Applications of Combinatorial Optimization

Content: Cover
 Title Page
 Copyright
 Contents
 Preface
 Chapter 1: Airline Crew Pairing Optimization
 1.1. Introduction
 1.2. Definition of the problem
 1.2.1. Constructing subnetworks
 1.2.2. Pairing costs
 1.2.3. Model
 1.2.4. Case without resource constraints
 1.3. Solution approaches
 1.3.1. Decomposition principles
 1.3.2. Column generation, master problem and subproblem
 1.3.3. Branching methods for finding integer solutions
 1.4. Solving the subproblem for column generation
 1.4.1. Mathematical formulation
 1.4.2. General principle of effective label generation. 1.4.3. Case of one single resource: the bucket method1.4.4. Case of many resources: reduction of the resource space
 1.4.4.1. Reduction principle
 1.4.4.2. Approach based on the Lagrangian relaxation
 1.4.4.3. Approach based on the surrogate relaxation
 1.5. Conclusion
 1.6. Bibliography
 Chapter 2: The Task Allocation Problem
 2.1. Presentation
 2.2. Definitions and modeling
 2.2.1. Definitions
 2.2.2. The processors
 2.2.3. Communications
 2.2.4. Tasks
 2.2.5. Allocation types
 2.2.5.1. Static allocation
 2.2.5.2. Dynamic allocation
 2.2.5.3. With or without pre-emption. 2.2.5.4. Task duplication2.2.6. Allocation/scheduling
 2.2.7. Modeling
 2.2.7.1. Modeling costs
 2.2.7.2. Constraints
 2.2.7.3. Objectives of the allocation
 2.2.7.3.1. Minimizing the execution duration
 2.2.7.3.2. Minimizing the global execution and communication cost
 2.2.7.3.3. Load balancing
 2.3. Review of the main works
 2.3.1. Polynomial cases
 2.3.1.1. Two-processor cases
 2.3.1.2. Tree case
 2.3.1.3. Other structures
 2.3.1.4. Restrictions on the processors or the tasks
 2.3.1.5. Minmax objective
 2.3.2. Approximability
 2.3.3. Approximate solution
 2.3.3.1. Heterogenous processors. 2.3.3.2. Homogenous processors2.3.4. Exact solution
 2.3.5. Independent tasks case
 2.4. A little-studied model
 2.4.1. Model
 2.4.2. A heuristic based on graphs
 2.4.2.1. Transformation of the problem
 2.4.2.2. Modeling
 2.4.2.3. Description of the heuristic
 2.5. Conclusion
 2.6. Bibliography
 Chapter 3: A Comparison of Some Valid Inequality Generation Methods for General 0-1 Problems
 3.1. Introduction
 3.2. Presentation of the various techniques tested
 3.2.1. Exact separation with respect to a mixed relaxation
 3.2.2. Approximate separation using a heuristic. 3.2.3. Restriction + separation + relaxed lifting (RSRL)3.2.4. Disjunctive programming and the lift and project procedure
 3.2.5. Reformulation-linearization technique (RLT)
 3.3. Computational results
 3.3.1. Presentation of test problems
 3.3.2. Presentation of the results
 3.3.3. Discussion of the computational results
 3.4. Bibliography
 Chapter 4: Production Planning
 4.1. Introduction
 4.2. Hierarchical planning
 4.3. Strategic planning and productive system design
 4.3.1. Group technology
 4.3.2. Locating equipment
 4.4. Tactical planning and inventory management.