7 Scheduling with Positional Effects Scheduling Independent Jobs Under Job-Dependent Positional Effect Scheduling Independent

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1 Contents Part I Models and Methods of Classical Scheduling 1 Models and Concepts of Classical Scheduling Classical Scheduling Models Machine Environment Job Characteristics Optimality Criteria Three-Field Classification Scheme Computational Complexity Time Complexity of Algorithms Hard and Easy Problems Implications to Scheduling Approximation Algorithms References Pairwise Interchange Argument and Priority Rules Minimizing a Linear Form Minimizing Total Completion Time on a Single Machine Minimizing the Sum of Products Minimizing Total Weighted Completion Time Minimizing Total Completion Time on Parallel Machines Uniform Machines Identical Machines Bibliographic Notes References Sequencing Under Precedence Constraints Graphs, Posets, and Other Definitions Reduction Graphs Series-Parallel Graphs xi

2 xii Contents 3.2 Priority-Generating Functions Minimizing Total Weighted Completion Time Minimizing a Linear Form Minimizing Makespan Versus Total Completion Time Minimizing Priority-Generating Functions Under Series-Parallel Constraints Bibliographic Notes References Relevant Boolean Programming Problems Linear Assignment Problems Methods for Solving the Rectangular Assignment Problem Minimizing Total Completion Times of Unrelated Machines Linear Assignment Problems with a Product Matrix Knapsack and Subset-Sum Problems Half-Product: Approximation and Relaxation Formulation and Approximation Convex Half-Product and Its Continuous Relaxation Symmetric Quadratic Functions Bibliographic Notes Assignment Problem Linear Knapsack Problem Half-Product Problem and Its Variants References Convex Sequences and Combinatorial Counting Introduction to Convex and V-Shaped Sequences Convexity of a Sequence Involving Sums of Functions of Ceilings Combinatorial Counting Bibliographic Notes References Part II Scheduling with Time-Changing Effects 6 Introduction to Time-Changing Effects Positional Effects Time-Dependent Effects Cumulative Effects References

3 Contents xiii 7 Scheduling with Positional Effects Scheduling Independent Jobs Under Job-Dependent Positional Effect Scheduling Independent Jobs Under Job-Independent Positional Effect Minimizing Makespan Minimizing Total Flow Time Scheduling with Series-Parallel Precedence Constraints Under Positional Effects Exponential Positional Effect Polynomial Positional Effect Bibliographic Notes References Scheduling with Pure and Combined Additive Start-Time-Dependent Effects Scheduling Independent Jobs Combined Effects Job-Dependent Linear Effects Job-Independent Linear Effects Scheduling Under Precedence Constraints Job-Dependent Linear Effects Job-Independent Linear Effects Bibliographic Notes General Additive Job-Independent Effects Linear Additive Job-Dependent Effects Linear Additive Job-Independent Effects Scheduling with Precedence Constraints References Scheduling with Pure and Combined Multiplicative Start-Time-Dependent Effects Scheduling Independent Jobs Job-Independent Combined Multiplicative Nonlinear Effects Job-Independent Combined Multiplicative Polynomial Effects Pure Multiplicative Linear Effects Scheduling Under Precedence Constraints Bibliographic Notes References

4 xiv Contents 10 Scheduling with Pure and Combined Cumulative Effects Scheduling Independent Jobs with a Combined Job-Independent Cumulative Effect Combining General Cumulative Effects with Positional Effects Combining Polynomial Cumulative Effects with Positional Effects Pure Cumulative Effects Job-Dependent Linear Generalized Cumulative Effect Job-Independent Linear Cumulative Effect Scheduling Under Precedence Constraints Minimizing Makespan Minimizing Total Completion Time Bibliographic Notes References Scheduling on Parallel Machines with Various Effects Combined Effects Identical and Uniform Machines Unrelated Machines Start-Time-Dependent Job-Dependent Linear Effects Minimizing Makespan: Complexity and Approximation Scheme Minimizing Total Flow Time: Complexity Start-Time-Dependent Job-Independent Linear Effects Identical and Uniform Machines Unrelated Machines Bibliographic Notes References Part III Scheduling with Rate Modifying Activities 12 General Framework for Studying Models with Rate-Modifying Activities Compulsory Maintenance Flexible Maintenance Rate-Modifying Activities Changing Processing Times and Rate-Modifying Activities References

5 Contents xv 13 Scheduling with Fixed Compulsory Maintenance Periods Makespan: Complexity and Approximation Single Maintenance Periodic Maintenance Weighted Total Flow Time: Complexity for the Non-resumable Scenario Properties of the Objective Function Useful Lower Bounds Computational Complexity Weighted Total Flow Time: Complexity for the Resumable Scenario Properties of the Objective Function Computational Complexity Weighted Total Flow Time: Approximation Algorithms and Schemes Constant Ratio Approximation Algorithms Approximation Schemes Bibliographic Notes Minimizing Makespan Minimizing Weighted Total Flow Time: Complexity Minimizing Weighted Total Flow Time: Approximation References Scheduling with Flexible Maintenance Flexible Maintenance: Start-Time Deadline Flexible Maintenance Within a Window Minimizing Makespan: Single Maintenance Minimizing Makespan: Periodic Maintenance Minimizing Total Completion Time Bibliographic Notes References Scheduling with Rate-Modifying Activities Single Rate-Modifying Maintenance on a Single Machine Minimizing Makespan Minimizing Total Completion Time Multiple Rate-Modifying Maintenance Periods on a Single Machine Minimizing Makespan Minimizing Total Completion Time Bibliographic Notes References

6 xvi Contents 16 Scheduling with Maintenance and Positional Effects Job-Dependent Deterioration Effects Computing Positional Weights Reduction to Rectangular LAP Job-Independent Effects Computing Positional Weights Reduction to LAP with a Product Matrix On the Fly Decision Making Binary Search in Convex Sequences Bibliographic Notes References Scheduling with Maintenance and Start-Time-Dependent Effects Computing Positional Weights Reduction to LAP with a Product Matrix On the Fly Decision Making Binary Search in Convex Sequences Bibliographic Notes References Scheduling with Rate-Modifying Activities and Enhanced Effects Enhanced Model Description Computing the Completion Times Minimizing the Makespan Minimizing the Total Completion Time Some Reduced Models Simple Combined Effects Pure Positional Effects Pure Time-Dependent Effects Bibliographic Notes References Scheduling with Maintenance and Linear Cumulative Effects Half-Product Reformulations Constant Maintenance: FPTAS via Subset-Sum The General Problem: FPTAS via Half-Product Bibliographic Notes References Scheduling with Rate-Modifying Activities on Parallel Machines Under Various Effects Generic Procedure for Parallel Machines

7 Contents xvii 20.2 Models with Rate-Modifying Activities Unrelated Machines Uniform Machines Models with Changing Processing Times and Rate-Modifying Activities Unrelated Machines Uniform Machines Bibliographic Notes References Index

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