Inhalt

•  
   Introduction
•  
  Mathematical Background
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   Graphs
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   Linear Optimization
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  Network Flows
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   Network Optimization
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   Multicommodity Flows
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   Multicriteria Optimization
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  Probability Theory
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   Discrete Probability Spaces
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   Continuous Probability Spaces
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  Problem Formulation and Objectives
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   Network Representation of Supply Chain Problems
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   Uncertainties in Supply Chains
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   Literature Review
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   Network Flow Problems
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   Robust Optimization
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   Stochastic Programming
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   Ant Colony Optimization
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   Heuristics in Supply Chain Management
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   Challenges
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  Adaption of the ACO Metaheuristic to Network Flow Problems
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   The Ant Colony Optimization Metaheuristic
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   ACO for Single-Commodity Flows
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   Construction Graph
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   Constraints
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   Initialization of the Pheromone Trails
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   Heuristic Information
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   Solution Construction
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   Update of the Pheromone Trails
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   ACO for Multicommodity Flows
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   Convergence Theory
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   Avoiding Small Amounts of Flow in Minimum Cost Network Flow Problems
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  Application of the Ant Colony Optimization Metaheuristic to the TMCFP
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   Parameters
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   Penalty Costs
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   Stopping Criterion
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   Variation
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  An Exact Approach using SOS 2 Conditions
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   Approximation of Nonlinear Functions using SOS 2 Conditions
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   TMCFP with SOS 2 Conditions
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   Branching for SOS 2 Conditions
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  Example-Problems
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   Avoiding Small Flows Example 1
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   Avoiding Small Flows Example 2
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   Avoiding Small Flows Example 3
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   Summary and Conclusions
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  Robust Optimization in Network Flows: Uncertain Costs
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   Problem Formulation and Objectives
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  Approach of Bertsimas and Sim
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   Model Formulation
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   Extension to Multicommodity Flows
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   Non-Integer Values for the Robustness Parameter
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  Ant Algorithm
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   Uniformly Distributed Costs
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   Gaussian Distributed Costs
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   Arbitrary Distribution
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  Problems
•  
   Single-Commodity Uncertain Cost Example
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   Single-Commodity Triangular Distributed Cost Example
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   Summary
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   Summary and Conclusions
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   Transformation of Uncertain Demands to Uncertain Costs
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  Transformation using Additional Information: Penalty and Storage Costs
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   The Transformation Process
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   Uncertain Demands Transformation Example 1
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  General Approach
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   The Transformation Process
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   Interpretation
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   Uncertain Demands Transformation Example 2
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   Summary and Conclusions
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  Robust Optimization in Network Flows: Uncertain Demands
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   Problem Formulation and Objectives
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   Ant Algorithm
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   Modification of the Network
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   Realization of Uncertain Demands
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   Variations
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   Supplements for the Multicommodity Version
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   Multicommodity Uncertain Demands Example
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   Recoverable Robustness
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   Linear Programming Recovery
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   Coincidental Covering
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   Translation of the Demand Scenarios
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   Extension to Multicommodity Flows
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   Recoverable Robustness Example
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   Summary and Conclusions
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  Stochastic Programming: Uncertain Demand
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   Two-Stage Linear Recourse Problems
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   Problem Formulation
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   The L-Shaped Method
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   Application to Supply Chain Problems
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   Extension of the L-Shaped Algorithm to Multicommodity Flows
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   The Multicommodity L-Shaped Method
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   Proof of Correctness and Convergence
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   Multicommodity Two-Stage Example
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   Recourse by Interexchange
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   Introduction of the Interexchange Recourse Scheme
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   Multicommodity Interexchange Two-Stage Example
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   Inventory Management
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   Network Extension for Inventory Management
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   Multicommodity Inventory Management Two-Stage Example
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   Summary and Conclusions
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   A Multicriteria Perspective
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  Scalarizations of the Multicriteria Optimization Problem
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   e-Constraint Scalarization
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   Weighted Sum Scalarization
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   Further Scalarizations
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   Relations between the Scalarizations
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   Sensitivity for the e-Constraint Scalarization
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   Summary and Conclusions
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  Computational Results: Numerical Tests
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   Random Network Generation
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   Threshold Minimum Cost Flow Problem
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   Uncertain Costs
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   Uncertain Demands
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   Summary and Conclusions
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   Computational Results: Reference Model
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   Ant Algorithm for Uncertain Demands
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   Transformation of Uncertain Demands to Uncertain Costs
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   Recoverable Robustness
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   Stochastic Two-Stage Linear Recourse Problem
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   Single Time Period
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   Recourse by Interexchange
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   Inventory Management: Multiple Time Periods
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   Summary and Conclusions
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   Final Conclusion and Future Research
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   List of Abbreviations