Answer to Question #237061 in Operations Research for opr

Question

i) Discuss the significance of operations research.

ii) Identify the limitations of operations research.

iii) Outline and briefly explain the five principle phases of operations research.

iv) Define the term linear programming and outline the four steps followed when formulating a linear programming model mathematically.

Answer 1

Operations research (often referred to as management science) is simply a

scientific approach to decision making that seeks to best design and operate a

system, usually under conditions requiring the allocation of scarce resources.

Operation research is mainly used in businesses to make bettter decisions. The following are advntages of operation research.

Improved Decision Making: As the above example shows, operations research techniques can take a muddle of factors and numbers and reduce them to simple formulas. These formulas will find the optimal solutions within the constraints of the problem.

Better Control: OR techniques give managers the tools that provide better direction and control over subordinates. A manager can use OR methods to set up performance standards for employees and identify areas that need improvement.

Higher Productivity: A significant use of OR is the ability to identify optimal solutions. A few examples are finding the best inventory mix, optimal utilization of manpower, most desirable use of plant machinery and highest-producing marketing campaigns.

Better Departmental Coordination: When the optimal results from OR analysis are shared with all departments, everyone works together toward the same goal. For example, the marketing department might coordinate their efforts with the schedules laid out by the production supervisor.

Operations research is important because it is a helpful tool used to solve complex problems under uncertainty. In business, very few things are certain, and managers must often make decisions based on their instincts instead of being able to use reliable data. Operations research techniques fill this void with methods that quantify issues and give business managers a better basis for making decisions.

There are a number of limitations of operations research which may be stated as follows:

1. In the quantitative analysis of operations research, certain assumptions and estimates are made for assigning quantitative values to factors involved. If such estimates are wrong, the result would be- equally misleading.

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2. Many management problems do not lend themselves to quantitative measurement and analysis. Intangible factors of any problem concerning human behaviour cannot be quantified accurately and all the patterns of relationships among the factors may not be covered. Accordingly, the outward appearance of scientific accuracy through the use of numbers and equations becomes unrealistic.

3. The quantitative methods of operations research are many cases costly, elaborate and sophisticated in nature. Although complex problems are fit for analysis by tools of operations research, relatively simple problems have no economic justification for this type of quantitative analysis.

4. A knowledge of some concepts of mathematics and statistics is prerequisite for adoption of quantitative analysis by the managers. According to the present training and experience of most managers, the actual use of these tools may be confined to a few cases.

5. Operations research is not a substitute for the entire process of decision making and it does not relieve the managers of their task of decision making. In one phase of decision making viz., selecton of best solution through the evaluation of alternatives, operations research comes into the picture.

The principal phases for implementing OR in practice include the following:

1. Defnition of the problem.

2. Co2struction of the model.

3. Solution of the model.

4. Validation of the model.

5. Implementation of the solution

1. Definition of the problem

This involves describing the scope of the problem under investigation, with

the aim of identifying three principal elements of the decision problem: de-

scription of the decision alternatives, determination of the objective of the

study, and specification of the limitations under which the modeled system

operates.

2. Construction of the model

This entails an attempt to translate the problem definition into mathemat-

ical relationships ensuring that the resulting model fits one of the standard

mathematical models, such as linear programming, reaching a solution by

using available algorithms.

3. Solution of the model

This is by far the simplest of all OR phases because it entails the use of

well-defined optimization algorithms.

4. Validation of the model

This checks whether or not the proposed model does what it purports to

do that is, does it adequately predict the behavior of the system under study?

5. Implementation of the solution

Implementation of the solution of a validated model involves the translation

of the results into understandable operating instructions to be issued to the

people who will administer the recommended system

Linear programming is a mathematical modeling technique in which a linear function is maximized or minimized when subjected to various constraints. The following are 4 steps

1. Understand the problem.
2. Describe the objective.
3. Define the decision variable
4. Write the objective function