Linear Programming: Introduction & Examples

Linear programming

2
Introduction
The Linear Programming (LP) has proven that it is a very
powerful method in the search for solutions to problems
arising from various areas,
The application of linear programming is extremely broad. It is
applied in industry, trade, finance, agriculture, marketing,
public service, etc.
The PL consists of two main parts:
Formulate the problem that concerns us,
Solving this problem.

3
Introduction
The following table shows some examples of actual use of Operations
Research by different organizations and profits and / or savings
achieved as a result by applying Linear Programming:
Organization Application Year Yearly savings
Dutch Ministry of Infrastructure and
the Environment (Netherlands
Rijkswaterstaat)
National Water management policy
development, adding new facilities,
operating and costs procedures
1985 $15 millions
Monsanto Corp. Production's operations optimization to
obey goals with a minimum cost 1985 $2 millions
Weyerhaeuser Co. Cutting trees optimization to maximize
wood products production 1986 $15 millions
Electrobras/CEPAL Brasil
Optimal allocation of hydraulic and thermic
resources in the national energy
generation system
1986 $43 millions
United Airlines
Shifts at book offices and airports
scheduling to accomplish with the
customer needs at minimal cost
1986 $6 millions

4
Introduction
CITGO Petroleum Corp. Optimization of refinement, offer, distribution and
commercialization of products operations 1987 $70 millions
Santos, Ltd., Australia Capital investment optimizing to produce natural gas
along 25 years in Australia 1987 $3 millions
Electric Power Research
Institute
Administration of oil and coal inventories for the
electric service with the intention of balancing
inventory costs and risks of remaining
1989 $59 millions
San Francisco Police
Department
Optimization programming and assignment of Patrol's
officers with a computed system 1989 $11 millions
Texaco Inc.
Optimizing the mixing of ingredients available in order
to obtain fuels which met with the quality requirements
and sales
1989 $30 millions
IBM Integration of a national network of spare parts
inventory to improve support service 1990
$20 millions
+ $250
millions in
minor
inventory

5
Introduction
U.S. Military Airlift
Command
Rapidity in the airplanes, crew, load and
passengers coordination to drive the evacuation
by air in the "Desert Storm" project in the Middle
Orient
1992 Victory
American Airlines
Design of a pricing, overbooking and flight
coordination structure system to enhance
benefits
1992
$500 millions
of additional
revenue
Yellow Freight System,
Inc.
Optimizing the design of the national transport
network and the scheduling of shipping routes in
the U.S.
1992 $17.3 millions
New Haven Health Dept. Design of an effective program of needles
change to combat the AIDS contagion 1993 33% less of contagions
AT&T Development of a computer system to design
call centers to guide customers 1993 $750 millions