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Introduction to Linear Programming and it’s relevance to a business Organization


Introduction to Linear Programming and it’s relevance to a business Organization

Author: Kingsley Mayor Omenaiko

A manager’s major responsibility at all times is how best to achieve the objectives of business subject to the constraints in the operating environment.

Unless the business achieves it’s objective that is profit oriented, the firm will not survive.

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It follows that the amount of the profit his firm makes is one of the most important measure of the firm’s performance.

Therefore, the constraints can take the form of limited resources such as time, labour, energy, material or money, etc.

When a manager attempts to solve a general type of problem by seeking an objective that is subject to constraints the technique called linear programming is used.

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  • Linear Programming is defined as a special technique for determining the optimum combination of scarce resources in the attainment of some objective of economic nature.
  • Linear Programming is a mathematical technique for determining the best allocation of a firm limited resource.
  • It is also defined as a method for solving problems in which an objective function must be maximized or minimized when considering certain constraints.

Application of Linear Programming

Linear Programming can be use to solve problems involving various human endeavor.

1) Blending of raw materials

Blending of various raw materials in order to meet specified requirements for a particular product.

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2) Raw material Allocation

Linear Programming assists management to optimize for buyers potential raw material resources for production and minimize transport cost.

3) Production scheduling

Linear Programming helps management to determine the most profitable combination of products to manufacturing bearing in mind their constraints.

4) Physical distribution

It helps management to determine the most economic and effective manner of allocating manufacturing plan and distribution centers.

5) Site Allocation

It helps management to decide which location is best for a new factory, warehouse and branch offices and where to eliminate existing facilities.

6) Advertising Media

It helps management to evaluate and analyze the effectiveness of advertising media in order to minimize cost.

7) Manpower management

It assists the personnel to analyze personnel policies in terms of the flow of people into and out of the firm.

8) Time Standard determination

Linear Programming assists time study personnel in determining a standard time for any particular activities or process.

Necessary Conditions for the Application of Linear Programming

  • Well defined objective function
  • There must be different alternative course of action
  • Objective function and constraints must be expressed mathematically
  • Linearity of decision variables
  • Resources must be limited in supply

Formulation of Linear programming Model

The following steps should be adopted in formulating Linear Programming Model

1) Identify the decision variables

Decision variables are mathematical symbols that represent levels of activity in the firm.

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2) Identify the Objective function

The Objective function is a linear mathematical relationship that describes the Objective of the firm in terms of the decision variables.

3) Identify the model Constraints

The model Constraints are also linear relationship of the decision variables. They represent the restrictions placed on the firm by the operating environment.

4) Write the standard Linear Programming Model ( model summary )

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