Defining a Business-Driven Optimization Problem

Defining a Business-Driven Optimization Problem

Shokoufeh Mirzaei (California State Polytechnic University, USA)
Copyright: © 2014 |Pages: 8
DOI: 10.4018/978-1-4666-5202-6.ch066
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Abstract

The purpose of this chapter is to provide fundamental information about business analytics and optimization for users ranging from college students to consultants and managers for a successful practice of data analytics. Therefore, this chapter does not contain any mathematical programming. Instead, it is a proof that defining an optimization problem is neither a privilege nor a talent issue, but the ability of simply putting puzzle pieces together using directives. This chapter is written based on the challenges that the author has experienced as a business analytics consultant and a researcher in the field.
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Background

Since early times, optimizing the performance of systems was an abiding interest of human. Despite the optimization concept, the large-scale practical optimization has a short history (Chinneck, 2000). Dantzig (1947) developed the first practical, large-scale optimization technique –simplex- during the World War II to solve the massive logistic problems which were originated by millions of people and machine resources involved (Rao, 1996). A few years after war and by advances in computer technology, “simplex” was completed. Since then, new optimization techniques are arriving on a daily basis. Optimization is yet an exciting hotbed of innovation with an excellent field for researchers (Richard, 2003). In the recent years, it has a spectacular breakthrough in businesses as most of business decisions have the objective of optimizing some desirable attributes. Big companies like IBM have made huge investments on business analytics tool and optimization technology. IBM alone expects to have 16 billion dollars in revenue from business analytics and optimization tools by 2015 (Bednarz, 2011).

There are several classifications of optimization problems available. One classification divides the problems to constrained and unconstrained. In the unconstrained optimization, the system under study has no constraint and there is no limitation for the results obtained. On the other hand, in the constrained optimization, the best result must satisfy a set of system constraints. Most of business problems are constrained by the system restrictions as well as the relations among the system elements. The most common classification of optimization problems in literature is based on the problems mathematical formulation. Some of the classifications which tie to the mathematical formulation of problems are linear programming, non-linear programming and integer programming. These names are borrowed from the nature of relations between the system elements. For instance, a linear programming implies that there is (are) linear relation(s) among the system elements. However, in real-life situations, relations among system elements are rarely linear and thus application of nonlinear programming is required. There are several branches for both linear and non-linear programming such as integer programming. For more insight about linear and non-linear programming, one can refer to Vanderbei (2001) and Bertsekas (1999).

Key Terms in this Chapter

Business Analytics: A set of tools and methods used for execrating business insight making from the available data or system structure. It provide meaningful information with dynamic and sophisticate methods of problem solving such as optimization.

Prescriptive Analytics: A system-driven approach of problem solving. It includes a set of methods such as optimization which are independent of the historical data and are built based on a system objective(s) and constraints.

Constrained Optimization: A class of optimization problems in which the value of decision variables is subject to a set of system constraints.

Predictive Analytics: A set of data–driven tools and methods to study a system behavior over time and to predict the future outcomes.

Objective Function: In the context of optimization, an objective function is the system objective presented as a function of decision variables. The ultimate goal of optimization is to find the value for decision variables in a way that this function is maximized or minimized.

Decision Variables: In the context of optimization, decision variables are unknown and controllable parameters of the system which finding their value is the purpose of problem solving effort. The value of decision values determines the system objective function value.

Constraints: System limitations in terms of the available resources such as capacity. For example, a manufacturing company is constrained by the available capacity of its suppliers.

Business Intelligence: The ability to collect, integrate, and organize the data in a way which received by the right source, at the right time, and via the right tool. It provides basic insights about the data by regenerating reports, queries, alerts, etc.

Linear Programming (LP): A class of optimization problems in which constraints and objective function(s) are represented as linear functions.

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