This report presents a series of models that can be used to find weekly schedules for therapists who provide ongoing treatment to patients scattered around a geographical region. In all cases, the patients’ appointment times and visit days are known prior to the beginning of the planning horizon. Variations in the model include single vs. multiple home bases, homogeneous vs. heterogeneous therapists, lunch break requirements, and a nonlinear cost structure for mileage reimbursement and overtime. The single home base and homogeneous therapist cases proved to be easy to solve and so were not investigated. This left two cases of interest: the first includes only lunch breaks while the second adds overtime and mileage reimbursement. In all, 40 randomly generated data sets were solved that consisted of either 15 or 20 therapists and between roughly 300 and 540 visits over five days. For each instance, we were able to obtain the minimum cost of providing home healthcare services for both models using CPLEX 12.2. The results showed that CPU time increases more rapidly than total cost as the total number of visits grows. In general, data sets with therapists who have different starting and ending locations are more difficult to solve than those whose therapists have the same home base. / text

During an emergency evacuation, most people will use their vehicles to evacuate. However, there is a group of people who do not have access to reliable transportation or for some reason cannot drive, even if they have their own automobiles - the carless. There are different groups of carless (disabled, medically homebound, poor or immigrant populations, etc.) who require different forms of transportation assistance during an emergency evacuation. In this study we focus on those carless who are physically intact and able to walk to a set of designated locations for transportation during an emergency, and we propose using public transit and school buses to evacuate this carless group. A model has been developed to accommodate the use of public transit and school buses to efficiently and effectively evacuate the carless. The model has two parts. Part 1 is a location problem which aims at congregating the carless at some specific locations called evacuation sites inside the affected area. To achieve this goal, the affected area is partitioned into zones and this congregating of the carless has been formulated as a Single Source Capacitated Facility Location Problem. Changes in the demand of the carless in zones over different periods of a day and over different days of the week have been considered and included in the model. A walking time constraint is explicitly considered in the model. A heuristic developed by Klincewicz and Luss (1986) has been used to solve this location model.Part 2 is a routing problem which aims at obtaining itineraries of buses to pick up the carless at evacuation sites and transport them to safe locations outside the affected area, such that the total number of carless evacuated with the given time limit is maximized. A Tabu search heuristic has been developed for solving the routing problem. Computational results show that the Tabu search heuristic efficiently and effectively solves the routing problem; in particular, the initial heuristic produces a high quality initial solution in very short time. This study has also made slight contribution to the development of the Tabu search technique.

This diploma thesis deals with static and dynamic capacitated messenger problem and its solving with heuristic algorithms. Different variations of the capacitated messenger problem were considered, with a single messenger or multiple messengers, with one depot or multiple depots in case of multiple messengers. Limited time for route realization was another modification that was considered. Modified nearest neighbour method, modified insertion method and modified exchange method were used to solve the problem. The main contribution of the thesis is deriving heuristics for described types of messenger problem and programming the algorithms in VBA (Visual Basic for Applications) in MS Excel. The results of computational experiments indicate that modified nearest neighbour method leads to better outcomes in static multiple messenger problems with a single depot, while modified insertion method is associated with lower values of objective function in static multiple messenger problem with multiple depots. Modified exchange method improves original solutions. Modified insertion method was approved for solving dynamic multiple messenger problems.