Quantitative Techniques - Introductions PPT.pptx

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1. Quantitative Techniques 5 June 2022 1 Mr. MUSTAQ MULLA, Teaching Assistant, Rani Channamma University Belagavi, P G Centre Jamakhandi Mr. MUSTAQ MULLA, M.Com NET and K-SET, Teaching Assistant, Rani Channamma University Belagavi, P G Centre Jamakhandi

2. Unit -1 Introduction Quantitative technique is a very powerful tool, by using this we can Judgment our production, maximize profits, minimize costs, and production methods can be oriented for the accomplishment of certain pre–determined objectives. Quantitative techniques used to solve many of the problems that arise in a business or industrial area. A large number of business problems, in the relatively recent past, have been given a quantitative representation with considerable degree of success. All this has attracted the students, business executives, public administrators a like towards the study of these techniques more and more in the present times. 5 June 2022 2 Mr. MUSTAQ MULLA, Teaching Assistant, Rani Channamma University Belagavi, P G Centre Jamakhandi

3. Meaning And definition : Quantitative techniques may be defined as those techniques which provide the decision makes a systematic and powerful means of analysis, based on quantitative data. It is a scientific method employed for problem solving and decision making by the management. Quantitative techniques are defined as “those statistical techniques which lead to numerical analysis of variables, affecting a decision situation and evaluation of alternative strategies to attain objectives of organizations.” 5 June 2022 3 Mr. MUSTAQ MULLA, Teaching Assistant, Rani Channamma University Belagavi, P G Centre Jamakhandi

4. Features Descriptions of quantitative techniques reveal following characteristics or features. Measurement : Measurement is the basis of quantitative technique. Measurement is assigning numbers to concepts and phenomena. Measurement generates necessary data. Numerical analysis : Another basic feature of quantitative techniques is numerical expression of variables and analysis there-no. Even qualitative characteristics or phenomenon can be transformed to numbers and symbols using quantitative techniques. Scientific method : Quantitative techniques for decision making are examples for the use of scientific methods of management. It offers a systematic and objective experimentation, observation and evaluation of best strategies. Decision making : It is a support system in decision making process. It provides decision makers with appropriate tools of evaluation and presentation. Options : Quantitative techniques should evaluate and reveal alternative strategies or options. There is no scope for decision where there is a single option. 5 June 2022 4 Mr. MUSTAQ MULLA, Teaching Assistant, Rani Channamma University Belagavi, P G Centre Jamakhandi

5. 6 Improvement : Quantitative techniques should replace personal judgment and intuition. It should lead to improved and quality decisions. Functions of quantitative techniques : Quantitative Techniques are those methods in which details of a problem or situation are expressed in numerical terms, so as to support decision making. Quantification : Critical factors affecting a decision situation is transformed into quantitative or numerical form. It is easy to comprehend, understand and delegate an issue in numerical form. Analysis : Quantitative techniques enable scientific and systematic study of any issue. It probes deep into the factors influencing the problem and helps to express the situation in a comprehensive form. Decision making : Quantitative techniques facilitate the process of decision making. It sets out all possible alternatives and enables a feasibility study of each so that the optimal alternative can be chosen. Deployment of resources: Quantitative techniques, if properly applied, leads to optimal allocation of available limited resources. It avoids wastages and less efficient usage of resources, and leads to conservation of resources. 5 June 2022 5 Mr. MUSTAQ MULLA, Teaching Assistant, Rani Channamma University Belagavi, P G Centre Jamakhandi

6. Scope of Quantitative Techniques    A few specific areas of application are mentioned below. Finance and Accounting:  Cash flow analysis, Capital budgeting, Dividend and Portfolio management, Financial planning. Marketing Management:  Selection of product mix, Sales resources allocation and Assignments. Production Management:  Facilities planning, Manufacturing, Aggregate planning, Inventory control, Quality control, Work scheduling, Job sequencing, Maintenance and Project planning and scheduling. Personnel Management:  Manpower planning, Resource allocation, Staffing, Scheduling of training programs. General Management:  Decision Support System and Management of Information Systems, MIS, Organizational design and control, Software Process Management and Knowledge Management. 5 June 2022 6 Mr. MUSTAQ MULLA, Teaching Assistant, Rani Channamma University Belagavi, P G Centre Jamakhandi

7. Classification of Quantitative Techniques: There are different types of quantitative techniques. We can classify them into three categories. They are: 1. Mathematical Quantitative Techniques 2. Statistical Quantitative Techniques 3. Programming Quantitative Techniques 5 June 2022 7 Mr. MUSTAQ MULLA, Teaching Assistant, Rani Channamma University Belagavi, P G Centre Jamakhandi

8. 1. Mathematical Quantitative Techniques Mathematical Quantitative Techniques: A technique in which quantitative data are used along with the principles of mathematics is known as mathematical quantitative techniques. Mathematical quantitative techniques involve: 1. Permutations and Combinations: Permutation means arrangement of objects in a definite order. The number of arrangements depends upon the total number of objects and the number of objects taken at a time for arrangement. The number of permutations or arrangements is calculated by using the following formula :- nPr = n ! (n-r)! Combination means selection or grouping objects without considering their order. The number of combinations is calculated by using the following formula:- n C r = n! (n-r) ! 5 June 2022 8 Mr. MUSTAQ MULLA, Teaching Assistant, Rani Channamma University Belagavi, P G Centre Jamakhandi

9. 2. Set Theory:- Set theory is a modern mathematical device which solves various types of critical problems. 3. Matrix Algebra: Matrix is an orderly arrangement of certain given numbers or symbols in rows and columns. It is a mathematical device of finding out the results of different types of algebraic operations on the basis of the relevant matrices. 4. Determinants: It is a powerful device developed over the matrix algebra. This device is used for finding out values of different variables connected with a number of simultaneous equations. 5. Differentiation: It is a mathematical process of finding out changes in the dependent variable with reference to a small change in the independent variable. 6. Integration: Integration is the reverse process of differentiation. 7. Differential Equation: It is a mathematical equation which involves the differential coefficients of the dependent variables. 5 June 2022 9 Mr. MUSTAQ MULLA, Teaching Assistant, Rani Channamma University Belagavi, P G Centre Jamakhandi

10. 2. Statistical Quantitative Techniques Statistical techniques are those techniques which are used in conducting the statistical enquiry concerning to certain Phenomenon. They include all the statistical methods beginning from the collection of data till interpretation of those collected data. Statistical techniques involve: 1. Collection of data: One of the important statistical methods is collection of data. There are different methods for collecting primary and secondary data. 2. Measures of Central tendency, dispersion, skewness and Kurtosis : Measures of Central tendency is a method used for finding the average of a series while measures of dispersion used for finding out the variability in a series. Measures of Skewness measures asymmetry of a distribution while measures of Kurtosis measures the flatness of peakedness in a distribution. 5 June 2022 10 Mr. MUSTAQ MULLA, Teaching Assistant, Rani Channamma University Belagavi, P G Centre Jamakhandi

11. 3. Correlation and Regression Analysis: Correlation is used to study the degree of relationship among two or more variables. On the other hand, regression technique is used to estimate the value of one variable for a given value of another. 4. Index Numbers: Index numbers measure the fluctuations in various Phenomena like price, production etc over a period of time, They are described as economic barometers. 5. Time series Analysis: Analysis of time series helps us to know the effect of factors which are responsible for changes: 6. Interpolation and Extrapolation: Interpolation is the statistical technique of estimating under certain assumptions, the missing figures which may fall within the range of given figures. Extrapolation provides estimated figures outside the range of given data. 7. Statistical Quality Control Statistical quality control is used for ensuring the quality of items manufactured. The variations in quality because of assignable causes and chance causes can be known with the help of this tool. Different control charts are used in controlling the quality of products. 5 June 2022 11 Mr. MUSTAQ MULLA, Teaching Assistant, Rani Channamma University Belagavi, P G Centre Jamakhandi

12. 8. Ratio Analysis: Ratio analysis is used for analyzing financial statements of any business or industrial concerns which help to take appropriate decisions. 9. Probability Theory: Theory of probability provides numerical values of the likely hood of the occurrence of events. 10. Testing of Hypothesis Testing of hypothesis is an important statistical tool to judge the reliability of inferences drawn on the basis of sample studies. 5 June 2022 12 Mr. MUSTAQ MULLA, Teaching Assistant, Rani Channamma University Belagavi, P G Centre Jamakhandi

13. 3. Programming Quantitative Techniques Programming techniques are also called operations research techniques. Programming techniques are model building techniques used by decision makers in modern times. Programming techniques involve: 1. Linear Programming: Linear programming technique is used in finding a solution for optimizing a given objective under certain constraints. 2. Queuing Theory: Queuing theory deals with mathematical study of queues. It aims at minimizing cost of both servicing and waiting. 5 June 2022 13 Mr. MUSTAQ MULLA, Teaching Assistant, Rani Channamma University Belagavi, P G Centre Jamakhandi

14. 3. Game Theory: Game theory is used to determine the optimum strategy in a competitive situation. 4. Decision Theory: This is concerned with making sound decisions under conditions of certainty, risk and uncertainty. 5. Inventory Theory: Inventory theory helps for optimizing the inventory levels. It focuses on minimizing cost associated with holding of inventories. 6. Net work programming: It is a technique of planning, scheduling, controlling, monitoring and co- ordinating large and complex projects comprising of a number of activities and events. It serves as an instrument in resource allocation and adjustment of time and cost up to the optimum level. It includes CPM, PERT etc. 7. Simulation: It is a technique of testing a model which resembles a real life situations 5 June 2022 14 Mr. MUSTAQ MULLA, Teaching Assistant, Rani Channamma University Belagavi, P G Centre Jamakhandi

15. 8. Replacement Theory: It is concerned with the problems of replacement of machines, etc due to their deteriorating efficiency or breakdown. It helps to determine the most economic replacement policy. 9. Non Linear Programming: It is a programming technique which involves finding an optimum solution to a problem in which some or all variables are non-linear. 10. Sequencing: Sequencing tool is used to determine a sequence in which given jobs should be performed by minimizing the total efforts. 11. Quadratic Programming: Quadratic programming technique is designed to solve certain problems, the objective function of which takes the form of a quadratic equation. 12. Branch and Bound Technique It is a recently developed technique. This is designed to solve the combinational problems of decision making where there are large number of feasible solutions. Problems of plant location, problems of determining minimum cost of production etc. are examples of combinational problems. 5 June 2022 15 Mr. MUSTAQ MULLA, Teaching Assistant, Rani Channamma University Belagavi, P G Centre Jamakhandi

16. Role of Quantitative Techniques These techniques are especially increasing since World War II in the technology of business administration. These techniques help in solving complex and intricate problems of business and industry. Quantitative techniques for decision making are, in fact, examples of the use of scientific method of management. Their role can be well understood under the following heads: Provide a tool for scientific analysis: These techniques provides 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. 5 June 2022 16 Mr. MUSTAQ MULLA, Teaching Assistant, Rani Channamma University Belagavi, P G Centre Jamakhandi

17. (ii) Provide solution for various business problems: These techniques are being used in the field of production, procurement, marketing, finance and 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 stock 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. (iii) Enable proper deployment of resources: It render valuable help in proper deployment of resources. For example, PERT enables us to determine the earliest and the latest times for each of the events and activities and thereby helps in identification of the critical path. All this helps in the deployment of the resources from one activity to another to enable the project completion on time. This techniques, thus, provides for determining the probability of completing an event or project itself by a specified date. ( iv) Helps in minimizing waiting and servicing costs: This 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 June 2022 17 Mr. MUSTAQ MULLA, Teaching Assistant, Rani Channamma University Belagavi, P G Centre Jamakhandi

18. (v) Assists in choosing an optimum strategy: Game theory is especially used to determine the optimum strategy in a competitive situation and enables the businessmen to maximise profits or minimize losses by adopting the optimum strategy. (vi) They render great help in optimum resource allocation Linear programming technique is used to allocate scarce resources in an optimum manner in problem of scheduling, product – mix and so on. (vii) Enable the management to decide when to buy and how much to buy: The techniques of inventory planning enables the management to decide when to buy and how much to buy. (viii) They facilitate the process of decision making: Decision theory enables the businessmen to select the best course of action when information is given to probabilistic form. Through decision tree techniques executive’s judgement can systematically be brought into the analysis of the problems. Simulation is an other 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 situation involving uncertainty where mathematical formulation is not possible. Even complex groups of variables can be handled through this technique. 5 June 2022 18 Mr. MUSTAQ MULLA, Teaching Assistant, Rani Channamma University Belagavi, P G Centre Jamakhandi

19. (ix) Through various quantitative techniques management can know the reactions of the integrated business systems: The Integrated Production Models techniques are used to minimise 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 O.R. techniques also help in management people 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. 5 June 2022 19 Mr. MUSTAQ MULLA, Teaching Assistant, Rani Channamma University Belagavi, P G Centre Jamakhandi

20. Functions of Quantitative Techniques: The following are the important functions of quantitative techniques: 1. To facilitate the decision-making process 2. To provide tools for scientific research 3. To help in choosing an optimal strategy 4. To enable in proper deployment of resources 5. To help in minimizing costs 6. To help in minimizing the total processing time required for performing a set of jobs 5 June 2022 20 Mr. MUSTAQ MULLA, Teaching Assistant, Rani Channamma University Belagavi, P G Centre Jamakhandi

21. Functions and Their Applications A function is a technical term used to symbolise relationship between variables. When one or more independent variables are related to dependent variables then the dependent variable is said to be the function of independent variables. A function explains the nature of relationship between dependent and independent variables. A relationship may be a formula or a graph or a mathematical equation, Classification of Functions We have already learnt that for a function f : AB, f associates all elements of set A to set B and each element of set A is associated to a unique element of a set B. Thus, we may associate different element of set B or we may associate more than one element of set A to same element of set B (but same element of set A cannot be associated with more than one element of set B). Also, all elements of set B may or may not have their pre-images in A. 5 June 2022 21 Mr. MUSTAQ MULLA, Teaching Assistant, Rani Channamma University Belagavi, P G Centre Jamakhandi

22. Functions Related To Economics: In the case of functions in economics, the variables are hypothetical quantities and not actual observable quantities as in physical science.The range and the domain of economics functions are made up of nonnegative quantities so that the graphs of these functions are in first quadrant only. In other words, for the purpose of economic analysis, only that part of a curve is relevant which lies in the first quadrant. 1. Demand Function: As we know that the quantity demanded of a particular commodity by the buyers in the market is depending on the price. As the prices increases, the demand is decreases shown as figure. If q is the quantity of a commodity demanded and p is the price then the demand function is given by : q = f (p) shows q depends on p price p = g (q) shows p depends on q 2. Supply function: Price of any particular commodity in the market depends on the quantity of supply. As the quantity of supply increases the price is also increases. If x is the quantity of supply and p is its price then the supply function is given by x = f (p) or p = f (x). 5 June 2022 22 Mr. MUSTAQ MULLA, Teaching Assistant, Rani Channamma University Belagavi, P G Centre Jamakhandi

23. Functions Related To Cost: 1 Total Cost Function. 2 Average Cost Function. 1 Total cost function: The total cost (C) which is equal to sum of fixed cost and variable cost, of production in a firm, is depending on the quantity produced of a particular commodity. As the production increases the total cost also increases. If x is the quantity produced at total cost T then the total cost function is given by T = f (x). 2 Average Cost Function: Average cost function or cost per unit is obtained by dividing the total cost function by the quantity produced. Average cost function , A = (T / x) = ( f (x) / x). 5 June 2022 23 Mr. MUSTAQ MULLA, Teaching Assistant, Rani Channamma University Belagavi, P G Centre Jamakhandi

24. 3 Total Revenue Function: The total revenue in a particular commodity of a firm is depending on the number units sold. If p is the price of any commodity and q is the quantity sold then the total revenue function is given by R = p.q , and the average revenue function or revenue per unit is obtained by dividing the total revenue function by the units of quantity sold, it is equal to price (p) of the commodity. AR = (R / q) = (Pq / q) = p = price 5. Profit Function: Profit on a particular commodity of a firm is equal to the difference or total revenue and the total cost the profit function is given by z = R – T. 6. Production Function: The output product is depending in the various inputs like capital, labour , raw material etc. If q is the output quantity of a particular commodity and x, y and z are the input variables in a firm then the production function as sin y. q = f (x, y, z) For example: If labour (1) and capital (K) are inputs variables then the output is given by Q = f (L, K) = ALα - Kβ , α + β = 1 where A, α and β are constants is known as Cobb-Douglas production function . 5 June 2022 24 Mr. MUSTAQ MULLA, Teaching Assistant, Rani Channamma University Belagavi, P G Centre Jamakhandi

25. 7. Consumption Function: The total consumption function of a firm is depending on the income as income increases the consumption expenditure also increases. If C is the consumption and I is the income then the consumption function given by C = f (5) = a + bI where a, b are constants. Example1: A company sells x tins of chicken each day at Rs. 80 per tin. the cost of production and selling price of these tins is Rs. 50 per tin plus a fixed daily overhead cost of Rs. 18,000. Determine the profit function. What is the profit if 2,000 tins are produced and sold a day? Find out the number of tins produced in a day with no profit and no loss. Solution: a). Per day x tins of chicken are produced with cost Rs. 80 per tin the revenue received per day is Revenue function R (x) = 80. x The cost of production per day cost function is c(x) = 1,800 + 50x If P (x) is the profit function is given by P (x) = R(x) - c(x) = 80x - (50x +1,800) = 30x - 1,800 If 2,000 tins are produced and sold in a day then the profit is given by P (2,000) = 30 × 2,000 - 18,000 = 60,000 - 18,000 = Rs. 42,000 b). for no profit and no loss then profit function is zero P (x) = 0 = 30x - 18,000 = 0 5 June 2022 25 Mr. MUSTAQ MULLA, Teaching Assistant, Rani Channamma University Belagavi, P G Centre Jamakhandi

26. USES OF QUANTITATE TECHNIQUES Business and Industry Quantitative techniques render valuable services in the field of business and industry. Today, all decisions in business and industry are made with the help of quantitative techniques. Some important uses of quantitative techniques in the field of business and industry are given below : 1. Quantitative techniques of linear programming is used for optimal allocation of scarce resources in the problem of determining product mix. 5 June 2022 26 Mr. MUSTAQ MULLA, Teaching Assistant, Rani Channamma University Belagavi, P G Centre Jamakhandi

27. 2. Inventory control techniques are useful in dividing when and how much items are to be purchase so as to maintain a balance between the cost of holding and cost of ordering the inventory 3. Quantitative techniques of CPM, and PERT helps in determining the earliest and the latest times for the events and activities of a project. This helps the management in proper deployment of resources. 4. Decision tree analysis and simulation technique help the management in taking the best possible course of action under the conditions of risks and uncertainty. 5. Queuing theory is used to minimize the cost of waiting and servicing of the customers in queues. 6. Replacement theory helps the management in determining the most economic replacement policy regarding replacement of an equipment. 5 June 2022 27 Mr. MUSTAQ MULLA, Teaching Assistant, Rani Channamma University Belagavi, P G Centre Jamakhandi

28. Methodology of Q.T. 5 June 2022 28 Mr. MUSTAQ MULLA, Teaching Assistant, Rani Channamma University Belagavi, P G Centre Jamakhandi

29. 1. Formulating the Problem : As a first step, it is necessary to clearly understand the problem situations. It is important to know how it is characterized and what is required to be determined. Initially it is important to identify the key decision and the objective from the problem. Then, it involves determination of the number of decision variables and the relationship between variables. The measurable guaranties that are represented through these variables are notified. Finally 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. Identifying these variables helps us to develop the model. For example, consider a manufacturer who is manufacturing three products A, B and C using two machines, I and II. Each unit of product A takes 2 minutes on machine I and 5 minutes on machine II. `Product B takes 1 minute on machine I and 3 minutes on machine II. Similarly, product C takes 4 minutes and 6 minutes on machine I and machine II, respectively. The total available time on machine I and machine II are 100 hours and 120 hours, respectively. Each unit of A yields a profit of Rs. 3.00, B yields Rs. 4.00 and C yields Rs. 5.00. What should be level of production of products A, B and C that should be manufactured by the company so as to maximize the profit? 5 June 2022 29 Mr. MUSTAQ MULLA, Teaching Assistant, Rani Channamma University Belagavi, P G Centre Jamakhandi

30. The decision variables, objective and constraints are identified from the problem. The company is manufacturing three products A, B and C. Let A be x1, B be x2 and C be x3. x1, x2 and x3 are the three decision variables in the problem. The objective is to maximize the profits. Therefore, the problem is to maximize the profit, i.e., to know how many units of x1, x2 and x3 are to be manufactured. There are two machines available, machine I and machine II with total machine hours available as 100 hours and 120 hours. The machine hours are the resource constraints, i.e., the machines cannot be used more than the given number of hours. To summarize, 1 Key decision     : How many units of x1, x2 and x3 are to be manufactured? 2 Decision variables     : x1, x2 and x3 3 Objective         : To maximize profit 4 Constraint         : Machine hours ​ 5 June 2022 30 Mr. MUSTAQ MULLA, Teaching Assistant, Rani Channamma University Belagavi, P G Centre Jamakhandi

31. 3. Developing a Suitable Model. A model is a mathematical representation of a problem situation. The mathematical model 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 subtracting selling price and cost price and multiplying the number of units sold. Assuming selling price, sp as Rs. 40 and cost price, cp as Rs. 20, the following mathematical model expresses the total profit, tp earned by selling number of unit x. T P = (SP – CP) x  T.P= (40 – 20) x  T P = 20 x 5 June 2022 31 Mr. MUSTAQ MULLA, Teaching Assistant, Rani Channamma University Belagavi, P G Centre Jamakhandi

32. 4. Acquiring the Input Data : Acquiring accurate data for input values are essential. Even though the model is a perfect representation of reality, improper data will result in misleading results. Collecting accurate data can be one of the most difficult steps in performing quantitative analysis. 5. Solving the Model : Solving the model involves manipulating the model to arrive at the optimal solution. In some cases, this requires that an equation be solved for the best decision. In other cases, you can use a trial and error method, trying various approaches and picking the one that results in the best solution 5 June 2022 32 Mr. MUSTAQ MULLA, Teaching Assistant, Rani Channamma University Belagavi, P G Centre Jamakhandi

33. 5. Validating the Model A validation is a complete test of the model to confirm that it provides an accurate representation of the real problem. This helps us in determining how good and realistic the solution is. During the model validation process, inaccuracies can be rectified by taking corrective actions, until the model is found to be fit. 6. Implementing the Results The final step is to implement the results. This is the process of incorporating the solution into the company. Even if the solution is optimal and will result in millions of dollars in additional profits, if managers resist the new solution, all of the efforts of the analysis are of no value. After the solution has been implemented, it should be closely monitored. Over time, there may be numerous changes that call for modifications of the original solution. A changing economy, fluctuating demand and model enhancements requested by managers and decision makers are only a few examples of changes that might require the analysis to be modified. 5 June 2022 33 Mr. MUSTAQ MULLA, Teaching Assistant, Rani Channamma University Belagavi, P G Centre Jamakhandi

34. Limitations Quantitative techniques though are a great aid to management but still they cannot be substitute for decision making. The choice of criterion as to what is actually best for the 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: 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 and such an equation may be correctly used for the solution of the business problems when the underlying assumptions and variables in t he 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. 5 June 2022 34 Mr. MUSTAQ MULLA, Teaching Assistant, Rani Channamma University Belagavi, P G Centre Jamakhandi

35. (ii ) High costs are involved in the use of quantitative techniques: Quantitative techniques usually prove very expensive. Services of specialised persons are invariably called for while using quantitative techniques. Even in big business organisations 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. (iii) Quantitative techniques do not take into consideration the intangible factors i.e., non measurable human factors: Quantitative techniques make no allowances 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. 5 June 2022 35 Mr. MUSTAQ MULLA, Teaching Assistant, Rani Channamma University Belagavi, P G Centre Jamakhandi

36. (iv) 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 final analysis many business decisions will involve human element. Thus, quantitative analysis is at best a supplement rather than, a substitute for management; subjective judgement is likely to remain a principal approach to decision making. 5 June 2022 36 Mr. MUSTAQ MULLA, Teaching Assistant, Rani Channamma University Belagavi, P G Centre Jamakhandi

37. Thank You 5 June 2022 Mr. MUSTAQ MULLA, Teaching Assistant, Rani Channamma University Belagavi, P G Centre Jamakhandi 37