Linear Programming: Blending

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Graduate Program in Business Information Systems

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Business Information Systems. Linear Programming and. Applications. Aslı Sencer Erdem. BIS 517-Aslı Sencer Erdem. BIS 517-Aslı Sencer Erdem ...

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Ch 7 LINEAR PROGRAMMING

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Typical Applications of Linear Programming in Business. 1. A manufacturer wants to develop a production schedule and inventory policy that will satisfy ...
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Linear programming is a technique which shows practical problems as a series of mathematical equations which can be manipulated to find the optimum or best solution. Blending is a graphical approach to linear programming which deals with resource allocation subject to constraints. It is a model which assists firms in deciding the best possible utilisation of limited resources. Each resource constraint is represented as a mathematical linear equation. A linear expression is an equation which links two variables, and if plotted on a graph, would be represented by a straight line. By plotting all the equations, the optimal use of the business's resources can be easily identified.

Blending can be useful to firms when deciding how to make the best use of their resources. Businesses can use this method to allocate factors of production so that profits are maximised or costs minimised, depending on the business's objective. Another advantage of blending is that is allows the business to decide a combination of the two goods to produce, as compared to other invest appraisal or decision making techniques where either one or the other option must be selected, but not both.

Blending is a fairly easy and fast technique as it only requires simple calculations. The results are also represented on a graph and so information can be seen visually and does not require much explanation. Additionally, computers can speed up the calculations and increase the accuracy of this method.

However, blending has its limitations. It does not take into account the market demand for the products. The assumption is that the optimum output level for each good will be sold profitably, which may not be the case. Producing at the most profitable output level will be irrelevant if the products cannot be sold.

This technique also assumes that resources can be switched between the two products at a constant rate of productivity. This may not be a realistic assumption. For example, the machines in a business may be designed to produce a particular product. If they are used to produce something else, they may not be as efficient or may have to be altered i.e. a machine built to produce Product A may require more time and resources to produce Product B. The same problem arises with labour. Workers skilled at producing a certain good may not be able to - or willing to - switch to manufacturing another. This technique assumes that machines and workers are able to switch easily between producing different goods and be equally capable at producing both. This can be almost impossible to achieve if the two products are very different.

Another limitation of blending is that this simple model only allows two products to be considered. In reality, firms produce many different products. The Simplex Method is used to cope with this, but requires detailed calculations and the use of computers. And so, this technique loses its advantage of being simple and quick to use if more than two goods are manufactured.

By solving problems quantitatively, blending ignores qualitative factors that need to be considered before adjusting the output level of a certain product. For example, more storage may be needed if the quantity of one product is increased as it may be bulkier than the other. Similarly, stricter quality control may be needed for one product as opposed to the other.

Nevertheless, blending is still a very useful operations management tool. It is simple and easy to understand, and far less complex than other decision making methods. However, due to its limitations, this method should not be used in isolation but should supplement market research and other forecasting and investment appraisal methods.

LINEAR PROGRAMMING is a technique which shows practical problems as a series of mathematical equations which can be manipulated to find the optimum or best solution. Blending is a graphical approach to linear programming which deals with resource allocation subject to constraints. It is a model which assists firms in deciding the best possible utilisation of limited resources. Each resource constraint is represented as a mathematical linear equation. A linear expression is an equation which links two variables, and if plotted on a graph, would be represented by a straight line. By plotting all the equations, the optimal use of the business's resources can be easily identified.

Blending can be useful to firms when deciding how to make the best use of their resources. Businesses can use this method to allocate factors of production so that profits are maximised or costs minimised, depending on the business's objective. Another advantage of blending is that is allows the business to decide a combination of the two goods to produce, as compared to other invest appraisal or decision making techniques where either one or the other option must be selected, but not both.

Blending is a fairly easy and fast technique as it only requires simple calculations. The results are also represented on a graph and so information can be seen visually and does not require much explanation. Additionally, computers can speed up the calculations and increase the accuracy of this method.

However, blending has its limitations. It does not take into account the market demand for the products. The assumption is that the optimum output level for each good will be sold profitably, which may not be the case. Producing at the most profitable output level will be irrelevant if the products cannot be sold.

This technique also assumes that resources can be switched between the two products at a constant rate of productivity. This may not be a realistic assumption. For example, the machines in a business may be designed to produce a particular product. If they are used to produce something else, they may not be as efficient or may have to be altered i.e. a machine built to produce Product A may require more time and resources to produce Product B. The same problem arises with labour. Workers skilled at producing a certain good may not be able to - or willing to - switch to manufacturing another. This technique assumes that machines and workers are able to switch easily between producing different goods and be equally capable at producing both. This can be almost impossible to achieve if the two products are very different.

Another limitation of blending is that this simple model only allows two products to be considered. In reality, firms produce many different products. The Simplex Method is used to cope with this, but requires detailed calculations and the use of computers. And so, this technique loses its advantage of being simple and quick to use if more than two goods are manufactured.

By solving problems quantitatively, blending ignores qualitative factors that need to be considered before adjusting the output level of a certain product. For example, more storage may be needed if the quantity of one product is increased as it may be bulkier than the other. Similarly, stricter quality control may be needed for one product as opposed to the other.

Nevertheless, blending is still a very useful operations management tool. It is simple and easy to understand, and far less complex than other decision making methods. However, due to its limitations, this method should not be used in isolation but should supplement market research and other forecasting and investment appraisal methods.

Linear programming

Some businesses are in the position where they manufacture a mix of items, say tables and chairs, but the quantity of each that they can make is constrained by the machines that they have. How do they optimise the use of their machines? How do they maximise the profit that they make?

Constraints might include:

• level of demand for a particular product or service;
• machine or staff limitations and availability; and,
• raw material availability.

Techniques that consider numerical relationships are known as quantitative techniques. One of the simplest quantitative techniques is linear programming. It is used to optimise the use of resources where the relationships between the objectives and resource limitations are linear, that is, they are directly related. For example, the number of products manufactured is directly proportional to the machine capacity.

Linear programming where there are more than a very few variables becomes impossible to do graphically, but there are powerful computer programmes available to assist.

Linear programming problems can be solved algebraically, for example, using a method known as the simplex method. A particular application of the simplex method is solving transport or distribution problems.

Imagine, for example, that you run a courier business, or manufacture a product that you have to distribute yourself to retail outlets throughout the country. Data can be presented to set out demand at a number of destinations served by stock from a number of locations. The objective is to identify the possible routes and minimise the cost of delivery.