Introduction to Mathematical Programming: Linear Programming
22 Pages Posted: 21 Oct 2008
Abstract
This note provides an introduction to mathematical programming (in general) and linear programming (in particular). A spreadsheet-based approach is used, accompanied by a graphical description of the fundamental underlying characteristics of resource-allocation problems exploited by linear programming.
Excerpt
UVA-QA-0377
INTRODUCTION TO MATHEMATICAL PROGRAMMING:
LINEAR PROGRAMMING
Introduction
While uncertainty is indisputably the primary source of difficulty in making business decisions, it is not the only source. Some decisions are difficult because a firm has a large number of profitable activities in which it can be engaged, but limited resources with which to undertake those activities. How to allocate resources to activities in this kind of situation is made particularly difficult when some activities make more effective use of certain resources, while other activities make more effective use of others. This difficulty can persist even if we are able to determine with great precision, the consequences of any particular resource allocation plan (hence little or no uncertainty). The difficulty stems from the sheer number of possible allocation schemes available and the complex and conflicting economic trade offs that have to be made involving how effectively different activities use different resources.
Mathematical programming is often an appropriate and valuable tool in this type of decision environment. Through the use of a mathematical model describing the relationships between the activities, resources, and objectives of the firm, the decision maker is freed from having to make the complex economic trade offs required to identify an optimal, in terms of the economics, allocation scheme, and is left to focus more intently on the less quantitative aspects of the allocation decision. Because the model can be developed and analyzed on a computer, the issue of the magnitude of the number of possible alternative allocation schemes becomes less significant.
. . .
Keywords: linear programming, planning, programming, quantitative analysis, general, resource allocation, spreadsheeets
Suggested Citation: Suggested Citation