Quantitative Techniques

Meaning of quantitative techniques, classification of quantitative techniques, Phases of operations research study, Important research techniques, role of quantitative techniques in business and industry, limitations of quantitative techniques

Quantitative techniques, also known as quantitative methods, are mathematical and statistical approaches used to analyze, interpret, and solve problems in various fields, including business, economics, engineering, social sciences, and more. These techniques involve the use of numerical data, mathematical models, and statistical analysis to make informed decisions and solve complex problems.

Numerous quantitative techniques are available in modern times. They can broadly be put under two groups: (a) Statistical techniques (b) Programming techniques.

Quantitative techniques can be classified into two major categories namely statistical techniques and programming techniques:


Statistical techniques are those techniques that are used in conducting the statistical inquiry concerning a certain phenomenon. They include all the statistical methods beginning from the collection of data till the task of interpretation of the collected data. More clearly, the methods of collection of statistical data, the technique of classification and tabulation of the collected data, the calculation of various satistical measures such as mean, standard deviation, coefficient of correlation, etc., the techniques of analysis and interpretation, and finally the task of deriving inferences and judging their reliability are some of the important statistical techniques.

Some of the important statistical techniques often used in business and industry are:

  • (i) Probability theory and sampling analysis. In many studies concerning business problems, the considerations of time and cost lead to examinations of only a few items of the universe. But the items selected should be as representative as possible of the total population. The selection process is called sampling. Samples are of two basic types:
    • (a) Probability or random samples are those which are so constructed that every element or item from the total population has equal probability of selection and the limits of probable error in relating results to the whole population are known mathematically in advance.
    • (b) Non-probability or purposive samples are those which are based on the choice of the selector.
  • (ii) Correlation and regression analysis: Correlation and regression analysis is another important statistical technique often used in business and industry. ‘Regression’ analysis examines the past trends of relationships between one variable, e.g., sales volume, and one or more than one other variables, e.g., advertising expenditure, cost of salesmen. Correlation analysis measures the closeness of such relationships. Thus, the ‘correlation’ and ‘regression’ analysis is used to study the degree of functional relationship among two or more variables and through this technique the value of one variable can be estimated if the value of another variable is known.
  • (iii) Index numbers: ‘Index Numbers’ constitute that statistical technique which measures fluctuations in prices, volume, economic activity or other variables over a period of time, relative to a base. The choice of the base period, the method of weighting and the selection of the components to be included in the index are the key factors concerning this statistical technique. Index numbers play an increasingly important role these days in decision-making problems for private enterprises as well as for the Government.
  • (iv) Time series analysis: Through this statistical technique, series of data over a period of time are analysed as to their chief types of fluctuations such as trend, cyclical, seasonal and irregular. Such an analysis helps the management in the field of interpreting sales, production, price or other variables over a period of time. This technique is of considerable significance in the field of short and long term business forecasting and greatly facilitates the seasonal as well as future planning of business operations.
  • (v) Interpolation and extrapolation: Interpolation is the statistical technique of estimating, under certain assumptions, the figures missing amongst the given values of the variable itself whereas extrapolation provides figures outside the given data. According to W.M. Harper — Interpolation consists in reading a value which lies between two extreme points; extrapolation means reading a value that lies outside the two extreme points.” This technique helps to ascertain the probable prices, business changes, the probable production and the like. It also fills the gaps in the available data besides being of great help in business forecasting.
    (vi) Ratio analysis: Ratio analysis technique as applied to business is a part of whole process of analysis of financial statements of any business or industrial concern to take credit decisions. This technique has emerged as most useful to bankers to study their customers’ balance sheets so as to have the clear idea about the growth of the concerns and also about the future trend of progress of such concerns. Under this technique various ratios (a ratio is simply one number expressed in terms of another) are worked out and interpreted with a view to find out mainly the financial stability, liquidity, profitability and the quality of management of the business and industrial concerns.
  • (vii) Statistical quality control: The technique of statistical quality coatrol is used by almost all the modern manufacturing industries. Under this technique the control of the quality is ensured by the application of the theory of probability to the results of examination of samples. The technique helps in separating the assignable causes from the chance causes. The technique of statistical quality control is applied through two phases—’Process Control’ and ‘Acceptance Sampling.’
    • (a) Process control (sometimes also known as control chart technique) is the application of statistical tools to industry to maintain quality of products. The standard of products are specified to which the quality must conform and then through the use of various control charts (XCbart, R-Chart etc.), it is seen whether the process is under control. The object of all this is to control the quality during the process of manufacture and thus to ensure that the quality of manufacturing is satisfactory and according to specific standards. Through this technique unnecessary waste of materials, time, etc., is avoided first by detecting faulty production and its causes and then by taking the corrective action immediately. This is how the quality of the product is ensured under statistical quality control.
      (b) Acceptance sampling (also known as product control lot acceptance sampling plan) is that phase of statistical quality control which attempts to decide whether to accept a lot with a desirable quality level or to reject a lot with an undesirable quality level on the basis of evidence provided by inspection of samples drawn at random from the lot. Thus the object of the acceptance sampling is to accept or reject a lot, once it has been manufactured. This helps in taking appropriate decisions concerning the purchase of a given lot.
  • (viii) Other statistical techniques:
    • Variance: The analysis of variance is a method of splitting the total variation of the given data into constituent parts that measure different sources of variation. This technique is used to test for the equality of the several sample means, usually more than two. For instance, three varieties of wheat are planted on several plots and their yields per hectare recorded. We might be interested in testing the null hypothesis that the three varieties produce an equal yield on average. This can easily be done by applying the technique of the analysis of variance. This technique is of great significance in all research studies concerning phenomena that are capable of quantitative measurements for ‘testing the differences between different groups of data for homogeneity.’ But when the phenomena cannot be measured quantitatively and we are interested in knowing the relationship (technically called the association) between two or more of such phenomena, we can use the technique of what is known as the theory of attributes. Under this technique, the coefficient of association and the like measures can be worked out and the inferences about the association between attributes can be drawn.


Programming techniques (or what is generally described as Operations Research or simply OR) are the model-building techniques used by decision-makers in modern times. They include a wide variety of techniques such as linear programming, theory of games, simulation, network analysis, queuing theory, and many other similar techniques. The following steps are generally involved in the application of the programming techniques:

  1. All quantifiable factors that are pertinent to the functioning of the business system under consideration are defined in mathematical language: variables (factors that are controllable) and parameters or coefficients (factors that are not controllable).
  2. Appropriate mathematical expressions are formulated which describe the inter-relations of all variables and parameters. This is what is known as the formulation of the mathematical model. This model describes the technology and the economics of a business through a set of simultaneous equations and inequalities.
  3. An optimum solution is determined on the basis of the various equations of the model satisfying the limitations and interrelations of the business system and at the same time maximizing profits or minimizing costs or coming as close as possible to some other goal or criterion.
  4. The solution values of the model, obtained as above, are then tested against actual observations. If necessary, the model is modified in the light of such observations, and the whole process is repeated till a satisfactory model is attained.
  5. Finally, the solution is put to work.


The various OR techniques require a basic knowledge of statistics, theory of probability, and mathematics since the different pluses of such techniques usually cover the following:

  1. Formulation of the problem in quantitative terms.
  2. Constructing a mathematical model in which the various components of the system under study and their inter-relationship are expressed in symbols that facilitate mathematical manipulations:
  3. Obtaining a solution from the model;
  4. Testing the validity of the model and the solution obtained from it;
  5. Controlling the model and its solution: (vi) Implementing the model, i.e., putting the solution to work


  • Some of the important OR techniques often used these days in business and industry are as under:
  • (i) Linear Programming: This technique is used in finding a solution for optimizing a given objective such as profit maximization or cost minimization under certain constraints. This technique is primarily concerned with the optimal allocation of limited resources for optimizing a given function. The name linear programming is because of the fact that the model in such cases consists of linear equations indicating linear relationship between the different variables of the system. Linear programming technique solves product-mix and distribution problems of business and industry. It is a technique used to allocate scarce resources in an optimum manner in problems of scheduling, product-mix and so on. Key factors under this technique include an objective function, choice among several alternatives, limits or constraints (stated in symbols) assumed to be linear and the variables.
  • (ii) Waiting Line, or Queuing, Theory: Waiting line or queuing theory deals with mathematical study of queues. The queues are formed whenever the current demand for service exceeds the current capacity to provide that service. Waiting line technique concems itself with the random arrival of customers at a service station where the facility is limited. Providing too much of capacity will mean idle time for servers and will lead to waste of money. On the other hand, if the queue becomes long there will be a cost due to waiting of units in the queue Waiting line theory, therefore, aims at minimizing the overall cost due to servicing and waiting. In other words, this technique is used to analyse the feasibility of adding facilities and to assess the amount and cost of waiting time. With its help we can find the optimal capacity to be installed which will lead to a sort of an economic balance between cost of service and cost of waiting.
  • (iii) Inventory Control/Planning: Inventory planning aims at optimizing inventory levels. Inventory may be defined as a useful idle resource which has economic value, eg, raw-materials, spare parts, finished products etc. Inventory planning, in fact, answers two questions viz. how much to buy and when to buy? Under this technique the main emphasis is on minimizing costs associated with holding of inventories, procurement of inventories and the shortage of inventories
  • (iv) Game Theory: Game theory is used to determine the optimum strategy in a competitive situation. Simplest possible competitive situation is that of two persons playing zero-sum game, ie a situation in which two persons are involved and one person wins exactly what the other loses. More complex competitive situations of the real life can as well be imagined where game theory can be used to determine the optimum strategy.
  • (v) Decision Theory: Decision theory concerns with making sound decisions under conditions of certainty, risk and uncertainty. There are three different kinds of situations under which decisions are made viz. deterministic, stochastic and uncertainty and the decision theory explains how to select a suitable strategy to achieve some object or goal under each of these three situations.
  • (vi) Network Analysis: Network analysis involves the determination of an optimum sequence of performing certain operations concerning some jobs in order to minimize overall time and/or cost. Programme Evaluation and Review Technique (PERT), Critical Path Method (CPM) and other network techniques such as Gantt Chart comes under Network Analysis. Key concepts under this technique are network of events and activities, resource allocation, time and cost considerations. network paths and critical paths
  • (vii) Simulation: Simulation is a technique of testing a model which resembles a real life situation. This technique is used to imitate an operation prior to actual performance. Two methods of simulation are there: One is Monte Carlo method of simulation and the other is system simulation method. The former one using random numbers is used to solve problems which involve conditions of uncertainty where in the mathematical formulation is impossible but in case of system simulation there is a reproduction of the operating environment and the system allows for analysing the response from the environment to alternative management actions. System simulation draws samples from a real population instead of drawing samples from a table of random numbers
  • (viii) Integrated Production: Models This technique aims at minimizing cost with respect to work force, production and inventory. This technique is a highly complex one and is used only by big business and industrial units. This technique can be used only when sales and costs statistics for a considerable long period are available.
  • (ix) Other Operation Research Techniques: In addition to the above stated OR techniques, there are several other techniques such as non- linear programming, dynamic programming, search theory, the theory of replacement and so on. A brief mention of some of these is as under:
    • (a) Non-linear programming is that form of programming in which some or all of the variables are curvilinear. In other words, this means that either the objective function or constraints or both are not in linear form. In most of the practical situations, we encounter with non- linear programming problems but for computation purpose we approximate them as linear programming problems. Even then there may be some non-linear programming problems which may not be fully solved by presently known methods.
    • (b) Dynamic programming refers to a systematic search for optimal solutions to problems that involve many highly complex inter-relations that are, moreover, sensitive to multistage effects such as successive time phases.
    • (c) Heuristic programming also known as discovery method refers to step by step search toward an optimum when a problem cannot be expressed in mathematical programming form. The search procedure examines successively a series of combinations that lead to stepwise improvements in the solution and the search stops when a near optimum has been found
    • (d) Integer programming is a special form of linear programming in which the solution is required in terms of integral numbers (ie. whole numbers) only.
    • (e) Algorithmic programming is just the opposite of Heuristic programming. It may also be termed as mathematical programming. This programming refers to a thorough and exhaustive mathematical approach to investigate all aspects of the given variables in order to obtain optimal solution.
    • (f) Quadratic programming refers to a modification of linear programming in which the objective equations appear in quadratic form, ie, they contain squared terms.
    • (g) Parametric programming is the name given to linear programming when the latter is modified for the purpose of inclusion of several objective equations with varying degrees of priority. The sensitivity of the solution to these variations is then studied.
    • (h) Probabilistic programming also known as stochastic programming, refers to linear programming that includes an evaluation of relative risks and uncertainties in various alternatives of choice for management decisions.
    • (i) Search theory concerns itself with search problems. A search problem is characterized by the need for designing a procedure to collect information on the basis of which one or more decisions are made. This theory is useful in places in which some events are known to occur but the exact location is not known. The first search model was developed during II World War to solve decision problems connected with air patrols and their search for submarines. “Advertising agencies search for customers’, ‘personnel departments search for good executives’ search for good executives are some of the examples of search theory’s application in business.
    • (j) Theory of replacement is concerned with predicting replacement costs and determining most economic replacement policy. There are two types of replacement models-first deals in replacing equipments that deteriorate with time, the second helps in establishing replacement policy for those equipments which fail completely and instantaneously. All these techniques are not simple but involve higher mathematics. The tendency today is to combine several of these techniques and form into more sophisticated and advanced programming models.

Quantitative techniques, especially Operations Research techniques, have gained increasing importance since World War II in the technology of business administration. These techniques greatly help in tackling the intricate and complex problems of modern business and industry. Quantitative techniques for decision-making are, in fact, examples of the use of the scientific method of management. Their role can be well understood under the following heads:

  1. They provide a tool for scientific analysis. These techniques provide the executives with a more precise description of the cause and effect relationship and risks underlying the business operations in measurable terms and this eliminates the conventional intuitive and subjective basis on which managements used to formulate their decisions decades ago. In fact, these techniques replace the intuitive and subjective approach of decision making by an analytical and objective approach. The use of these techniques has transformed the conventional techniques of operational and investment problems in business and industry. Quantitative techniques, thus, encourage and enforce disciplined thinking about organizational problems.
  2. They provide solution for various business problems. The quantitative techniques are being used in the field of production, procurement, marketing, finance and other allied fields. Problems like how best can the managers and executives allocate the available resources to various products so that in a given time the profits are maximum or the cost is minimum? Is it possible for an industrial enterprise to arrange the time and quantity of orders of its stocks such that the overall profit with given resources is maximum? How far is it within the competence of a business manager to determine the number of men and machines to be employed and used in such a manner that neither remains idle and at the same time the customer or the public has not to wait unduly long for service? and similar other problems can be solved with the help of quantitative techniques. Similarly, we might have a complex of industries steel, machine tools and others… all employed in the production of one item, say, steel. At any particular time we have alternative choices of allocating resources such as money, steel and tools for producing autos, building steel factories or tool factories. What should be the policy which optimizes the total number of autos produced over a given period? The quantitative techniques are capable of providing an answer in such a situation.
    Planning decisions in business and industry are largely governed by the picture of anticipated demands. The potential long range profits of the business may vary in accordance with different possible demand patterns. The quantitative techniques serve to develop a scientific basis for coping with the uncertainties of future demands. Thus, in dealing with the problem of uncertainty over future sales and demands, the quantitative techniques can be used to generate “a least risk” plan.
    At times there may be a problem of finding an acceptable definition of long-range company objectives. Management may be confronted with different view points-some may stress the desirability of maximizing of net profits whereas others may focus attention primarily on the minimization of costs. Quantitative techniques (specially that of mathematical programming such as linear programming) can help resolve such dilemmas by permitting systematic evaluation of the best strategies for attaining different objectives. These techniques can also be used for estimating the worth of technical innovations as also of potential profits associated with the possible changes in rules and policies.
    How much changes can there be in the data on which a planning formulation is based without undermining the soundness of the plan itself? How accurately must managements know cost coefficients, production performance figures and other factors before it can make planning decisions with confidence? Many of the basic data required for the development of long-range plans are uncertain. Such uncertainties though cannot be avoided but through various quantitative techniques the management can know how critical such uncertainties are and this in itself is a great help to business planners. The technique of ‘Decision Tree’ or the Sensitivity analysis can specially be used for the purpose.
  3. They enable proper deployment of resources. Quantitative techniques render valuable help in proper deployment of resources. For example, Programme Evaluation and Review Technique (PERT) enables us to determine the earliest and the latest times for each of the events and activities and thereby helps in the identification of the critical path. All this helps in the deployment of resources from one activity to another to enable the project completion on time. This technique, thus, provides for determining the probability of completing an event or project itself by a specified date.
  4. They help in minimizing waiting and servicing costs. The waiting line or queuing theory helps the management men in minimizing the total waiting and servicing costs. This technique also analyses the feasibility of adding facilities and thereby helps the business people to take a correct and profitable decision.
  5. They enable the management to decide when to buy and how much to buy. The main object of the inventory planning is to achieve balance between the cost of holding stocks and the benefits from stock holding. Hence, the technique of inventory planning enables the management to decide when to buy and how much to buy.
  6. They assist in choosing an optimum strategy. Game theory is specially used to determine the optimum strategy in a competitive situation and enables the businessmen to maximize profits or minimize losses by adopting the optimum strategy.
  7. They render great help in optimum resource allocation. Linear programming technique is used to allocate scarce resources in an optimum manner in problems of scheduling, product- mix and so on. This technique is popularly used by modern managements in resource allocation and in affecting optimal assignments
  8. They facilitate the process of decision making. Decision theory enables the businessmen to select the best course of action when information is given in probabilistic form. Through decision tree (a network showing the logical relationship between the different parts of a complex decision and the alternative courses of action in any phase of a decision situation) technique executive’s judgement can systematically be brought into the analysis of the problems. Simulation is another important technique used to imitate an operation or process prior to actual performance. The significance of simulation lies in the fact that it enables in finding out the effect of alternative courses of action in a situation involving uncertainty where mathematical formulation is not possible. Even complex groups of variables can be handled through this technique
  9. Through various quantitative techniques management can know the reactions of the integrated business systems. The Integrated Production Models technique is used to minimize cost with respect to work force, production and inventory. This technique is quite complex and is usually used by companies having detailed information concerning their sales and costs statistics over a long period. Besides, various other OR techniques also help management people in taking decisions concerning various problems of business and industry. The techniques are designed to investigate how the integrated business system would react to variations in its component elements and or external factors.
  10. Statistical techniques are also of great help to businessmen in more than one way. Some of the statistical techniques are of considerable importance in sales forecasting whereas others facilitate comparisons between the various phenomena overtime. Through statistical quality control techniques it can be seen whether the process is under control or not and if the same is not under control, then corrective measures can immediately be thought of sampling theory enables to take decisions for the entire universe on the basis of sample studies and various significance tests prove an important tool to judge the reliability of inferences drawn on the basis of sample studies. This is of great help to people responsible for taking decisions in business and industry. Similarly, regression analysis, variance analysis, time-series analysis, and index numbers are other very useful statistical techniques in the hands of businessmen particularly in context of estimation and future planning.


Quantitative techniques though are a great aid to management as outlined above but still, they cannot be a substitute for decision-making. The choice of a criterion as to what is actually best for a business enterprise is still that of an executive who has to fall back upon his experience and judgement. This is so because of the several limitations of quantitative techniques. Important limitations of these techniques are as given below:

  1. The inherent limitation concerning mathematical expressions. Quantitative techniques involve the use of mathematical models, equations and similar other mathematical expressions. Assumptions are always incorporated in the derivation of an equation or model and such an equation or model may be correctly used for the solution of the business problems when the underlying assumptions and variables in the model are present in the concerning problem. If this caution is not given due care then there always remains the possibility of wrong application of the quantitative techniques. Quite often the operations researchers have been accused of having many solutions without being able to find problems that fit.
  2. High costs are involved in the use of quantitative techniques. Quantitative techniques usually prove very expensive. Services of specialized persons are invariably called for (and along with it the use of computer) while using quantitative techniques. As such only big concerns can think of using such techniques. Even in big business organizations we can expect that quantitative techniques will continue to be of limited use simply because they are not in many cases worth their cost. As opposed to this a typical manager, exercising intuition and judgement, may be able to make a decision very inexpensively. Thus, the use of quantitative techniques is a costlier affair and this in fact constitutes a big and important limitation of such techniques.
  3. Quantitative techniques do not take into consideration the intangible factors i.e., non-measurable human factors. Quantitative techniques make no allowance for intangible factors such as skill, attitude, vigour of the management people in taking decisions but in many instances success or failure hinges upon the consideration of such non-measurable intangible factors. There cannot be any magic formula for getting an answer to management problems; much depends upon proper managerial attitudes and policies.
  4. Quantitative techniques are just the tools of analysis and not the complete decision making process. It should always be kept in mind that quantitative techniques, whatsoever it may be, alone cannot make the final decision. They are just tools and simply suggest best alternatives but in the final analysis many business decisions will involve human element. Thus, quantitative analysis is at best a supplement to rather than a substitute for management; subjective judgement is likely to remain a principal approach to decision making.