Essays in marketing, economics, and optimization
Keywords: Management Science and Engineering.

This thesis includes four self-contained essays on marketing, economics, and optimization, all sharing a common theme: creating numerical models and algorithms to tackle computationally challenging optimization problems. The first essay considers geographic sub-branding via manufacture location in marketing. Manufacture location, as part of geographic product identity, is becoming a significant differential factor among a variety of products and a sub-branding element in various markets, but there is little empirical research on how manufacture location influences consumer preference and purchase choices. The first barrier comes naturally from the market. Most of the time, manufacture location is completely correlated with product characteristics. I was fortunately able to acquire both data and a whole year research grant from Ford Motor Company. New car buyer data in the Chinese automobile market makes possible the analysis of manufacture location as a geographic sub-branding element. Hedonic price analysis gives us a quick and intuitive view of how much consumers are willing to pay for geographic sub-branding products, and also motivates our new brand and sub-brand definition for a BLP-type random coefficient discrete choice model. However, using General Method of Moments (GMM) to estimate the variance-covariance matrix of consumer brand taste coefficients poses another challenge for all existing optimization solvers. To prevent indefinite unknown variance-covariance matrices in the constraints of the optimization problem from terminating the solver, I reformulate the optimization program and successfully solve the problem. If the computation becomes more difficult, we can also apply our new algorithm NCL, which is described in details in the third essay. Our results reveal the strong substitution patterns in the market and confirm our definition and framework of brand and geographic identity. Furthermore, our method can be helpful in the analysis of branding and sub-branding in other empirical settings. The second essay studies optimal income taxation with multidimensional taxpayer types in economics. This engendered the subject of the third essay: stabilized optimization via an NCL algorithm in numerical optimization. The income taxation literature has generally focused on economies where individuals differ only in their productivity, i.e., income. In reality, people differ in many ways. In our models, we consider people's productivity, basic needs, distaste for work, the elasticity of labor supply, and the elasticity of demand for consumption. We find that extra dimensions give us substantially different and interesting results. In certain cases, high-productivity people may pay negative tax. Therefore, considering income taxation in multiple dimensions is essential, and again is computationally challenging. All existing optimization solvers fail to find optimal solutions. Eventually, we transformed the model, created a new algorithm (NCL), and solved the high-dimension difficult optimization problems. The nonlinearly constrained augmented Lagrangian algorithm (NCL) we created was motivated by the bound-constrained and the linearly constrained augmented Lagrangian algorithms (BCL and LCL). To facilitate implementation, we take advantage of the mathematical programming language AMPL. We did not have to write fifty thousand lines of Fortran code to implement NCL. The third essay on algorithm NCL was published this year in Numerical Analysis and Optimization. The taxation part remains as a working paper. I am excited about not only solving the complex income taxation models, but also creating a general algorithm that can be applied to tough mathematical models in different fields. For instance, our algorithm NCL can be easily adapted to nonlinear pricing in economics and marketing. The fourth essay considers reliable and efficient solution of genome-scale models of metabolism and macromolecular expression. For many years, scientific computing has advanced in two complementary ways: improved algorithms and improved hardware. In order to solve the large and complicated biochemical network of metabolism in systems biology, we made use of improved machine precision and created algorithms utilizing software-simulated quadruple precision arithmetic and successfully solved both original and reformulated optimization models. This essay is published in Scientific Reports. Today, our linear and non-linear quadruple precision solver quadMINOS is supporting the research of systems biologists in their COBRA (COnstraint-Based Reconstruction and Analysis) Toolbox, and it can also help researchers in many other areas. As my advisor Professor Michael Saunders predicts: ``Just as double precision floating-point hardware revolutionized scientific computing in the 1960s, the advent of the quadruple precision data type, even in software, brings us to a new era of greatly improved reliability in optimization solvers.''.