Business Viewpoint of Linear Programming
In “real life” linear programming is part of a very important area of mathematics called optimization techniques- used every day in the organization and allocation of resources. These systems can have dozens or hundreds of variables. They are extensively used in business and economics, but may also be used to solve certain engineering problems. It also helps business owners determine the optimal way to allocate resources among different projects to gain the maximum or minimum output.
Economics examples include:
- Leontief’s input-output model
- Determination of shadow prices
- Heavily used in microeconomics
Business examples include:
- Maximizing profit for a factory that makes a number of different products from same raw material and resources
- Company management (planning, production, transportation, technology, etc.)
- For most part, most companies aim to maximize profit/minimize costs
Engineering examples include:
- Chebyshev approximation
- Design of structures
Many practical problems in operations research can be expressed as linear programming problems. Linear programming was used during WWII in area of food to help keep food costs down, but also meet soldiers’ dietary requirements with meal planning. This was one of first uses of linear programming. Business managers can also use optimization to produce concrete, measurable improvements in performance and operations. They can use it to reduce costs, improve profitability, reduce risks, use resources effectively, and automate decision processes to improve speed of responses/allow managers to focus attention on critical uncertainties rather than routine decisions.
Economics examples include:
- Leontief’s input-output model
- Determination of shadow prices
- Heavily used in microeconomics
Business examples include:
- Maximizing profit for a factory that makes a number of different products from same raw material and resources
- Company management (planning, production, transportation, technology, etc.)
- For most part, most companies aim to maximize profit/minimize costs
Engineering examples include:
- Chebyshev approximation
- Design of structures
Many practical problems in operations research can be expressed as linear programming problems. Linear programming was used during WWII in area of food to help keep food costs down, but also meet soldiers’ dietary requirements with meal planning. This was one of first uses of linear programming. Business managers can also use optimization to produce concrete, measurable improvements in performance and operations. They can use it to reduce costs, improve profitability, reduce risks, use resources effectively, and automate decision processes to improve speed of responses/allow managers to focus attention on critical uncertainties rather than routine decisions.
Examples of uses in business include:
- Diet design - Capital budgeting - Gaming strategy - Resource conservation - Resource/materials allocation - Transportation problems - Economic predictions and growth problems - Corporate restructuring - Product mix planning - Financial portfolios Restaurants use linear programming in all of these areas: - Menu planning - Meal production - To increase overall profits |
Airlines use linear programming in all of these areas:
- Optimize profits and minimize expenses - Different fares on seats on a plane (seat, time of purchase, etc.) - Use to find how many tickets would sell at what price - Routes, pilot scheduling, layovers, etc. - Which pilots in the air at what time and when - Maximize amount of time in the air - Pilot specializations (fly certain types of planes, routes) - Pilot salary Some other examples of linear programming practices include the following: - Farmers use linear programming to increase revenue of optimize their operations - Amusement Parks- help make decisions about queue lines - Overall increase in economic efficiency in business operations |
Relating Linear Programing to Organizational Concerns
Linear Programming models can be used in areas of business such as Supply Chain Management as part of Decision Support Systems. Management must regularly make decisions about how to allocate its resources to various activities to best meet the company’s organizational objectives. Businesses nowadays carry operational risks such as customer demand, supply, and cost. Most quantitative analyses and methods using linear programming are focused on these risks. Various models such as product mix, blending (material mixing), inventory, and transportation models are used to maximize or minimize cost or profit for the business.
For Example…
A business may want to maximize profit. They would use a product mix model and alter variables such as the number of products to produce to attain this maximization of profit. Typically, some constraints in this scenario would include resource limits (time, labor, material) and perhaps a constraint on the maximum/minimum quantity of a certain product to be produced.
A business may also have an organizational concern that carries risk in having too much or too little of products A and B. They may also have a blending scenario where the variable would be the amount of materials to combine to produce one unit of product. Constraints in this scenario would be resource limits to create X amount of A or B, or demand requirements for each type of product or service.
Linear Programming models can help put greater visibility in the network and help mitigate risk in business.
FedEx, a best-in-class distribution company, saw the need for network optimization in designing a distribution strategy that bettered its business partner’s practices. In 2006, FedEx studied 197 publicly-held distributors and found some issues.
For Example…
A business may want to maximize profit. They would use a product mix model and alter variables such as the number of products to produce to attain this maximization of profit. Typically, some constraints in this scenario would include resource limits (time, labor, material) and perhaps a constraint on the maximum/minimum quantity of a certain product to be produced.
A business may also have an organizational concern that carries risk in having too much or too little of products A and B. They may also have a blending scenario where the variable would be the amount of materials to combine to produce one unit of product. Constraints in this scenario would be resource limits to create X amount of A or B, or demand requirements for each type of product or service.
Linear Programming models can help put greater visibility in the network and help mitigate risk in business.
FedEx, a best-in-class distribution company, saw the need for network optimization in designing a distribution strategy that bettered its business partner’s practices. In 2006, FedEx studied 197 publicly-held distributors and found some issues.
Conclusion: to increase profitability, distributors must focus on getting more out of existing assets.
How? Optimization by programming methods.
FedEx found that the median public distributor spends about $61 million in managing their network through optimization. A well-designed network model using combinations of linear and mixed integer programing with 10% improvement in managing this cost would increase operating income by 22%. Distributors would be able to respond to increasingly demanding customers while reducing inventory investments and minimzed costs due to linear programming.
How? Optimization by programming methods.
FedEx found that the median public distributor spends about $61 million in managing their network through optimization. A well-designed network model using combinations of linear and mixed integer programing with 10% improvement in managing this cost would increase operating income by 22%. Distributors would be able to respond to increasingly demanding customers while reducing inventory investments and minimzed costs due to linear programming.
Information on the Markets
Linear programming is highly effective and successful in the distribution and manufacturing industry. Areas of improvement that can lead to success in this industry include (but are not limited to)
- Reduced operating costs
- Reduced inventory levels
- Reduced transportation costs
Many distributor’s networks are ineffective. They overlook how a well-designed and optimized distribution network can lead to revenue growth, increased customer service, and profitability. An optimized network can mitigate risk as well as manage investments in inventory.
Healthcare Company example:
FedEx in combination with a major healthcare company (unnamed) analyzed their healthcare network after seeing high operating costs and low profits. They had 12 facilities spread across 7 countries and were on schedule to consolidate facilities. Reducing the 12 facilities down to 2 would’ve reduced cost and investment savings over $7 million. The company had to account for facilities requirements that the 2-location model could not meet the constraints (customer service variable as well). Solution after linear formulation resulted in a 5-location model, $5 million in system-wide savings, and all while passing constraint values on customer service. As we can see, sometimes tradeoffs are required. While the consolidation of facilities down from 12 to 2 would’ve yielded a bigger result in savings, the healthcare company could not meet its customer service requirements with that model. Optimization by linear programming maximized savings while satisfying the healthcare company’s requirements constraints.
Just to go along with the manufacturing industry and optimizing business system-wide through methods like linear programming:
Manufacturing accounts for 16 percent of global GDP and 14 percent of employment
- Reduced operating costs
- Reduced inventory levels
- Reduced transportation costs
Many distributor’s networks are ineffective. They overlook how a well-designed and optimized distribution network can lead to revenue growth, increased customer service, and profitability. An optimized network can mitigate risk as well as manage investments in inventory.
Healthcare Company example:
FedEx in combination with a major healthcare company (unnamed) analyzed their healthcare network after seeing high operating costs and low profits. They had 12 facilities spread across 7 countries and were on schedule to consolidate facilities. Reducing the 12 facilities down to 2 would’ve reduced cost and investment savings over $7 million. The company had to account for facilities requirements that the 2-location model could not meet the constraints (customer service variable as well). Solution after linear formulation resulted in a 5-location model, $5 million in system-wide savings, and all while passing constraint values on customer service. As we can see, sometimes tradeoffs are required. While the consolidation of facilities down from 12 to 2 would’ve yielded a bigger result in savings, the healthcare company could not meet its customer service requirements with that model. Optimization by linear programming maximized savings while satisfying the healthcare company’s requirements constraints.
Just to go along with the manufacturing industry and optimizing business system-wide through methods like linear programming:
Manufacturing accounts for 16 percent of global GDP and 14 percent of employment
If Industries that implement linear programming methods into their decision have to consider any policy, it would be environmental policy- environmental policies based on food, energy, or air (emissions).
For example, companies may need to formulate diets for dairy cattle with environmental policies in mind, or formulating max output for power plants while adhering to the Kyoto Protocol for greenhouse gas emissions. The Kyoto Protocol was adopted in Kyoto, Japan in December 1997.
For example, companies may need to formulate diets for dairy cattle with environmental policies in mind, or formulating max output for power plants while adhering to the Kyoto Protocol for greenhouse gas emissions. The Kyoto Protocol was adopted in Kyoto, Japan in December 1997.
Commercial Providers
Linear programming software or suites that contain linear programming capabilities (like most ERP suites) can range from $10,000 per user to $250,000 per user depending on company size and licensing requirements. There are consultants, vendors of the software themselves, or 3PL companies (like FedEx) who provide network analysis services for $25,000 - $500,000.
IBM’s CPLEX Optimization Studio was developed over 20 years ago. It was named after its simplex method implemented in the C programming language (although it supports other interfaces today).
CPLEX Optimizer solves integer programming problems for business to produce precise and logical decisions. Its algorithm solvers for linear programming, mixed integer programming, and quadratic programming are able to solve problems with millions of constraints and variables. Variables and constraints can be easily modified, as well as the ability to modify objective, bound and matrix coefficients.
LogicTools
A Supply Chain Optimization software that helps in network design, planning, inventory planning, and optimization solutions to reduce costs and maximize profit. This bundle is also based on CEPLEX (above) and is also provided by IBM’s ILOG subsidiary. Not only that, but it’s compatible with IBM’s i2 platform.
Manugistics software bundle by JDA
Another supply chain optimization package. Manugistics was acquired by JDA software group in 2006. More than 3,200 companies worldwide use this software to solve their toughest business challenges. Industries include Aerospace, Transportation, Pharmacy, Manufacturing, Distribution, and Retail.
CPLEX Optimizer solves integer programming problems for business to produce precise and logical decisions. Its algorithm solvers for linear programming, mixed integer programming, and quadratic programming are able to solve problems with millions of constraints and variables. Variables and constraints can be easily modified, as well as the ability to modify objective, bound and matrix coefficients.
LogicTools
A Supply Chain Optimization software that helps in network design, planning, inventory planning, and optimization solutions to reduce costs and maximize profit. This bundle is also based on CEPLEX (above) and is also provided by IBM’s ILOG subsidiary. Not only that, but it’s compatible with IBM’s i2 platform.
Manugistics software bundle by JDA
Another supply chain optimization package. Manugistics was acquired by JDA software group in 2006. More than 3,200 companies worldwide use this software to solve their toughest business challenges. Industries include Aerospace, Transportation, Pharmacy, Manufacturing, Distribution, and Retail.