Modeling and Solution Approaches for Non-traditional Network Flow Problems with Complicating Constraints

In this dissertation, we model three network-based optimization problems. Chapter 2 addresses the question of what the operation plan should be for interdependent infrastructure systems in resource-constrained environments so that they collectively operate at the highest level. We develop a network-based operation model of these systems that accounts for interdependencies among them. To solve this large-scale model, a solution approach is proposed that relatively quickly generates high-quality solutions to the problem. Chapter 3 presents a routing model for a single train within a railyard with the objective of minimizing the total length traveled by train. The difference between this problem and the traditional shortest path is that the route must accommodate the length of the train at any time, subject to yard tracks’ configuration. This problem has application in the railway industry where they need to solve the single-train routing problem repeatedly for simulations of train movements in large complex yards. We develop an optimal polynomial-time algorithm that solves an important special case of the problem. Chapter 4 extends the problem defined in Chapter 3 to a two-train routing problem with the objective of minimizing the overall time possible to schedule the routes in a conflict-free manner. We propose a routing problem that indirectly aims to decrease the overall scheduling time for the two trains. We develop a scheduling model that compares the performance of the solution obtained by the proposed routing model with the solutions obtained by solving the problem as two separate single-train yard routing problems. The comparison indicates a better performance obtained by the proposed routing model for specific problems

Poisson Distributed Individuals Control Charts with Optimal Limits

The conventional method used in attribute control charts is the Shewhart three sigma limits. The implicit assumption of the Normal distribution in this approach is not appropriate for skewed distributions such as Poisson, Geometric and Negative Binomial. Normal approximations perform poorly in the tail area of the these distributions. In this research, a type of attribute control chart is introduced to monitor the processes that provide count data. The economic objective of this chart is to minimize the cost of its errors which is determined by the designer. This objective is a linear function of type I and II errors. The proposed control chart can be applied to Poisson, Geometric and Negative Binomial as the underlying distribution of count data. Control limits in this chart is calculated optimally since it is based on the probability distribution of the data and can detect a directional shift in the process rate. Some numerical results for the optimal design of the proposed control chart are provided. The expected cost of the control chart is compared to that of a one sided c chart. The effects of changing the available parameters on the cost, errors and the optimal limits of the proposed control chart are shown graphically