Optimization is a natural human tendency. When we encounter a problem, our mind automatically dissects it, evaluates alternatives for possible courses of action, and lets us choose the best course of action. This sequence of events (dissection, evaluation, and action) constitutes the basis of optimization. Optimization can be qualitative or quantitative. Qualitative optimization involves individual judgments and preferences, such as a sociologist predicting social unrest in a community resulting from a political decision or a financial analyst predicting the most likely return a government could earn from a securities portfolio based on their own personal experience, knowledge, and skill. Quantitative optimization, on the other hand, requires precise mathematical rules to produce the best result.
As a concept, optimization is nothing new. The ancient Greeks, Romans, and Egyptians are known to have used it extensively in many of their works of art, architecture, and astronomy. Optimization plays just an important role in government today as it did centuries ago. The use of optimization as a means to improving performance can be found in almost every sphere of governmental activity. As the public demand for lean and efficient government continues to increase, so does the need for better and more efficient optimization tools to deal with the complex tasks of everyday government. This chapter presents a brief discussion of the nature of optimization, focusing in particular on classical optimization and two special cases of suboptimization that have received considerable attention in the literature: inventory and queuing models, with an emphasis on application in government.
In conventional terms, optimization means maximizing or minimizing an objective function, such as maximizing revenue for a government or minimizing cost(s) of operation for a service agency. To a mathematician, optimization does not necessarily mean maximization or minimization since there may be more than one mathematical