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Linear Optimization in Retail Settings

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Submitted By joshorellana92
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Abstract
In the summer of 2013, I received summer employment in one of the many manufacturing facilities the company, ALDI, utilizes in the southern United States. As a junior employee, I was tasked with analyzing the utilization of current resources and find the superlative combination of the resources available. However, as an undergraduate student, I had not studied mathematical formulas that would allow me to find the optimal solution. In this paper, I will use both linear optimization and goal programming to take a number of sets of data to analyze and discover the optimal use of various constraints of resources. The paper will be divided into three different sections with a specific method applied in the first two sections, and a final section to describe the possible errors in the solutions presented in the prior two sections.
In the first section, I will use linear optimization to take various sets of resources and distribute them appropriately among various products to find the best allocation to achieve maximum revenues. Linear optimization is the name of a branch of applied mathematics that deals with solving optimization problems of a particular form.1 Put simply, linear programming is finding the best outcome possible using a linear mathematical model. The constraints are linear inequalities of the variables used in the cost function. This method is the best available and of the most use given the present goal of achieving the maximum revenue possible for the company.
In the second section, I will use goal programming to take into account the second set of constraints that faces many companies—labor. Since ALDI was a private company that sold its 1 Schulze, Mark A. "Linear programming for optimization." Perceptive Scientific Instruments, Inc (1998).
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own manufactured products, I also had to study the labor that was utilized when selling the product

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