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# FORMULATING A LINEAR PROGRAMMING MODEL

IP.com Disclosure Number: IPCOM000128829D
Original Publication Date: 1956-Jul-09
Included in the Prior Art Database: 2005-Sep-19
Document File: 4 page(s) / 22K

## Publishing Venue

Software Patent Institute

## Related People

Dantzig, G.B.: AUTHOR [+3]

## Abstract

Linear Programming Defined.....1 Linear Programming is defined as a technique for building a model to describe the interrelations of the components of a system. The relationship between activities and items of the system constitutes the linear programming model and gives rise to the central mathematical problem. II. The L.P. Model Illustrated.....4 A simplified oil refinery example is used to illustrate the principles of building a linear programming model.

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THIS DOCUMENT IS AN APPROXIMATE REPRESENTATION OF THE ORIGINAL.

FORMULATING A LINEAR PROGRAMMING MODEL

G. B. Dantzig

P-893
July 9, 1956

The RAND Corporation 1700 MAIN ST. SANTA MONICA CALIFORNIA

SUMMARY Page

Linear Programming Defined.....1

Linear Programming is defined as a technique for building a model to describe the interrelations of the components of a system.

The relationship between activities and items of the system constitutes the linear programming model and gives rise to the central mathematical problem.
II. The L.P. Model Illustrated.....4
A simplified oil refinery example is used to illustrate the principles of building a linear programming model.

FORMULATING A LINEAR PROGRAMMING MODEL [ title ]

G. B. Dantzig

I. Linear Programming Defined

One of the reasons why the programming tool has assumed importance, both in industry and in the military establishment, is that it is a method for studying the behavior of systems. In philosophy it is close to what some describe as the distinguishing feature of management science or operations research, to wit: "Operations are considered as an entity. The subject matter studied is not the equipment used, nor the morale of the participants, nor the physical properties of the output, it is the combination of these in total as an economic process."1

To many the term "linear programming" refers to mathematical methods for solving linear inequality systems. While this may be the central mathematical problem it is not its definition. Linear programming is a technique for building a model for describing the interrelations of the

1 Operations Research for Management, C. C. Hermann and J. F. Magee, Harvard Bus. Rev., July, 1953.

Rand Corporation Page 1 Jul 09, 1956

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FORMULATING A LINEAR PROGRAMMING MODEL

components of a system. As such it is probably the simplest mathematical model that can be constructed of any value for broad programming problems or industry and government. Thus the importance of the linear programming model is that it has wide applicability.

Suppose that the system under study (which may be one actually in existence or one which we wish to design) is a complex of machines, people, facilities, and supplies. It has certain over-all reasons for its existence. For the military it may be to provide a striking force or for industry it may be to produce certain types of products.

The linear programming approach is to consider the entire system as decomposable into a number of elementary functions called "activities"; each type of activity in abstracted to be a kind of "black box" into which flow tangible things such as supply and money and out of which may flow the products of manufacture or trained crews for the military. What goes on inside the "box" is the concern of the engineer or the educator, but to the programmer only the rates of flow in and out are of interest.

The next step in building a model is to select some unit for measuring the quantity of each activi...