Optimization Models for Rail Car Fleet Management

1. Introduction
1.1 Problem statement
1.2 Main objectives
1.3 Structure of the book

2. Review of the models for rail freight car fleet management
2.1 Operational models
2.1.1 Empty freight car inventory management problems
2.1.2 Empty freight car distribution
2.1.2.1 Deterministic approaches
2.1.2.2 Stochastic approaches
2.1.2.3 Hybrid approaches
2.1.3 Freight car pooling concept
2.1.4 Combined allocation of empty and loaded cars
2.2 Tactical and strategic models for freight car management
2.2.1 Service network design problem
2.2.2 Demand estimation
2.2.2.1 Models for production and attraction
2.2.2.2 Distribution models
2.2.2.3 Models for modal split
2.2.2.4 Assignment models
2.2.3 Rail freight car fleet sizing models

3 Centralized and decentralized Model for empty freight car scheduling
3.1 Characteristics of decentralized managerial-control functions in the process of empty freight car allocation
3.2 Centralized network model
3.3 Solution method of triaxial transportation problem
3.4 Decentralization of the main managerial functions in the empty car allocation process
3.5 Decentralized terminal model of empty freight car allocation
3.6 Validation of proposed model

4. Fuzzy multiobjective rail freight car fleet composition
4.1 The best rail freight car fleet mix problem
4.1.1 Classification of freight cars
4.1.2 Utilization of freight cars according to their characteristics
4.1.3 Proposed problem solution
4.1.3.1 The selection of relevant criteria
4.1.3.2 Analytic Hierarchy Process (AHP)
4.1.3.3 Theoretical basics of AHP
4.1.3.4 Mathematical basics of AHP
4.1.3.5 Fuzzy extension of AHP method
4.1.4 Fuzzy AHP method for the best rail freight car fleet mix problem
4.2 The best rail freight car fleet size problem
4.2.1 Theoretical foundations of the problem solution
4.2.2 Fuzzy multi-objective linear programming
4.2.3 Statement and solution of the problem

5. Fuzzy random model for rail freight car fleet management based on optimal control theory
5.1 Fuzzy preliminaries
5.1.1 Fuzzy sets
5.1.2 Fuzzy numbers
5.1.3 Triangular fuzzy matrices
5.1.4 The main features of triangular fuzzy matrices
5.1.5 Inverse triangular fuzzy matrices
5.1.6 Defuzzification of triangular fuzzy numbers
5.1.7 Fuzzy random variables
5.2 Fuzzy stochastic model for rail freight car fleet sizing and allocation
5.2.1 Model parameters
5.2.2 Objective functional
5.2.3 Problem constraints
5.2.4 Fuzzy state vector estimation
5.2.5 Proposed approach for solving the problem based on the fuzzy linear quadratic Gaussian regulator
5.2.6 The components of weighting matrices A, B and L
5.2.7 Choosing the components of the fuzzy weighting matrix
5.3 Numerical experiments
5.4 Comparative analysis of the results of the fuzzy random and random model

6. Stochastic model for heterogeneous rail freight car fleet management based on the model predictive control
6.1 Discrete time MPC framework for rail freight car fleet sizing and allocation problem
6.2 Design variables
6.3 System performance measure and constraints
6.4 State vector estimation
6.5 Forecasting the state of rail freight cars by Arima-Kalman method
6.5.1 Components of weighted matrices A, B and L
6.5.2 The components of matrix
6.6 MPC controller
6.6.1 Optimization problem
6.6.2 Detailed description of the MPC approach
6.6.3 Numerical experiments

7. Distributed and decentralized approaches for rail freight car management
7.1 Distributed model predictive rail freight car management
7.1.1 Problem description
7.1.2 Cooperative model predictive control for freight car flow planning
7.2 Decentralized model predictive rail freight car management
7.3 Numerical example

8. Conclusions
References