Stochastic Modeling and Optimization: Methods and Applications

Most processes in life are prone to randomness, which can be both a challenge and an aid in mathematical modeling and optimization. In this dissertation, this randomness is studied through various modeling methods and (stochastic) optimization algorithms. It is shown how these can be developed for and applied to diverse problems in the domains of healthcare, manufacturing and search engine optimization. The key modeling methods are Markov chains and discrete-event models, and the key optimization algorithms are stochastic approximation algorithms and evolutionary algorithms. The following is addressed:
• A three-step framework for capacity planning in nursing homes is developed that includes a shift scheduling algorithm and a genetic algorithm that assigns nurses to daily tasks.
• A neural network metamodeler is developed that integrates biased analytical queuing features to estimate the throughput of a tandem line. This metamodeler is applied to a variety of optimization problems, such as the buffer allocation problem.
• An algorithm based on pseudo-gradient methods is developed to optimize a function over the stationary distribution of a Markov chain.
• The emergency response process of electric ambulances is modeled to determine the influence of transitioning from a diesel to an electric fleet on the response times.