1 Introduction
Operations Research, in a narrow sense, is the application of scientific models,
especially mathematical and statistical ones, to decision making problems.
The present course material is devoted to parts of mathematics that are used
in Operations Research.1.1 Mathematics and OR
In order to clarify the understanding of the relation between two disciplines,
let us examine Figure 1.1. The scientific inquiry has two aims:- cognitive: knowing for the sake of knowing
- instrumental: knowing for the sake of doing
If A is Bis a proposition, and if B belongs to A, the proposition is analytic.
It can be validated logically. All analytic propositions are a priori. They are
tautologies like "all husbands are married". If B is outside of A, the proposition
is synthetic and cannot be validated logically. It can be a posteriori like "all
African-Americans have dark skin" and can be validated empirically, but there
are difficulties in establishing necessity and generalizability like "Fenerbahce
beats Galatasaray".
Mathematics is purely analytical and serves cognitive inquiry. Operations
Research is (should be) instrumental, hence closely related to engineering,
management sciences and social sciences. However, like scientific theories, Op-
erations Research - refers to idealized models of the world,
- employs theoretical concepts,
- provides explanations and predictions using empirical knowledge.
The purpose of this material is to review the related mathematical knowledge
that will be used in graduate courses and research as well as to equip the
student with the above three tools of Operations Research.