In this thesis, we propose a hierarchical level decision support system for workforce planning in medical equipment maintenance services. In strategic level, customer clusters and the total number of field engineers is determined via a mixed integer programming and simulation. In MIP, we aim to find the minimum number of field engineers. Afterwards, we analyze service measures such as response time via simulation. In tactical level, quarterly training program for the field engineers is determined via mixed integer programming and the results are interpreted in terms of service level via simulation.

Inferring and anticipation of genetic networks based on experimental data and environmental measurements is a challenging research problem of mathematical modeling. In this thesis, we discuss gene-environment network models whose dynamics are represented by a class of time-continuous systems of ordinary differential equations containing unknown parameters to be optimized. Accordingly, time-discrete version of that model class is studied and improved by using different numerical methods. In this aspect, 3rd-order Heun&rsquo / s method and 4th-order classical Runge-Kutta method are newly introduced, iteration formulas are derived and corresponding matrix algebras are newly obtained. We use nonlinear mixed-integer programming for the parameter estimation and present the solution of a constrained and regularized given mixed-integer problem. By using this solution and applying the 3rd-order Heun&rsquo / s and 4th-order classical Runge-Kutta methods in the timediscretized model, we generate corresponding time-series of gene-expressions by this thesis. Two illustrative numerical examples are studied newly with an artificial data set and a realworld data set which expresses a real phenomenon. All the obtained approximate results are compared to see the goodness of the new schemes. Different step-size analysis and sensitivity tests are also investigated to obtain more accurate and stable predictions of time-series results for a better service in the real-world application areas. The presented time-continuous and time-discrete dynamical models are identified based on given data, and studied by means of an analytical theory and stability theories of rarefication, regularization and robustification.

The focus of this dissertation is the advancement of theory and computation related to exact precision mathematical programming. Optimization software based on floating-point arithmetic can return suboptimal or incorrect resulting because of round-off errors or the use of numerical tolerances. Exact or correct results are necessary for some applications. Implementing software entirely in rational arithmetic can be prohibitively slow. A viable alternative is the use of hybrid methods that use fast numerical computation to obtain approximate results that are then verified or corrected with safe or exact computation. We study fast methods for sparse exact rational linear algebra, which arises as a bottleneck when solving linear programming problems exactly. Output sensitive methods for exact linear algebra are studied. Finally, a new method for computing valid linear programming bounds is introduced and proven effective as a subroutine for solving mixed-integer linear programming problems exactly. Extensive computational results are presented for each topic.

Practically all everyday life tasks from economic transactions to entertainment depend on the availability of electricity. Some customers have come to expect a higher level of power quality and availability from their electric utility. Federal and state standards are now mandated for power service quality and utilities may be penalized if the number of interruptions exceeds the mandated standards. In order to meet the requirement for safety, reliability and quality of supply in distribution system, adaptive relaying and optimal network reconfiguration are proposed. By optimizing the system to be better prepared to handle a fault, the end result will be that in the event of a fault, the minimum number of customers will be affected. Thus reliability will increase. The main function of power system protection is to detect and remove the faulted parts as fast and as selectively as possible. The problem of coordinating protective relays in electric power systems consists of selecting suitable settings such that their fundamental protective function is met under the requirements of sensitivity, selectivity, reliability, and speed. In the proposed adaptive relaying approach, weather data will be incorporated as follows. By using real-time weather information, the potential area that might be affected by the severe weather will be determined. An algorithm is proposed for adaptive optimal relay setting (relays will optimally react to a potential fault). Different types of relays (and relay functions) and fuses will be considered in this optimization problem as well as their coordination with others. The proposed optimization method is based on mixed integer programming that will provide the optimal relay settings including pickup current, time dial setting, and different relay functions and so on. The main function of optimal network reconfiguration is to maximize the power supply using existing breakers and switches in the system. The ability to quickly and flexibly reconfigure the power system of an interconnected network of feeders is a key component of Smart Grid. New technologies are being injected into the distribution systems such as advanced metering, distribution automation, distribution generation and distributed storage. With these new technologies, the optimal network reconfiguration becomes more complicated. The proposed algorithms will be implemented and demonstrated on a realistic test system. The end result will be improved reliability. The improvements will be quantified with reliability indexes such as SAIDI.

Multinomial selection problem procedures are ranking and selection techniques that aim to select the best (most probable) alternative based upon a sequence of multinomial observations. The classical formulation of the procedure design problem is to find a decision rule for terminating sampling. The decision rule should minimize the expected number of observations taken while achieving a specified indifference zone requirement on the prior probability of making a correct selection when the alternative configurations are in a particular subset of the probability space called the preference zone. We study the constrained version of the design problem in which there is a given maximum number of allowed observations. Numerous procedures have been proposed over the past 50 years, all of them suboptimal. In this thesis, we find via linear programming the optimal selection procedure for any given probability configuration. The optimal procedure turns out to be necessarily randomized in many cases. We also find via mixed integer programming the optimal non-randomized procedure. We demonstrate the performance of the methodology on a number of examples. We then reformulate the mathematical programs to make them more efficient to implement, thereby significantly expanding the range of computationally feasible problems. We prove that there exists an optimal policy which has at most one randomized decision point and we develop a procedure for finding such a policy. We also extend our formulation to replicate existing procedures. Next, we show that there is very little difference between the relative performances of the optimal randomized and non-randomized procedures. Additionally, we compare existing procedures using the optimal procedure as a benchmark, and produce updated tables for a number of those procedures. Then, we develop a methodology that guarantees the optimal randomized and non-randomized procedures for a broad class of variable observation cost functions -- the first of its kind. We examine procedure performance under a variety of cost functions, demonstrating that incorrect assumptions regarding marginal observation costs may lead to increased total costs. Finally, we investigate and challenge key assumptions concerning the indifference zone parameter and the conditional probability of correct selection, revealing some interesting implications.

Major challenges in the management of blood supply chain are related to the shortage and wastage of the blood products. Given the perishability characteristics of blood which can be stored up to a limited number of days, if hospitals and blood centers keep an excessive number of blood units on inventory, wastages may occur. On the other hand, if sufficient number of blood units are not stored on inventory, shortages of this resource may cause the cancellations of important activities and increase the fatality rates at hospitals. Three mathematical models have been developed with the goal to improve the efficiency of blood related activities at blood centers and hospitals. The first model uses an integer programming (IP) approach to identify the optimal order levels that minimizes the total cost, shortage and wastage levels of blood products at a hospital within a specified planning horizon. The IP model explicitly considers the age of blood inventory, uncertain demand, the demand for two types of patients and crossmatch-to-transfusion ratio. The second model formulates the different shortage and inventory distribution strategies of a blood center supplying blood products to multiple hospitals. The third model develops a vehicle routing problem for blood centers to minimize the daily distance travelled by bloodmobiles during the blood collection process. Optimal routing for each bloodmobiles is identified using CPLEX solver, branch \& bound and column generation algorithms and their solution times are compared.

This dissertation is a collection of previously-published manuscript and conference papers. In this dissertation, we will deal with a stochastic unit commitment problem with cooling systems for gas generators, a robust unit commitment problem with demand response and uncertain wind generation, and a power grid vulnerability analysis with transmission line switching. The latter two problems correspond to our theoretical contributions in two-stage robust optimization, i.e., how to efficiently solve a two-stage robust optimization, and how to deal with mixed-integer recourse in robust optimization. Due to copyright issue, this dissertation does not include any methodology papers written by the author during his PhD study. Readers are referred to the author's website for a complete list of publications.

Home healthcare has been a growing sector of the economy over the last three decades with roughly 23,000 companies now doing business in the U.S. producing over $56 billion in combined annual revenue. As a highly fragmented market, profitability of individual companies depends on effective management and efficient operations. This dissertation aims at reducing costs and improving productivity for home healthcare companies. The first part of the research involves the development of a new formulation for the therapist routing and scheduling problem as a mixed integer program. Given the time horizon, a set of therapists and a group of geographically dispersed patients, the objective of the model is to minimize the total cost of providing service by assigning patients to therapists while satisfying a host of constraints concerning time windows, labor regulations and contractual agreements. This problem is NP-hard and proved to be beyond the capability of commercial solvers like CPLEX. To obtain good solutions quickly, three approaches have been developed that include two heuristics and a decomposition algorithm. The first approach is a parallel GRASP that assigns patients to multiple routes in a series of rounds. During the first round, the procedure optimizes the patient distribution among the available therapists, thus trying to reach a local optimum with respect to the combined cost of the routes. Computational results show that the parallel GRASP can reduce costs by 14.54% on average for real datasets, and works efficiently on randomly generated datasets. The second approach is a sequential GRASP that constructs one route at a time. When building a route, the procedure tracks the amount of time used by the therapists each day, giving it tight control over the treatment time distribution within a route. Computational results show that the sequential GRASP provides a cost savings of 18.09% on average for the same real datasets, but gets much better solutions with significantly less CPU for the same randomly generated datasets. The third approach is a branch and price algorithm, which is designed to find exact optima within an acceptable amount of time. By decomposing the full problem by therapist, we obtain a series of constrained shortest path problems, which, by comparison are relatively easy to solve. Computational results show that, this approach is not efficient here because: 1) convergence of Dantzig-Wolfe decomposition is not fast enough; and 2) subproblem is strongly NP-hard and cannot be solved efficiently. The last part of this research studies a simpler case in which all patients have fixed appointment times. The model takes the form of a large-scale mixed-integer program, and has different computational complexity when different features are considered. With the piece-wise linear cost structure, the problem is strongly NP-hard and not solvable with CPLEX for instances of realistic size. Subsequently, a rolling horizon algorithm, two relaxed mixed-integer models and a branch-and-price algorithm were developed. Computational results show that, both the rolling horizon algorithm and two relaxed mixed-integer models can solve the problem efficiently; the branch-and-price algorithm, however, is not practical again because the convergence of Dantzig-Wolfe decomposition is slow even when stabilization techniques are applied. / text

Amusement parks are a huge business. Guest experiences determine the success or failure for an amusement park. This report suggests an approach to improve guest experience by managing guest flow. The guest happiness optimization problem is formulated into a visitor routing management model. The constraints for this model include attraction attributes and guest behavior. To build the attraction constraints, their information is first gathered from internet, field studies and surveys, and then input into simulation software. Constraints on guest behavior are set up with a literature study and a guest survey. A two phase heuristic is developed to solve this problem with constraints. Candidate routes are generated with a route construction algorithm in the first phase. Visitor distribution and selection on these candidate routes are determined in the second phase using a mixed integer programming solver. Visitor routes are then recommended to the park’s operator side, for them to distribute to guests visiting on their vacations. Data from Disney Epcot are collected and applied in the case study to implement the methodology in this report. Attraction operations capability is maintained at the current level with no additional cost for the project, while guest satisfaction is improved by ensuring the number and type of attractions they visit. In addition, average waiting time for visitors is reduced by at least 70% in the recommended operation strategy. / text

Many digital signal processing and real-time streaming systems are modeled using dataflow graphs, such as Synchronous Dataflow (SDF) and Cyclo-static Dataflow (CSDF) graphs that allow static analysis and optimization techniques. However, mapping of such descriptions into tightly constrained real-time implementations requires optimization of resource sharing, buffering and scheduling across a multi-dimensional latency-throughput-area objective space. This requires techniques that can find the Pareto-optimal set of implementations for the designer to choose from. In this work, we address the problem of multi-objective mapping and scheduling of SDF and CSDF graphs onto heterogeneous multi-processor platforms. Building on previous work, this thesis extends existing two-stage hybrid heuristics that combine an evolutionary algorithm with an integer linear programming (ILP) model to jointly optimize throughput, area and latency for SDF graphs. The primary contributions of this work include: (1) extension of the ILP model to support CSDFGs with additional buffer size optimizations; (2) a further optimization in the ILP-based scheduling model to achieve a runtime speedup of almost a factor of 10 compared to the existing SDFG formulation; (3) a list scheduling heuristic that replaces the ILP model in the hybrid heuristic to generate Pareto-optimal solutions at significantly decreased runtime while maintaining near-optimality of the solutions within an acceptable gap of 10% when compared to its ILP counterparts. The list scheduling heuristic presented in this work is based on existing modulo scheduling approaches for software pipelining in the compiler domain, but has been extended by introducing a new concept of mobility-based rescheduling before resorting to backtracking. It has been proved in this work that if mobility-based rescheduling is performed, the number of required backtrackings and hence overall complexity and runtime is less. / text