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Price and inventory decisions are key levers of profit for firms. A manager needs to understand the impacts of pricing, ordering and stocking decisions not only on today's operations but also on future demand. In this dissertation we investigate these intertwining decisions by incorporating inter-temporal effects of pricing decisions through reference prices. We introduce three significant extensions to reference price models to provide more meaningful insight into pricing, inventory and ordering decisions. We first present a threshold reference model. The threshold model incorporates zones of insensitivity around expected price that moderate the reference impacts on demand. This provides a rigourous model that is flexible enough to handle different pricing strategies such as single everyday low pricing (EDLP), high-low pricing (HiLo) and other general price cycles. We develop two solution approaches and provide computational results. We next introduce a reference model with stochastic demand. There is considerable previous research supporting the consideration of variability in pricing and inventory decisions and this is especially true in the context of inter-temporal demand interactions based on pricing decisions. We find that the introduction of stochastic elements can actually increase or decrease the length of the price cycle for some consumers in a reference model depending on the parameters of the model. This extends the stochastic demand model and bridges to reference models for improved managerial insight. The final model presented is the dynamic lot sizing model. When prices and production decisions or order quantities are determined simultaneously the interactions need to be considered to optimize profits. The reference model incorporates the inter-temporal price effects to provide a clearer picture of the optimal decision. The inclusion of reference effects does change the optimal decision. / Thesis / Doctor of Philosophy (PhD)

There are increasing economic incentives within the chemical process industry towards demand driven operation with product diversification, requiring flexible operation in responsive plants. In continuous processes, this is realized through steady-state transitions but requires consideration of process dynamics arising from operation that is inherently transient in nature. The steady-state economic optimum is typically defined at the intersection of constraints, and requires multivariable control with optimal constraint handling capabilities. Thus, constrained model predictive control is well-suited to realize the profit potential at the economic optimum. In this thesis, feasible and optimal steady-state transitions are achieved using reference management with consideration of the closed-loop dynamics of constrained model predictive control. The supervisory control scheme is used to determine the optimal setpoint trajectory which is subsequently tracked by regulatory control, incorporating feedback for the rejection of high frequency disturbances and eliminating steady-state offset in the presence of model mismatch. The separation of economic and control objectives enables the lower level to be tuned for stability and the upper level to be tuned for performance. The mathematical formulation results in a multi-level optimization problem with an economic objective function at the upper level, and a series of control performance objective functions arising from constrained model predictive control at the lower levels. The solution strategy proposed converts the multi-level optimization problem into a single-level optimization problem using the Karush-Kuhn-Tucker conditions, and solves the resulting complementarity conditions using an interior point approach. Alternative objective formulations are investigated based on maximizing profit during transient operation. The first formulation is typically based on a quadratic objective function minimizing the transition time, indirectly improving economic operation by reducing the amount of off-specification product produced. The second formulation is based on the explicit consideration of economics. The profit calculated during transient operation is based on the difference between the revenue generated by the production of acceptable product within specified univariate product quality bands, and the operational costs of raw materials and utilities. The resulting linear objective function is further extended to incorporate control performance considerations to improve conditioning for gradient based optimization. The proposed methodology is applied to a single-input single-output linear system, demonstrating the potential benefits of simultaneous rather than sequential optimization in terms of computational efficiency and solution reliability. Alternative objective function and constraint formulations are investigated, and the effect on the optimal solution assessed. In particular, the possibility of indeterminacy is shown and handled using hierarchical optimization. The methodology is also demonstrated on additional examples including non-minimum phase systems and multi-input multi-output linear systems. Application to a multi-input multi-output nonlinear system corresponding to styrene polymerization using the proposed methodology is detailed. The set of differential and algebraic equations defining the process is discretized using orthogonal collocation on finite elements. The optimal operation during grade transitions based on explicit consideration of economics is determined, and additional improvements realized by manipulating the production rate. Finally, reference management with online re-optimization is investigated for a single-input single-output linear system based on a bias update, and the improvement in closed-loop performance assessed for output disturbances and model mismatch. The methodology is also demonstrated on a multi-input multi-output system based on a linear model when applied to the nonlinear process. The proposed methodology developed for steady-state transitions may also be applied to batch operation, startups and shutdowns. Future extensions include analysis of closed-loop stability due to the incorporation of feedback within the cascade control scheme, and the explicit consideration of uncertainty. / Thesis / Master of Applied Science (MASc)

This dissertation explores the importance of the payoff structure and beliefs for noncooperative games. Chapter 2 considers instances where the payoffs and the objectives may not be very clear to the players or the analyst. We develop a model for analyzing such games using a vector of reference utilities which are included in the definition of the game and assumed to be shared by all players. These are used to obtain the true utilities in the game. Conditions for the existence of equilibrium are identified by allowing players to have beliefs about the others. The solution concept is applied to the Traveler's Dilemma and a duopoly. In Chapter 3 a non-cooperative model of network formation is developed. Agents form links based on the cost of the link and its assessed benefit. Link formation is one-sided, i.e., agents can initiate links with other agents without their consent, provided the agent forming the link makes the appropriate investment. The model builds on the work of Bala and Goyal, but allows for agent heterogeneity by allowing for different failure probabilities. We investigate Nash networks that exhibit connectedness and redundancy and provide an explicit characterization of star networks. Efficiency and Pareto-optimality issues are discussed through examples. We also explore the consequences of three alternative specifications which address criticisms of such communication networks. Chapter 4 examines noncooperative fuzzy games. Both in fuzzy noncooperative games and in abstract economies, players impose mutual restrictions on their available strategic choices. Here we combine these two theories: A player tries to minimize the restrictions he imposes on others, while respecting the restrictions imposed by others on him, but does not explicitly pursue any other objectives of his own. We establish existence of an equilibrium in this framework. In Chapter 5 normal form game is modeled using tools from fuzzy set theory. We extend the decision theory framework of Bellman and Zadeh (1970) to a game-theoretic setting. The formulation is preliminary / Ph. D.

The youth market has been characterized as one of the most coveted market segments because of its spending power and tremendous potential for becoming lifetime customers (Bush, Martin, & Bush, 2004). The product market for adolescents is expected to grow to more than $208 billion by 2011, according to a report from market research firm Packaged Facts (Sass, 2007). Apparel, jewelry, and cosmetics are top product categories for adolescent girls and are important products used by adolescents to portray personal identity (Ossorio, 1995). Because of adolescents' buying power and the important role apparel plays in adolescents' lives, it is important for apparel marketers to understand the adolescent consumer market. The purpose of this research was to examine the relationship between each of three independent variables (i.e., reference groups, clothing symbolism, and clothing involvement) and adolescents' clothing purchase intentions and clothing behavior, and whether the three variables are predictors of adolescents' clothing purchase intentions and clothing behavior. Reference groups are a source of instrumental and emotional support, offering adolescents a sense of belonging during their physical, emotional, and cognitive adjustment (Blackwell, Miniard, & Engel, 2001). Adolescents may have many different types of reference groups. The reference groups included in the currents study were friends, popular girls, and parents. Specifically in the current study, ninth grade girls' perceptions of friends' clothing behavior, popular girls' clothing behavior, and parents' opinions concerning clothing behavior were examined for their relationship to the ninth grade girls' clothing purchase intentions and behavior. The second independent variable was clothing symbolism. Adolescents may use clothing as a symbol (i.e., clothing symbolism) to express their actual self-concepts or to attain their ideal self-concepts (Erickson, 1983; Solomon & Rabolt, 2004). Two types of clothing symbolism were included in the study: the degree of congruity between actual self-concept and the perceived images of four outfits (i.e., actual self and clothing image congruity) and the degree of congruity between ideal self-concept and the perceived images of four outfits (i.e., ideal self and clothing image congruity). The third independent variable was clothing involvement. Viera (2009) found that young consumers are highly involved with clothing. The degree of clothing involvement may be closely related to adolescent girls' clothing purchase intentions and their clothing behavior. A conceptual model that formed the framework for this study was developed by integrating several theories, propositions, and research findings in the literature. Based on the framework, 16 research questions were formulated. Focus groups provided input for questionnaire development, and four outfit images, one each considered sexy, conservative, springy, or sporty, were identified and included in the questionnaire. Before the main data collection, the questionnaire was pilot tested and revised. Data collection was conducted at three high schools in central Virginia, and 353 female students in the ninth grade participated. Standard and stepwise multiple regression analyses were used to address the research questions. Among the four outfit images, that with a sexy image was found to have the highest mean score for ideal self-concept, indicating that participants would most like to view themselves sexy. Results of a factor analysis for clothing involvement revealed three factors: clothing importance, clothing expressions, and clothing brand perceptions. Participants had fairly high mean scores for all three clothing involvement factors. Among those three factors, clothing importance had the highest mean. In addition, results showed that participants perceived that their friends and popular girls would most often wear the outfit with a sporty image, and they also perceived that their parents would most like them to wear an outfit with a sporty image. The sporty outfit image also had the highest mean for participants' clothing purchase intentions and clothing behavior among the four outfit images. Results of one of the stepwise regressions, for the sexy outfit image showed that perceptions of reference groups' clothing behavior or opinions (i.e., friends' clothing behavior, parents' opinions concerning clothing behavior, popular girls' clothing behavior), one type of clothing symbolism (i.e., ideal self and clothing image congruity), and one clothing involvement factor (i.e., clothing importance) predicted adolescent girls' purchase intentions for the outfit with a sexy image. The results for wearing clothing with a sexy image when hanging out with friends were slightly different from those for purchase intentions. For the behavior of wearing an outfit with a sexy image, the variable "perceptions of popular girls' clothing behavior" was not a predictor, but actual self and clothing image congruity was. For the springy outfit image, all the perceptions of reference groups' clothing behavior or opinions and actual self and clothing image congruity were the best predictors of participants' clothing behavior; however only friends' clothing behavior and popular girls' clothing behavior were significant predictors of adolescent girls' purchase intentions for this outfit image. For the conservative and sporty outfit images, only the perceptions of reference groups' clothing behavior or opinions predicted adolescent girls' clothing purchase intentions and clothing behavior. In conclusion, the research findings suggest a powerful relationship between adolescent girls' perceptions of reference groups' clothing behavior or opinions about clothing behavior and the girls' own clothing behavior and purchase intentions. Participants' perceptions of reference groups' clothing behavior or opinions were the best predictors of the participants' clothing behavior and purchase intentions for all four outfits. Furthermore, clothing symbolism (e.g., using a sexy outfit to express or attain a sexy image) appears to motivate ninth grade girls to wear clothing with a sexy or springy image. The girls would wear a sexy outfit to portray their actual self-concepts and attain their ideal self-concepts. They also would wear outfits with a springy image to portray themselves. Additionally, the more the participants in this study considered clothing to be important, the more likely they were to purchase and wear a sexy image outfit; however the participants indicated that, of the four outfit images in the study, they most purchase and wear clothing like the sporty image outfit the most for hanging out with friends in comparison to the other three outfit images. Based on the findings, suggestions and implications for parents, educators, and marketers were provided. / Ph. D.

In this thesis, we measure the impact of reference semantics on programming and reasoning. We designed a survey to compare how well programmers perform under three different programming paradigms. Two of the paradigms, object-copying and swapping use value semantics, while the third, reference-copying, uses reference semantics. We gave the survey to over 25 people. We recorded number of questions answered correctly in each paradigm and the amount of time it took to answer each question. We looked at the overall results as well as the results within various levels of Java experience. Based on anecdotal evidence from the literature, we expected questions based on value semantics to be easier than questions based on reference semantics. The results did not yield differences that were statistically significant, but they did conform to our general expectations. While further investigation is clearly needed, we believe that this work represents an important first step in the empirical analysis of a topic that has previously only been discussed informally. / Master of Science