de
en
Close
Detailsuche
Bibliotheken
Projekt
Imprint
Privacy Policy
de
en
Close
Imprint
Privacy Policy
jump to main content
Search Details
Quicksearch:
OK
Result-List
Title
Title
Content
Content
Page
Page
Search the document
Network flow problems with uncertain input data in the context of supply chain management applications / von Simone Gast. 2010
Content
Introduction
Mathematical Background
Graphs
Linear Optimization
Network Flows
Network Optimization
Multicommodity Flows
Multicriteria Optimization
Probability Theory
Discrete Probability Spaces
Continuous Probability Spaces
Problem Formulation and Objectives
Network Representation of Supply Chain Problems
Uncertainties in Supply Chains
Literature Review
Network Flow Problems
Robust Optimization
Stochastic Programming
Ant Colony Optimization
Heuristics in Supply Chain Management
Challenges
Adaption of the ACO Metaheuristic to Network Flow Problems
The Ant Colony Optimization Metaheuristic
ACO for Single-Commodity Flows
Construction Graph
Constraints
Initialization of the Pheromone Trails
Heuristic Information
Solution Construction
Update of the Pheromone Trails
ACO for Multicommodity Flows
Convergence Theory
Avoiding Small Amounts of Flow in Minimum Cost Network Flow Problems
Application of the Ant Colony Optimization Metaheuristic to the TMCFP
Parameters
Penalty Costs
Stopping Criterion
Variation
An Exact Approach using SOS 2 Conditions
Approximation of Nonlinear Functions using SOS 2 Conditions
TMCFP with SOS 2 Conditions
Branching for SOS 2 Conditions
Example-Problems
Avoiding Small Flows Example 1
Avoiding Small Flows Example 2
Avoiding Small Flows Example 3
Summary and Conclusions
Robust Optimization in Network Flows: Uncertain Costs
Problem Formulation and Objectives
Approach of Bertsimas and Sim
Model Formulation
Extension to Multicommodity Flows
Non-Integer Values for the Robustness Parameter
Ant Algorithm
Uniformly Distributed Costs
Gaussian Distributed Costs
Arbitrary Distribution
Problems
Single-Commodity Uncertain Cost Example
Single-Commodity Triangular Distributed Cost Example
Summary
Summary and Conclusions
Transformation of Uncertain Demands to Uncertain Costs
Transformation using Additional Information: Penalty and Storage Costs
The Transformation Process
Uncertain Demands Transformation Example 1
General Approach
The Transformation Process
Interpretation
Uncertain Demands Transformation Example 2
Summary and Conclusions
Robust Optimization in Network Flows: Uncertain Demands
Problem Formulation and Objectives
Ant Algorithm
Modification of the Network
Realization of Uncertain Demands
Variations
Supplements for the Multicommodity Version
Multicommodity Uncertain Demands Example
Recoverable Robustness
Linear Programming Recovery
Coincidental Covering
Translation of the Demand Scenarios
Extension to Multicommodity Flows
Recoverable Robustness Example
Summary and Conclusions
Stochastic Programming: Uncertain Demand
Two-Stage Linear Recourse Problems
Problem Formulation
The L-Shaped Method
Application to Supply Chain Problems
Extension of the L-Shaped Algorithm to Multicommodity Flows
The Multicommodity L-Shaped Method
Proof of Correctness and Convergence
Multicommodity Two-Stage Example
Recourse by Interexchange
Introduction of the Interexchange Recourse Scheme
Multicommodity Interexchange Two-Stage Example
Inventory Management
Network Extension for Inventory Management
Multicommodity Inventory Management Two-Stage Example
Summary and Conclusions
A Multicriteria Perspective
Scalarizations of the Multicriteria Optimization Problem
e-Constraint Scalarization
Weighted Sum Scalarization
Further Scalarizations
Relations between the Scalarizations
Sensitivity for the e-Constraint Scalarization
Summary and Conclusions
Computational Results: Numerical Tests
Random Network Generation
Threshold Minimum Cost Flow Problem
Uncertain Costs
Uncertain Demands
Summary and Conclusions
Computational Results: Reference Model
Ant Algorithm for Uncertain Demands
Transformation of Uncertain Demands to Uncertain Costs
Recoverable Robustness
Stochastic Two-Stage Linear Recourse Problem
Single Time Period
Recourse by Interexchange
Inventory Management: Multiple Time Periods
Summary and Conclusions
Final Conclusion and Future Research
List of Abbreviations