Optimization of logistics

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Cover; Title Page; Copyright Page; Table of Contents; Introduction; Chapter 1. Modeling and Performance Evaluation; 1.1. Introduction; 1.2. Markovian processes; 1.2.1. Overview of stochastic processes; 1.2.2. Markov processes; 1.2.2.1. Basics; 1.2.2.2. Chapman-Kolmogorov equations; 1.2.2.3. Steady-state probabilities; 1.2.2.4. Graph associated with a Markov process; 1.2.2.5. Application to production systems; 1.2.3. Markov chains; 1.2.3.1. Basics; 1.2.3.2. State probability vectors; 1.2.3.3. Fundamental equation of a Markov chain; 1.2.3.4. Graph associated with a Markov chain 1.2.3.5. Steady states of ergodic Markov chains1.2.3.6. Application to production systems; 1.3. Petri nets; 1.3.1. Introduction to Petri nets; 1.3.1.1. Basic definitions; 1.3.1.2. Dynamics of Petri nets; 1.3.1.3. Specific structures; 1.3.1.4. Tools for Petri net analysis; 1.3.1.5. Properties of Petri nets; 1.3.2. Non-autonomous Petri nets; 1.3.3. Timed Petri nets; 1.3.4. Continuous Petri nets; 1.3.4.1. Fundamental equation and performance analysis; 1.3.4.2. Example; 1.3.5. Colored Petri nets; 1.3.6. Stochastic Petri nets; 1.3.6.1. Firing time; 1.3.6.2. Firing selection policy 1.3.6.3. Service policy1.3.6.4. Memory policy; 1.3.6.5. Petri net analysis; 1.3.6.6. Marking graph; 1.3.6.7. Generator of Markovian processes; 1.3.6.8. Fundamental equation; 1.3.6.9. Steady-state probabilities; 1.3.6.10. Performance indices (steady state); 1.4. Discrete-event simulation; 1.4.1. The role of simulation in logistics systems analysis; 1.4.2. Components and dynamic evolution of systems; 1.4.3. Representing chance and the Monte Carlo method; 1.4.3.1. Uniform distribution U [0, 1]; 1.4.3.2. The Monte Carlo method; 1.4.4. Simulating probability distributions 1.4.4.1. Simulating random events1.4.4.2. Simulating discrete random variables; 1.4.4.3. Simulating continuous random variables; 1.4.5. Discrete-event systems; 1.4.5.1. Key aspects of simulation; 1.5. Decomposition method; 1.5.1. Presentation; 1.5.2. Details of the method; Chapter 2. Optimization; 2.1. Introduction; 2.2. Polynomial problems and NP-hard problems; 2.2.1. The complexity of an algorithm; 2.2.2. Example of calculating the complexity of an algorithm; 2.2.3. Some definitions; 2.2.3.1. Polynomial-time algorithms; 2.2.3.2. Pseudo-polynomial-time algorithms 2.2.3.3. Exponential-time algorithms2.2.4. Complexity of a problem; 2.2.4.1. Polynomial-time problems; 2.2.4.2. NP-hard problems; 2.3. Exact methods; 2.3.1. Mathematical programming; 2.3.2. Dynamic programming; 2.3.3. Branch and bound algorithm; 2.4. Approximate methods; 2.4.1. Genetic algorithms; 2.4.1.1. General principles; 2.4.1.2. Encoding the solutions; 2.4.1.3. Crossover operators; 2.4.1.4. Mutation operators; 2.4.1.5. Constructing the population in the next generation; 2.4.1.6. Stopping condition; 2.4.2. Ant colonies; 2.4.2.1. General principle