In this thesis, we study the repair shop scheduling problem(repair-to-stock) and the production/inventory system pricing and production scheduling problem(make-to-stock). For both types of problems, we compare the performance of different scheduling policies. For the make-to-stock type problem, we also study the performance of different pricing strategies. The optimal repair/production scheduling policy of both problems is difficult to characterize, and, therefore, is only formulated as a Markov Decision Process to numerically compute the optimal cost/profit. As an alternative, we propose the dynamic Myopic policy, which is easy to implement. The numerical study we have conducted demonstrates that the performance of Myopic policy is superior compared to the alternative policies and yields costs very close to the optimal for the repair-to-stock type problem. On the other hand, for the make-to-stock type problems, the performance of Myopic policy is not superior compared to the alternative policies when dynamic pricing strategy is implemented.

Many problems that arise in the real world are difficult to solve partly because they present computational challenges. Many of these challenging problems are optimization problems. In the real world we are generally interested not just in solutions but in the cost or benefit of these solutions according to different metrics. Hence, finding optimal solutions is often highly desirable and sometimes even necessary. The most effective computational approach for solving such problems is to first model them in a mathematical or logical language, and then solve them by applying a suitable algorithm. This thesis is concerned with developing practical algorithms to solve optimization problems modeled in a particular logical language, MAXSAT. MAXSAT is a generalization of the famous Satisfiability (SAT) problem, that associates finite costs with falsifying various desired conditions where these conditions are expressed as propositional clauses. Optimization problems expressed in MAXSAT typically have two interacting components: the logical relationships between the variables expressed by the clauses, and the optimization component involving minimizing the falsified clauses. The interaction between these components greatly contributes to the difficulty of solving MAXSAT. The main contribution of the thesis is a new hybrid approach, MaxHS, for solving MAXSAT. Our hybrid approach attempts to decouple these two components so that each can be solved with a different technology. In particular, we develop a hybrid solver that exploits two sophisticated technologies with divergent strengths: SAT for solving the logical component, and Integer Programming (IP) solvers for solving the optimization component. MaxHS automatically and incrementally splits the MAXSAT problem into two parts that are given to the SAT and IP solvers, which work together in a complementary way to find a MAXSAT solution. The thesis investigates several improvements to the MaxHS approach and provides empirical analysis of its behaviour in practise. The result is a new solver, MaxHS, that is shown to be the most robust existing solver for MAXSAT.

Many problems that arise in the real world are difficult to solve partly because they present computational challenges. Many of these challenging problems are optimization problems. In the real world we are generally interested not just in solutions but in the cost or benefit of these solutions according to different metrics. Hence, finding optimal solutions is often highly desirable and sometimes even necessary. The most effective computational approach for solving such problems is to first model them in a mathematical or logical language, and then solve them by applying a suitable algorithm. This thesis is concerned with developing practical algorithms to solve optimization problems modeled in a particular logical language, MAXSAT. MAXSAT is a generalization of the famous Satisfiability (SAT) problem, that associates finite costs with falsifying various desired conditions where these conditions are expressed as propositional clauses. Optimization problems expressed in MAXSAT typically have two interacting components: the logical relationships between the variables expressed by the clauses, and the optimization component involving minimizing the falsified clauses. The interaction between these components greatly contributes to the difficulty of solving MAXSAT. The main contribution of the thesis is a new hybrid approach, MaxHS, for solving MAXSAT. Our hybrid approach attempts to decouple these two components so that each can be solved with a different technology. In particular, we develop a hybrid solver that exploits two sophisticated technologies with divergent strengths: SAT for solving the logical component, and Integer Programming (IP) solvers for solving the optimization component. MaxHS automatically and incrementally splits the MAXSAT problem into two parts that are given to the SAT and IP solvers, which work together in a complementary way to find a MAXSAT solution. The thesis investigates several improvements to the MaxHS approach and provides empirical analysis of its behaviour in practise. The result is a new solver, MaxHS, that is shown to be the most robust existing solver for MAXSAT.

Bayesian process control is a statistical process control (SPC) scheme that uses the posterior state probabilities as the control statistic. The key issue is to decide when to restore the process based on real-time observations. Such problems have been extensively studied in the framework of partially observable Markov decision processes (POMDP), with particular emphasis on the structure of optimal control policy. Almost all existing structural results on the optimal policies are limited to the two-state processes, where the class of control-limit policy is optimal. However, the two-state model is a gross simplification, as real production processes almost always involve multiple states. For example, a machine in the production system often has multiple failure modes differing in their effects; the deterioration process can often be divided into multiple stages with different degradation levels; the condition of a complex multi-unit system also requires a multi-state representation. We investigate the optimal control policies for multi-state processes with fixed sampling scheme, in which information about the process is represented by a belief vector within a high dimensional probability simplex. It is well known that obtaining structural results for such high-dimensional POMDP is challenging. Firstly, we prove that for an infinite-horizon process subject to multiple competing assignable causes, a so-called conditional control limit policy is optimal. The optimal policy divides the belief space into two individually connected regions, which have analytical bounds. Next, we address a finite-horizon process with at least one absorbing state and show that a structured optimal policy can be established by transforming the belief space into a polar coordinate system, where a so-called polar control limit policy is optimal. Our model is general enough to include many existing models in the literature as special cases. The structural results also lead to significantly efficient algorithms for computing the optimal policies. In addition, we characterize the condition for some out-of-control state to be more desirable than the in-control state. The existence of such counterintuitive situation indicates that multi-state process control is drastically different from the two-state case.

Alternate Level of Care (ALC) patients are patients that stay in the acute care setting while waiting to be transferred to an ALC facility. They are not receiving the appropriate type of care and are occupying acute care resources. ALC patients occupy 5,200 patient beds everyday in Canada, and 12 percent of these ALC patients die during their waiting period. This study evaluates Toronto General Hospital's (TGH) discharge policy in the General Surgery and General Internal Medicine (GIM) departments using a discrete-event simulation. For long-term care ALC patients, it was found that applying to one extra application or maximizing the number of short waiting list facilities in their total number of applications significantly reduces the number of ALC days and the number of died in hospital patients. Knowing if discharge policies can decrease ALC days is not only significant to TGH but also to other health care institutions.

Alternate Level of Care (ALC) patients are patients that stay in the acute care setting while waiting to be transferred to an ALC facility. They are not receiving the appropriate type of care and are occupying acute care resources. ALC patients occupy 5,200 patient beds everyday in Canada, and 12 percent of these ALC patients die during their waiting period. This study evaluates Toronto General Hospital's (TGH) discharge policy in the General Surgery and General Internal Medicine (GIM) departments using a discrete-event simulation. For long-term care ALC patients, it was found that applying to one extra application or maximizing the number of short waiting list facilities in their total number of applications significantly reduces the number of ALC days and the number of died in hospital patients. Knowing if discharge policies can decrease ALC days is not only significant to TGH but also to other health care institutions.

Bayesian process control is a statistical process control (SPC) scheme that uses the posterior state probabilities as the control statistic. The key issue is to decide when to restore the process based on real-time observations. Such problems have been extensively studied in the framework of partially observable Markov decision processes (POMDP), with particular emphasis on the structure of optimal control policy. Almost all existing structural results on the optimal policies are limited to the two-state processes, where the class of control-limit policy is optimal. However, the two-state model is a gross simplification, as real production processes almost always involve multiple states. For example, a machine in the production system often has multiple failure modes differing in their effects; the deterioration process can often be divided into multiple stages with different degradation levels; the condition of a complex multi-unit system also requires a multi-state representation. We investigate the optimal control policies for multi-state processes with fixed sampling scheme, in which information about the process is represented by a belief vector within a high dimensional probability simplex. It is well known that obtaining structural results for such high-dimensional POMDP is challenging. Firstly, we prove that for an infinite-horizon process subject to multiple competing assignable causes, a so-called conditional control limit policy is optimal. The optimal policy divides the belief space into two individually connected regions, which have analytical bounds. Next, we address a finite-horizon process with at least one absorbing state and show that a structured optimal policy can be established by transforming the belief space into a polar coordinate system, where a so-called polar control limit policy is optimal. Our model is general enough to include many existing models in the literature as special cases. The structural results also lead to significantly efficient algorithms for computing the optimal policies. In addition, we characterize the condition for some out-of-control state to be more desirable than the in-control state. The existence of such counterintuitive situation indicates that multi-state process control is drastically different from the two-state case.

A margin account is a type of brokerage account that allows investors to buy and sell financial securities using credit. The account’s margin requirement is the amount of collateral required, from the investor, to cover the funds or securities extended by the broker to the investor. In Canada, the primary driver of an account’s margin requirement is the account’s Capital Charge [CC] which is calculated using a set of regulatory rules. The regulations are degenerate in that hundreds of valid CCs often exist for a single account. This work outlines a linear optimization model for selecting the minimal CC out of the set of valid CCs for a given margin account. The method proposed is consistent with all of the regulatory requirements and is guaranteed optimal in most cases. Relative to existing methods, the new method produced an average CC reduction of approximately 2% and displayed qualitatively better run-times.

The purpose of this work was to study the ability of the Slacks-Based Model of Data Envelopment Analysis in the prediction of corporate failure of non-manufacturing companies as compared to Altman’s Z’’ score model. This research looks at non-manufacturing firms specifically and attempts to classify companies without looking at the asset size of the firm. A DEA model based on the Altman’s Z’’ score financial ratios was created as well as a revised DEA model. The overall accuracy of the models showed the revised DEA model to be more accurate than the original DEA model as well as the Altman Z’’ score. This indicated that bankruptcy could be predicted without the use of total assets or liabilities as variables. This also showed the ability of an SBM DEA model to predict bankruptcy.

Linear assets are among the largest and most important engineered systems; their reliability is of the utmost importance. This thesis presents an overview of the reliability estimation methods used for the various types of linear assets, both observation- and statistically-based. While observation-based reliability monitoring and estimation methods are necessarily particular to a certain type of asset, statistically-based methods developed for one type can potentially inform those used for another. Therefore, this thesis looks to point out commonalities in the methods for the statistical evaluation of the reliability of various types of linear assets, develop and extend reliability models and methods with this knowledge, and suggest how maintenance strategies may be improved. To help illustrate and test the models described in this paper a case study was conducted with a utility operator; this thesis shows the modelling results from the study, and demonstrates the model’s use in a maintenance decision model.