Introduction

Scientific methods have been man’s outstanding asset to pursue an ample number of activities. It is analysed that whenever some national crisis, emerges due to the impactof political, social, economic or cultural factors the talents from all walks of life amalgamatetogether to overcome the situation and rectify the problem. In this chapter we will seehow the quantitative techniques had facilitated the organization in solving complexproblems on time with greater accuracy. The historical development will facilitate inmanagerial decision-making & resource allocation, The methodology helps us in studyingthe scientific methods with respect to phenomenon connected with human behaviourlike formulating the problem, defining decision variable and constraints, developing asuitable model, acquiring the input data, solving the model, validating the model,implementing the results. The major advantage of mathematical model is that its facilitatesin taking decision faster and more accurately.







HISTORICAL DEVELOPMENT

During the early nineteen hundreds, Fredrick W. Taylor developed the scientificmanagement principle which was the base towards the study of managerial problems.Later, during World War II, many scientific and quantitative techniques were developedto assist in military operations. As the new developments in these techniques were foundsuccessful, they were later adopted by the industrial sector in managerial decision-makingand resource allocation. The usefulness of the Quantitative Technique was evidencedby a steep growth in the application of scientific management in decision-making invarious fields of engineering and management. At present, in any organization, whethera manufacturing concern or service industry, Quantitative Techniques and analysis areused by managers in making decisions scientifically.




ABOUT QUANTITATIVE TECHNIQUE
Quantitative Techniques adopt a scientific approach to decision-making. In this approach,past data is used in determining decisions that would prove most valuable in the future.The use of past data in a systematic manner and constructing it into a suitable model forfuture use comprises a major part of scientific management. For example, consider aperson investing in fixed deposit in a bank, or in shares of a company, or mutual funds, orin Life Insurance Corporation. The expected return on investments will vary dependingupon the interest and time period. We can use the scientific management analysis to findout how much the investments made will be worth in the future. There are many scientificmethod software packages that have been developed to determine and analyze the problems.




METHODOLOGY OF QUANTITATIVE TECHNIQUES
The methodology adopted in solving problems is as follows:

1.Formulating the Problem
As a first step, it is necessary to clearly understand the problem situations. It is importantto know how it is characterized and what is required to be determined. Firstly, the keydecision and the objective of the problem must be identified from the problem. Then, thenumber of decision variables and the relationship between variables must be determined.The measurable guaranties that are represented through these variables are notified.The practical limitations or constraints are also inferred from the problem


2. Defining the Decision Variables and Constraints
In a given problem situation, defining the key decision variables are important. Identifyingthese variables helps us to develop the model. For example, consider a manufacturerwho is manufacturing three products A, B and C using two machines, I and II. Each unitof product A takes 2 minutes on machine I and 5 minutes on machine II. Product Btakes 1 minute on machine I and 3 minutes on machine II. Similarly, product C takes 4minutes and 6 minutes on machine I and machine II, respectively. The total availabletime on machine I and machine II are 100 hours and 120 hours, respectively. Each unitof A yields a profit of Rs. 3.00, B yields Rs. 4.00 and C yields Rs. 5.00. What should belevel of production of products A, B and C that should be manufactured by the companyso as to maximize the profit?The decision variables, objective and constraints are identified from the problem.

3. Developing a Suitable Model
A model is a mathematical representation of a problem situation. The mathematicalmodel is in the form of expressions and equations that replicate the problem. For example,the total profit from a given number of products sold can be determined by subtractingselling price and cost price and multiplying the number of units sold. Assuming sellingprice, sp as Rs. 40 and cost price, cp as Rs. 20, the following mathematical modelexpresses the total profit, tp earned by selling number of unit x.