Chapter
1.6 Variance of the Performance Measure: OtherProduction Systems
1.7 Processing Time Variance in Scheduling
1.8 Analytic Evaluation of Expectation and Variance of a Performance Measure
1.9 Organization of the Book
2 Robust Scheduling Approaches to Hedge
2.2 Modeling Processing Time Uncertainty
2.3 Robust Scheduling for Single-Machine Systems
2.3.1 Properties of Robust Schedules
2.3.2 Solution Approaches for ADRSP
2.4 bold0mu mumu Raw-Robust Scheduling for Single-Machine Systems
2.4.1 Dominance Properties of bold0mu mumu Raw -Robust Schedules
2.4.2 Solution Approaches for bold0mu mumu Raw-RSP
2.4.3 Extensions of the bold0mu mumu Raw-RSP
2.4.4 Solution Approaches for bold0mu mumu Raw -RSPVR
2.5 Robust Scheduling for Two-Machine Flow Shops
2.5.1 Properties of Two-Machine Flow-Shop Robust Schedules
2.5.1.1 Discrete Processing Time Scenarios
2.5.1.2 Continuous Processing Time Intervals
2.5.2 Solution Approaches for the TM-ADRSP
2.5.2.1 Branch-and-Bound Algorithm for TM-ADRSP
2.5.2.2 Heuristic Approaches for TM-ADRSP
3 Expectation-Variance Analysis in Stochastic Multiobjective Scheduling
3.2 Expectation-Variance-EfficientSequences/Nondominated Schedules
3.3 Identification of Expectation-Variance-Efficient Sequences
3.3.1 Approaches for Identifying EV-Efficient Sequences
3.3.1.1 Dynamic Programming Approach (EV-DP)
3.3.1.2 Linear-Assignment-Problem Approach (EV-LAP)
3.4 Identification of Extreme EV-Efficient Sequences
3.4.1 Linear-Assignment-Problem Approach (XEV-LAP)
3.5 Preferred Schedule for Bicriteria Single-Machine Scheduling
3.5.1 Upperward 100bold0mu mumu Raw Percentile Minimum Schedule
3.5.2 Combined Nondominated Schedules
3.5.3 Combined Upperward 100bold0mu mumu Raw Percentile Minimum Schedules
3.5.4 Algorithmic Procedure for Preferred Schedule Selection
3.6 Preferred Schedule for Bicriteria Parallel-Machine Scheduling
3.6.1 Fixed-Job-Assignment Case
3.6.1.1 Individual Evaluation
3.6.1.2 Overall Evaluation
3.6.2 General Parallel-Machine Case
3.6.3 Algorithmic Procedure for Preferred Schedule Selection
4.2 Completion-Time-Based Objectives
4.2.1 Total Completion Time
4.2.2 Total Weighted Completion Time
4.2.3 Total Weighted Discounted Completion Time
4.2.3.1 Determination of E[e−rC[j] ]
4.2.3.2 Determination of var[e−rC[j] ]
4.2.3.3 Determination of cov[e−rC[i] , e−rC[j] ]
4.3 Due-Date-Based Objectives
4.3.2 Total Weighted Tardiness
4.3.3 Total Number of Tardy Jobs
4.3.4 Total Weighted Number of Tardy Jobs
5.2 Permutation Flow Shops with Unlimited Intermediate Storage
5.2.1 Expectation and Variance of Makespan
6.2 Job Shops with Unlimited Intermediate Storage andNo Recirculation
6.2.1 Expectation and Variance of Makespan
6.2.1.2 Determining the Makespan
6.3 Job Shops with Unlimited Intermediate Storage andwith Recirculation
7 Parallel-Machine Models
7.2 Parallel Machines with No Preemptions
7.2.1 Makespan with No Preemptions
7.2.1 Makespan with No Preemptions
7.2.2 Total Completion Time with No Preemptions
7.3 Parallel Machines with Preemptions
8 The Case of General Processing Time Distribution
8.1.1 Finite-Mixture Models
8.1.2 Maximum-Likelihood Fitting of Mixture Models
8.1.2.1 Algorithm Fit Normal Mixture
8.1.3 Related Issues in Model Fitting
8.1.3.1 Number of Components in a Mixture
8.1.3.2 Starting Values and Stopping Criteria for the EM Algorithm
8.1.3.3 Adjusting Moments after the MLE Fitting of the Mixture
8.2 Application of Mixture Models for Estimating the Moments of Various Performance Measures of a Schedule
8.2.1 Estimating Expectation and Variance of Tardiness
8.2.2 Estimating Expectation and Variance of a Unit Penalty Function
8.2.3 Single-Machine Problems
8.2.3.2 Total Weighted Tardiness
8.2.3.3 Total Number of Tardy Jobs
8.2.3.4 Total Weighted Number of Tardy Jobs
8.2.4.1 Algorithm MixtureJobShop
8.2.5 Flow-Shop and Parallel-Machine Problems
8.2.5.2 Parallel Machines Without Preemption
8.2.5.3 Parallel Machine with Preemptions
8.2.6.1 Salmond’s Approach
8.2.6.2 Williams’ Approach
8.2.6.3 Runnalls’ Approach
8.2.7 Application to Stochastic Activity Network
8.2.7.1 Approximation Procedure
9.1 Significance of This Work
A.1 Analysis for a Single-Machine Total Tardiness Problem
A.2 Analysis for a Single-Machine Total Number ofTardy Jobs Problem
A.3 Analysis for a Single-Machine Maximum Lateness Problem
A.4.1 Starting the Software
A.4.6 Specifying Distributions
Stochastic Scheduling
：Expectation-Variance Analysis of a Schedule
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