependent Linear Effects -- 8.1.3 Job-Independent Linear Effects -- 8.2 Scheduling Under Precedence Constraints -- 8.2.1 Job-Dependent Linear Effects -- 8.2.2 Job-Independent Linear Effects -- 8.3 Bibliographic Notes -- 8.3.1 General Additive Job-Independent Effects -- 8.3.2 Linear Additive Job-Dependent Effects -- 8.3.3 Linear Additive Job-Independent Effects -- 8.3.4 Scheduling with Precedence Constraints -- References -- 9 Scheduling with Pure and Combined Multiplicative Start-Time-Dependent Effects -- 9.1 Scheduling Independent Jobs -- 9.1.1 Job-Independent Combined Multiplicative Nonlinear Effects -- 9.1.2 Job-Independent Combined Multiplicative Polynomial Effects 9.1.3 Pure Multiplicative Linear Effects -- 9.2 Scheduling Under Precedence Constraints -- 9.3 Bibliographic Notes -- References -- 10 Scheduling with Pure and Combined Cumulative Effects -- 10.1 Scheduling Independent Jobs with a Combined Job-Independent Cumulative Effect -- 10.1.1 Combining General Cumulative Effects with Positional Effects -- 10.1.2 Combining Polynomial Cumulative Effects with Positional Effects -- 10.2 Pure Cumulative Effects -- 10.2.1 Job-Dependent Linear Generalized Cumulative Effect -- 10.2.2 Job-Independent Linear Cumulative Effect -- 10.3 Scheduling Under Precedence Constraints -- 10.3.1 Minimizing Makespan -- 10.3.2 Minimizing Total Completion Time -- 10.4 Bibliographic Notes -- References -- 11 Scheduling on Parallel Machines with Various Effects -- 11.1 Combined Effects -- 11.1.1 Identical and Uniform Machines -- 11.1.2 Unrelated Machines -- 11.2 Start-Time-Dependent Job-Dependent Linear Effects -- 11.2.1 Minimizing Makespan: Complexity and Approximation Scheme -- 11.2.2 Minimizing Total Flow Time: Complexity -- 11.3 Start-Time-Dependent Job-Independent Linear Effects -- 11.3.1 Identical and Uniform Machines -- 11.3.2 Unrelated Machines -- 11.4 Bibliographic Notes -- References -- Part III Scheduling with Rate Modifying Activities -- 12 General Framework for Studying Models with Rate-Modifying Activities -- 12.1 Compulsory Maintenance -- 12.2 Flexible Maintenance -- 12.3 Rate-Modifying Activities -- 12.4 Changing Processing Times and Rate-Modifying Activities -- References -- 13 Scheduling with Fixed Compulsory Maintenance Periods -- 13.1 Makespan: Complexity and Approximation -- 13.1.1 Single Maintenance -- 13.1.2 Periodic Maintenance -- 13.2 Weighted Total Flow Time: Complexity for the Non-resumable Scenario -- 13.2.1 Properties of the Objective Function -- 13.2.2 Useful Lower Bounds 13.2.3 Computational Complexity -- 13.3 Weighted Total Flow Time: Complexity for the Resumable Scenario -- 13.3.1 Properties of the Objective Function -- 13.3.2 Computational Complexity -- 13.4 Weighted Total Flow Time: Approximation Algorithms and Schemes -- 13.4.1 Constant Ratio Approximation Algorithms -- 13.4.2 Approximation Schemes -- 13.5 Bibliographic Notes -- 13.5.1 Minimizing Makespan -- 13.5.2 Minimizing Weighted Total Flow Time: Complexity -- 13.5.3 Minimizing Weighted Total Flow Time: Approximation -- References -- 14 Scheduling with Flexible Maintenance -- 14.1 Flexible Maintenance: Start-Time Deadline -- 14.2 Flexible Maintenance Within a Window -- 14.2.1 Minimizing Makespan: Single Maintenance -- 14.2.2 Minimizing Makespan: Periodic Maintenance -- 14.2.3 Minimizing Total Completion Time -- 14.3 Bibliographic Notes -- References -- 15 Scheduling with Rate-Modifying Activities -- 15.1 Single Rate-Modifying Maintenance on a Single Machine -- 15.1.1 Minimizing Makespan -- 15.1.2 Minimizing Total Completion Time -- 15.2 Multiple Rate-Modifying Maintenance Periods on a Single Machine -- 15.2.1 Minimizing Makespan -- 15.2.2 Minimizing Total Completion Time -- 15.3 Bibliographic Notes -- References -- 16 Scheduling with Maintenance and Positional Effects -- 16.1 Job-Dependent Deterioration Effects -- 16.1.1 Computing Positional Weights -- 16.1.2 Reduction to Rectangular LAP -- 16.2 Job-Independent Effects -- 16.2.1 Computing Positional Weights -- 16.2.2 Reduction to LAP with a Product Matrix -- 16.2.3 On the Fly Decision Making -- 16.2.4 Binary Search in Convex Sequences -- 16.3 Bibliographic Notes -- References -- 17 Scheduling with Maintenance and Start-Time-Dependent Effects -- 17.1 Computing Positional Weights -- 17.2 Reduction to LAP with a Product Matrix -- 17.3 On the Fly Decision Making -- 17.4 Binary Search in Convex Sequences 17.5 Bibliographic Notes -- References -- 18 Scheduling with Rate-Modifying Activities and Enhanced Effects -- 18.1 Enhanced Model Description -- 18.2 Computing the Completion Times -- 18.3 Minimizing the Makespan -- 18.4 Minimizing the Total Completion Time -- 18.5 Some Reduced Models -- 18.5.1 Simple Combined Effects -- 18.5.2 Pure Positional Effects -- 18.5.3 Pure Time-Dependent Effects -- 18.6 Bibliographic Notes -- References -- 19 Scheduling with Maintenance and Linear Cumulative Effects -- 19.1 Half-Product Reformulations -- 19.2 Constant Maintenance: FPTAS via Subset-Sum -- 19.3 The General Problem: FPTAS via Half-Product -- 19.4 Bibliographic Notes -- References -- 20 Scheduling with Rate-Modifying Activities on Parallel Machines Under Various Effects -- 20.1 Generic Procedure for Parallel Machines -- 20.2 Models with Rate-Modifying Activities -- 20.2.1 Unrelated Machines -- 20.2.2 Uniform Machines -- 20.3 Models with Changing Processing Times and Rate-Modifying Activities -- 20.3.1 Unrelated Machines -- 20.3.2 Uniform Machines -- 20.4 Bibliographic Notes -- References -- Index |
| Title | Scheduling with Time-Changing Effects and Rate-Modifying Activities |
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