Accurate data for input values are essential. Even though the model is well constructed,it is important that the input data is correct to get accurate results. Inaccurate data willlead to wrong decisions.
1.4.5Solving the Model
Solving is trying for the best result by manipulating the model to the problem. This is doneby checking every equation and its diverse courses of action. A trial and error methodcan be used to solve the model that enables us to find good solutions to the problem.
1.4.6Validating the Model
A validation is a complete test of the model to confirm that it provides an accuraterepresentation of the real problem. This helps us in determining how good and realisticthe solution is. During the model validation process, inaccuracies can be rectified bytaking corrective actions, until the model is found to be fit.
1.4.7Implementing the Results
Once the model is tested and validated, it is ready for implementation. Implementationinvolves translation/application of solution in the company. Close administration andmonitoring is required after the solution is implemented, in order to address any proposedchanges that call for modification, under actual working conditions.
1.5ADVANTAGES OF MATHEMATICAL MODELLING
The advantages of mathematical modelling are many:(a)Models exactly represent the real problem situations.(b)Models help managers to take decisions faster and more accurately.(c)Models save valuable resources like money and time.(d)Large and complex problems can be solved with ease.(e)Models act as communicators to others by providing information and impact inchanging conditions.
1.6SCOPE OF QUANTITATIVE TECHNIQUE
The scope and areas of application of scientific management are very wide in engineeringand management studies. Today, there are a number at quantitative software packagesavailable to solve the problems using computers. This helps the analysts and researchersto take accurate and timely decisions. This book is brought out with computer basedproblem solving. A few specific areas are mentioned below.
Finance and Accounting:
Cash flow analysis, Capital budgeting, Dividend andPortfolio management, Financial planning.
Marketing Management:
Selection of product mix, Sales resources allocationand Assignments.
Production Management:
Facilities planning, Manufacturing, Aggregate planning,Inventory control, Quality control, Work scheduling, Job sequencing, Maintenanceand Project planning and scheduling.
Personnel Management:
Manpower planning, Resource allocation, Staffing,Scheduling of training programmes.
General Management:
Decision Support System and Management of InformationSystems, MIS, Organizational design and control, Software Process Managementand Knowledge Management.
1.7.1Origin and Growth of Statistics
Statistics, as a subject, has a very long history. The origin of STATISTICS is indicated bythe word itself which seems to have been derived either from the Latin word 'STATUS'or from the Italian word 'STATISTA' or may be from the German word 'STATISTIK.'The meaning of all these words is 'political state'. Every State administration in the pastcollected and analysed data. The data regarding population gave an idea about the possiblemilitary strength and the data regarding material wealth of a country gave an idea aboutthe possible source of finance to the State. Similarly, data were collected for other purposesalso. On examining the historical records of various ancient countries, one might findthat almost all the countries had a system of collection of data. In ancient Egypt, the dataon population and material wealth of the country were collected as early as 3050B.C., for the construction of pyramids. Census was conducted in Jidda in 2030 B.C. andthe population was estimated to be 38,00,000. The first census of Rome was done asearly as 435 B.C. After the 15th century the work of publishing the statistical data wasalso started but the first analysis of data on scientific basis was done by Captain JohnGraunt in the 17th century. His first work on social statistics, ‘Observation on LondonBills of Mortality' was published in 1662. During the same period the gamblers of westerncountries had started using statistics, because they wanted to know the more preciseestimates of odds at the gambling table. This led to the development of the 'Theory of Probability'.
Meaning and Definition of Statistics
The meaning of the word 'Statistics' is implied by the pattern of development of thesubject. Since the subject originated with the collection of data and then, in later years,the techniques of analysis and interpretation were developed, the word 'statistics' hasbeen used in both the plural and the singular sense. Statistics, in plural sense, means aset of numerical figures or data. In the singular sense, it represents a method of studyand therefore, refers to statistical principles and methods developed for analysis andinterpretation of data.Statistics has been defined in different ways by different authors. These definitions canbe broadly classified into two categories. In the first category are those definitions whichlay emphasis on statistics as data whereas the definitions in second category emphasisestatistics as a scientific method
Statistics as Data
Statistics used in the plural sense implies a set of numerical figures collected with referenceto a certain problem under investigation. It may be noted here that any set of numericalfigures cannot be regarded as statistics. There are certain characteristics which must besatisfied by a given set of numerical figures in order that they may be termed as statistics.Before giving these characteristics it will be advantageous to go through the definitionsof statistics in the plural sense, given by noted scholars.
Characteristics of Statistics as Data
On the basis of the above definitions we can now state the following characteristics of statistics as data :1.
Statistics are numerical facts:
In order that any set of facts can be called asstatistics or data, it must be capable of being represented numerically orquantitatively. Ordinarily, the facts can be classified into two categories : (a) Factsthat are measurable and can be represented by numerical measurements.Measurement of heights of students in a college, income of persons in a locality,yield of wheat per acre in a certain district, etc., are examples of measurable facts.(b) Facts that are not measurable but we can feel the presence or absence of thecharacteristics. Honesty, colour of hair or eyes, beauty, intelligence, smoking habitetc., are examples of immeasurable facts. Statistics or data can be obtained insuch cases also, by counting the number of individuals in different categories. Forexample, the population of a country can be divided into three categories on thebasis of complexion of the people such as white, whitish or black.2.
Statistics are aggregate of facts:
A single numerical figure cannot be regardedas statistics. Similarly, a set of unconnected numerical figures cannot be termed asstatistics. Statistics means an aggregate or a set of numerical figures which arerelated to one another. The number of cars sold in a particular year cannot beregarded as statistics. On the other hand, the figures of the number of cars sold invarious years of the last decade is statistics because it is an aggregate of relatedfigures. These figures can be compared and we can know whether the sale of carshas increased, decreased or remained constant during the last decade.It should also be noted here that different figures are comparable only if they areexpressed in same units and represent the same characteristics under differentsituations. In the above example, if we have the number of Ambassador cars soldin 1981 and the number of Fiat cars sold in 1982, etc., then it cannot be regarded asstatistics. Similarly, the figures of, say, measurement of weight of students shouldbe expressed in the same units in order that these figures are comparable with oneanother.3.
Statistics are affected to a marked extent by a multiplicity of factors:
Statisticaldata refer to measurement of facts in a complex situation, e.g., business or economicphenomena are very complex in the sense that there are a large number of factorsoperating simultaneously at a given point of time. Most of these factors are evendifficult to identify. We know that quantity demanded of a commodity, in a givenperiod, depends upon its price, income of the consumer, prices of other commodities,taste and habits of the consumer. It may be mentioned here that these factors areonly the main factors but not the only factors affecting the demand of a commodity.Similarly, the sale of a firm in a given period is affected by a large number of factors. Data collected under such conditions are called statistics or statistical data.4.
Statistics are either enumerated or estimated with reasonable standard of accuracy:
This characteristic is related to the collection of data. Data are collectedeither by counting or by measurement of units or individuals. For example, thenumber of smokers in a village are counted while height of soldiers is measured.
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