A multiple server facility location problem with resources subject to congestion

This thesis describes the mathematical model and solution methods that are used to model the congestion and solve the problem of locating multiple server facilities with resources subject to congestion in a single product environment. A non-linear mixed-integer programming model is developed to determine a cost-minimizing allocation of servers and the demands to each facility while each facility is required to maintain a certain level of service quality indicated by the number of waiting customers or orders. A Lagrangian Relaxation (LR) heuristic that utilizes existing heuristic methods and a newly developed dynamic programming algorithm are developed to solve the presented problem. Computational experiments and sensitivity analysis based on random and published data sets are conducted. As an alternative solution method for solving the presented problem, a Column Generation (CG) heuristic is also developed for solving the model. The same dynamic programming algorithm introduced for solving the Lagrangian Relaxation subproblems and the existing heuristics are utilized to generate columns and provide lower and upper bounds of the optimal solution. The performance of the developed column generation heuristic is also tested on the same random and published data sets. Computational comparisons with the developed Lagrangian heuristic showed high performance of the column generation heuristic in terms of duality gaps and computational times. The presented results proved that the clearing functions are an efficient tool for modeling the congestion and the accuracy of the developed heuristics. A case study for locating hydrogen refueling infrastructures in the Northeastern United States is also presented. An initial hydrogen fuel supply network for the Northeastern United States which includes the metropolitan areas of Boston, Philadelphia, Washington D.C. and New York City is designed. Stochastic demands are extracted from U.S. census tract data using predictive analytics and Geographical Information System (GIS) methodologies. The presented optimization model and solution algorithms are applied to find the location of the refueling stations and allocated demands, number of servers and the number of waiting vehicles for each station. A Discrete Event Simulation (DES) model is presented to monitor the performance of the optimization model's solution in terms of station's utilization rates and average number of waiting vehicles. Finally, conclusions and highlights about important aspects of the thesis and future works are presented.