Linear Programming

The development of linear programming has been ranked among the most important scientific advances of the mid 20th century. Its impact since the 1950’s has been extraordinary. Today it is a standard tool used by some companies (around 56%) of even moderate size. Linear programming uses a mathematical model to describe the problem of concern. Linear programming involves the planning of activities to obtain an optimal result, i.e., a result that reaches the specified goal best (according to the mathematical model) among all feasible alternatives.

Linear Programming as seen by various reports by many companies has saved them thousands to even millions of dollars. Since this is true why isn’t everyone using Linear Programming? Maybe the reason is because there has never been an in-depth experiment focusing on certain companies that do or do not use linear programming. My main argument is that linear programming is one of the most optimal ways of resource allocation and making the most money for any company today.

I used (in conjunction with another field supporter вЂ" My Dad) the survey method to ask 28 companies that were in Delaware, New Jersey, and Pennsylvania whether they were linear programming users. In addition, I wanted to examine the effect of the use of linear programming across three different but key decision support areas of the participating companies to include (1) Planning (2) Forecasting and (3) Resource Allocation. The companies were selected randomly from the Dunn & Bradstreet Database of companies and also from the CNN and Yahoo Databases of company performances. All these data sources are available free of charge.

The three key measures that I wanted to use to examine the impact of LP on company results were EPS, (Earnings per Share; explained later) the ROI%, (Rate on Investment or the Rate of Return; explained later) and Profit. I used these three measures as they are key measures that Wall Street Investors look at when they examine a company’s performance.

This research is limited to understanding how Linear Programming (i.e., Optimization) has affected the results of companies generally, if at all, and is based on my own view (in this case my hypothesis) that companies that do use LP actually derive some benefit from doing so.

Introduction

The development of linear programming has been ranked among the most important scientific advances of the mid 20th century and I must agree with this assessment. Its impact since the 1950’s has been extraordinary. Today it is an industry standard optimization tool that is thought to have saved many millions of dollars for some companies or businesses in the various industrialized countries of the world; and its use in other sectors of society has also been growing.

A major proportion of all scientific computer development is devoted to one linear programming function or another and published articles describing important LP applications now number in the hundreds. Even though vast amounts of money have been saved using linear programming very few corporations in the United States of America are using it.

After scouring websites and articles that date back to the 1980’s I have found very little hard research on why every company should use linear programming (LP). There has been some research involving LP but this has been very narrow and limited to sectors like defense and manufacturing. The research I found was insufficient to prove that LP is among the most effective methods to optimize planning, forecasting or resource allocation decisions as it was not wholly devoted to examining the impact of the use of LP on company results.

There are also various methods within a company that are similar to LP and these have been used before the 1950’s which is when LP was introduced. Most of the largest companies in the world are not using LP and this is because most of the companies in the world today started before the 1950’s. Thus they have not switched to the latest method and they might be losing profit if my hypothesis proves to be correct. My goal is to prove that LP is a useful contributor to the profits and returns on investments of those companies that use LP.

I believe that every company should be using LP and I have hypothesized that linear programming increases both EPS, ROI and by definition Profit. This research therefore assumes that a company not using LP would have made less money than one that did use LP. The sample is 28 companies and I felt this would be sufficient as a sample size as statisticians typically recommend a minimum of 20 data points (in this case