Engineering Optimization

25Effects of Uncertainty

25.1 Introduction

In optimization a major source of uncertainty is in the “givens,” which are the coefficient values that represent forecast conditions and are the basis for the optimization. Because of these “givens,” uncertainty is usually not obvious or expected. For example, basis‐type givens in an application could be the expected number of customers, the price of electricity, the composition of raw material from a mine, and the time duration per day that a person will be on the computer. Another category of givens is the assumptions about conditions. These could include ambient temperature or humidity, the competition’s introduction of new products or pricing, or customer buying trends. In classic word problems, the givens are exactly, precisely specified and have no uncertainty.

For example, the question might be “If the average word length is 5 characters per word, and there are 500 words in an essay, what page size is optimum?” If a page size is one word too small, then two pages are needed, which wastes paper. Alternately, if a page is very large, excess paper is wasted. The givens are 5 characters per word and 500 words. Assumptions will be that punctuation and paragraph characters are included in the average characters per word and that margins and font are standard. The model is that each word is spaced by one blank and a space character follows each word except for the last word. The model is that a character has a height of 3/16th and ...