Banks occasionally employ frontier efficiency analyses to objectively identify best practices within their organizations. Amongst the frontier efficiency analyses identified in the literature, Data Envelopment Analysis (DEA) was found to be one of the leading approaches. DEA has been successfully applied in many bank branch performance evaluations using traditional intermediation, profitability and production approaches. However, there has been little focus on assessing the growth potential of individual branches. This research presents six models that examine four perspectives of branch growth. Each model was applied to the branch network of one of Canada’s top five banks to gauge the growth potential of individual branches and to provide tailored improvement recommendations. Using various analysis methodologies, the results of each model were examined and their functionality assessed. Based on these findings, three models were deemed to produce significant results, while the remaining three failed to attain viable results.

Polynomial programming, a class of non-linear programming where the objective and the constraints are multivariate polynomials, has attracted the attention of many researchers in the past decade. Polynomial programming is a powerful modeling tool that captures various optimization models. Due to the wide range of applications, a research topic of high interest is the development of computationally efficient algorithms for solving polynomial programs. Even though some solution methodologies are already available and have been studied in the literature, these approaches are often either problem specific or are inapplicable for large-scale polynomial programs. Most of the available methods are based on using hierarchies of convex relaxations to solve polynomial programs; these schemes grow exponentially in size becoming rapidly computationally expensive. The present work proposes methods and implementations that are capable of solving polynomial programs of large sizes. First we propose a general framework to construct conic relaxations for binary polynomial programs, this framework allows us to re-derive previous relaxation schemes and provide new ones. In particular, three new relaxations for binary quadratic polynomial programs are presented. The first two relaxations, based on second-order cone and semidefinite programming, represent a significant improvement over previous practical relaxations for several classes of non-convex binary quadratic polynomial problems. The third relaxation is based purely on second-order cone programming, it outperforms the semidefinite-based relaxations that are proposed in the literature in terms of computational efficiency while being comparable in terms of bounds. To strengthen the relaxations further, a dynamic inequality generation scheme to generate valid polynomial inequalities for general polynomial programs is presented. When used iteratively, this scheme improves the bounds without incurring an exponential growth in the size of the relaxation. The scheme can be used on any initial relaxation of the polynomial program whether it is second-order cone based or semidefinite based relaxations. The proposed scheme is specialized for binary polynomial programs and is in principle scalable to large general combinatorial optimization problems. In the case of binary polynomial programs, the proposed scheme converges to the global optimal solution under mild assumptions on the initial approximation of the binary polynomial program. Finally, for binary polynomial programs the proposed relaxations are integrated with the dynamic scheme in a branch-and-bound algorithm to find global optimal solutions.

Populus tremuloides Michx. (trembling aspen) is a tree species native to much of North America, characterized by an excurrent crown with horizontal to ascending branches and a dominant terminal leader. An unusual clone of trembling aspen was discovered in the 1940s near Hafford, Saskatchewan. This clone demonstrates abnormal crown morphology, in which vigorous shoots bend down, ultimately leading to an overall twisted or crooked appearance. The objectives of the present study were to investigate the mechanism of shoot bending by (1) characterizing the process and timing of bending, (2) evaluating structural aspects of developing wild-type and crooked aspen shoots, and (3) comparing anatomical features of bending shoots with wild-type shoots. L-system reconstruction models of 3-D digitized shoot development revealed dramatic bending midway through the growing season. Morphological analyses revealed that crooked aspen shoots had greater taper compared to the wild-type, typically known to create shoots resist deflection and bending. However, preliminary strength analyses indicated that crooked aspen shoots were less rigid, with smaller values of Young’s modulus compared to wild-type shoots. Anatomical investigations revealed differences in several structural tissues between developing wild-type and crooked aspen shoots, and differences within crooked aspen shoots. Primary phloem fibres on the upper side of bending shoots maintained relatively large lumens while those on the lower side were fully lignified, similar to those of mature vertically oriented wild-type leader shoots. These differences may result in differential extension growth early in development, and/or uneven mechanical support later on, ultimately resulting in bending due to self-weight. Gelatinous fibres (G-fibres), characteristic of tension wood (TW), were found throughout older wild-type and vertically oriented crooked aspen shoots; however, G-fibres were only found on the lower side of crooked aspen shoots. These lateral differences could have contributed to shoot bending by actively bending shoots downwards, or lack of TW on the upper side may not have prevented biomechanical bending from self weight. Nevertheless, shoot bending stops at the end of the growing season, suggesting that the mechanisms involved in creating bent shoots are only functional during the first growing season.

In this study, a single machine batch-scheduling problem with incompatible jobs and dynamic arrivals is examined. The objective function is the minimization of the total flow time of the jobs. For solving problems a case specific branch and bound algorithm with a heuristic upper bound scheme and two alternative lower bound procedures is used. An extensive computational experiment is conducted to investigate the effects of certain parameters on the computation time. For the most difficult parameter combination branch and bound algorithm can solve the problems about 25 jobs with 4 different job types in a 10 minutes time on average. For the problem types with higher number of jobs and the most difficult parameter combination proposed upper bound heuristic can be used to obtain near optimal solutions.

In this study, we address job sequencing and tool switching problem arising in Flexible Manufacturing Systems. We consider a single machine with limited tool slots on its tool magazine. The available tool slots cannot accommodate all the tools required by all jobs, therefore tool switches between jobs are required. A single tool transporter with limited capacity is used in transporting the tools from the storage area to the machine. Our aim is to minimize the number of tool transporter movements. We provide two mixed integer linear programming formulations of the problem, one of which is based on the traveling salesman problem. We develop a Branch-and-Bound algorithm powered with various lower and upper bounding techniques for optimal results. In order to obtain good solutions in reasonable times, we propose Beam Search algorithms. Our computational results reveal the satisfactory performance of the B&amp / B algorithm for moderate sized problems. Moreover, Beam Search techniques perform well for large-sized problems.

In this thesis, we develop an exact algorithm for an assembly line balancing problem with equipment selection decisions. Two objectives are considered: minimizing the total equipment costs and the number of workstations. Our aim is to choose the type of the equipment(s) in every workstation and determine the assignment of the tasks to each workstation and equipment type. We aim to propose a set of efficient solutions for each problem and leave the choice of the best solution to the decision maker&rsquo / s preferences. A branch and bound algorithm is developed whose efficiency is increased with some dominance rules and powerful lower bounds. Moreover, modified ranked positional weight heuristic method is used as initial upper bound. The effectiveness of the proposed procedure is demonstrated by computational analysis in which the effects of changing certain parameter values are investigated. We find that our algorithm is capable of solving the problem instances with up to 25 tasks and 5 equipments.

In this study, we consider the disassembly problem of end-of-life (EOL) products for recovering valuable parts or assemblies. All parts obtained by disassembly processes of an EOL product may not be profitable due to their high recovery costs. Our problem is to select the parts to be released and determine the associated disassembly tasks so as to maximize the total profit. We first tackle the simple part selection problem, and then introduce a time constraint for the tasks to be performed for selected parts and search for incomplete time constrained sequences. We formulate our first problem as a Mixed Integer Problem and show that the constraint set of this formulation is totally unimodular. We also provide the dual formulation of our problem and its interpretation. For time-constrained part selection problem we propose a branch-and-bound algorithm. We first develop some reduction mechanism to reduce the size of the problem. Our solution procedure is capable of solving problems with up to 94 parts and tasks.

In the refining industry, the cost of a power system interruption is dominated by an associated loss of production. Power distribution within a refinery includes a set of production units within a highly inter-dependent process, where the outage of a single unit affects the production of additional units. This thesis proposes a method to quantify the impact of this cascading effect, called the criticality enhancement function, in which a process reliability model is introduced to link electrical outage cut-sets with lost production. Power system criticality is analyzed using four different approaches to the calculation of annual expected impact from load point interruptions on a case study of the 125,000 barrel-per-day Petro-Canada Edmonton Refinery. This thesis demonstrates how employment of the proposed technique, with its marriage of electrical and process reliability models, enables the most accurate estimation of the impact of power system interruptions.

Identification of salt- resistant tree species and genotypes is needed for rehabilitation of lands affected by salinity in Mexico. This dissertation consists of four studies for analyzing the responses of Pinus leiophylla seedlings to salt. In the first study, resistance to salt stress was studied in six-month-old seedlings from eight different sources of seed collected from the areas with contrasting precipitation levels. Plants from the xeric areas were shorter and had smaller stem diameters but were less sensitive to salt stress and recovered faster from salt injury compared with the plants from mesic sites, suggesting that morphological and physiological adaptations to drought were helpful with salt stress resistance. In the second study, fascicle needle production and tissue ion accumulation were examined in NaCl-treated three-month-old seedlings from two populations of the xeric origin and two populations from the mesic areas. Seedlings from the xeric population of San Felipe developed fewer fascicles and had shorter needles compared with seedlings from the remaining three populations. NaCl treatment delayed the emergence of fascicles and reduced the fascicle needle production and needle length. However, the extent of needle injury and ion accumulation in shoots were lower in the San Felipe seedlings compared with the other studied populations. In the third study, the effects of branch pruning and seedling size on total transpiration and accumulation of Na+ and Cl- in tissues were examined. Total plant transpiration, as affected by plant size and branch pruning, was correlated with Na+ and Cl- needle concentrations and needle necrosis. Branch pruning reduced ion accumulation in the shoots and needle necrosis levels in short seedlings but not in the tall seedlings. In the fourth study, sprouting and physiological responses of 16 month-old-seedling to salt were examined. NaCl treatment concentrations of 100, 150, and 200 mM reduced gas exchange and root hydraulic conductance, caused needle injury and triggered sprouting of adventitious shoots. Sprouting from the upper parts of the main stem and lateral branches was three times greater with 100 and 150 mM NaCl compared with 200 mM NaCl treatment but, at the base of the stem, sprout numbers were similar for all NaCl treatments.

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