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# Quantitative Techniques: Introduction

Teacher à Rani Channamma university, PG Centre, Jamkhandi, Karnataka
6 Jul 2022
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### Quantitative Techniques: Introduction

1. QUANTITATIVE TECHNIQUES Chapter I - Introduction Meaning and Definition of Quantitative Techniques, Linkage between Business Decision Making and Quantitative Techniques, Different Quantitative Techniques, Areas for Application of Quantitative Techniques in Business. Types of Decisions; Steps in Decision Making; Quantitative Analysis and Decision Making; Different types of Models Quantitative Analysis and Decision Making; Different types of Models and their Uses; Model Building Steps. Prepared by Mr. Dayananda Huded M.Com, NET, KSET Teaching Assistant, Rani Channamma University, PG Centre, Jamkhandi E-Mail: dayanandch65@gmail.com
2. HISTORY  Quantitative management is not a modern business idea but a management theory that came into existence after World War II. Business owners initially used it in Japan to pick up the pieces of the devastation caused by the war and started taking baby steps toward reconstruction. It focuses on the following elements of business operations:  Customer satisfaction  Business value enhancement Business value enhancement  Empowerment of employees  Creating synergy among teams  Creating quality products  Preventing defects  Being responsible for quality  Focusing on continuous improvement  Leveraging statistical measurement  Remaining focused on the processes  Commitment to refinement and learning
3. MEANING  Quantitative techniques in management as a collection of mathematical and statistical tools. They’re known by different names, such as management science or operation research. In modern business methods, statistical techniques are also viewed as a part of quantitative management techniques.  When appropriately used, quantitative approaches to management can become a powerful means of analysis, leading to effective decision-making. These techniques help resolve complex business problems by leveraging systematic resolve complex business problems by leveraging systematic and scientific methods.  Quantitative techniques in management involve using various elements of quantities, including numbers, symbols and mathematical expressions. They act as supplements to help decision-makers in making the proper judgment. These are powerful business tools that allow managers to optimize outcomes with limited resources.  The term Decision Science / Quantitative Techniques (QT) /Operations Research (OR) describes the discipline that is focused on the application of Information Technology (IT) for well-versed decision-making.
4.  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 for future use comprises a major part of scientific management.  For example, consider a person investing in fixed deposit in a bank, or in shares of a company, or mutual funds, or in Life Insurance Corporation. The expected return on Life Insurance Corporation. The expected return on investments will vary depending upon the interest and time period. We can use the scientific management analysis to find out how much the investments made will be worth in the future.  There are many scientific method software packages that have been developed to determine and analyze the problems.
5. DEFINITIONS OF QT  According to C.R. Kothari :  "Quantitative Techniques may be defined as those technique which provide the decision maker with a systematic and powerful means of analysis and help, based on quantitative in exploring policies for achieving pre-determined goals”.  Quantitative techniques are those statistical and programming techniques, which help decision makers solve many problems, especially those concerning business and industry.  Quantitative techniques are those techniques that provide the decision makers with systematic and powerful means of analysis, based on quantitative data, for achieving predetermined goals. based on quantitative data, for achieving predetermined goals.  Quantitative research is defined as a systematic investigation of phenomena by gathering quantifiable data and performing statistical, mathematical, or computational techniques.  Quantitative research collects information from existing and potential customers using sampling methods and sending out online surveys, online polls, questionnaires, etc., the results of which can be depicted in the form of numerical. After careful understanding of these numbers to predict the future of a product or service and make changes accordingly.
6.  Operational research/QT is the application of the methods of science to complex problems in the direction and management of large systems of men, machines, materials, and money in the industry, business, govt. and defence. - Operations Research Society, UK  QT is concerned with scientifically deciding how to best design and operate man machines systems usually requiring the allocation of scarce resources. -Operations Research Society, US  Operation research/QT is applied design theory. It uses any  Operation research/QT is applied design theory. It uses any scientific, mathematical or logical means to attempt to cope with the problems that confront the executive, when he tries to achieve a through going rationality in dealing with his decision problems. - D. W. Miller & M. K. Stan  Operation research/QT is a scientific approach to problem solving for executives management. - H. M. Wagner
7. LINKAGE BETWEEN BUSINESS DECISION MAKING AND QUANTITATIVE TECHNIQUES  Quantitative techniques include methods or tools, which focus on objective measurement, and analysing numbers in order to draw conclusion about given problems.  These are more relevant to problems of complex business situations.  Quantitative methods seek to measure various offering-, consumer-, or market-related phenomena in an entire population and to explain patterns of predefined offering-, consumer-, or market-related phenomena through causal inference or teleological explanation.  QT used to collect quantitative data from the research study. If any organization would like to conduct a customer satisfaction  If any organization would like to conduct a customer satisfaction survey, a customer satisfaction survey template can be used. Through this survey, an organization can collect quantitative data and metrics on the goodwill of the brand or organization in the mind of the customer based on multiple parameters such as product quality, pricing, customer experience, etc.  collecting feedback from the event attendees about the value that they see from the event. By using an event survey template, the organization can collect actionable feedback about satisfaction levels of customers during various phases of the event such as the sales, pre and post-event, the likelihood of recommending the organization to their friends and colleagues, hotel preferences for the future events and other such questions.
8. DIFFERENT QUANTITATIVE TECHNIQUES/CLASSIFICATION/TYPES OF QT Different QT/Classification/Types of QT Mathematical QT Statistical QT Programming QT 1. Permutation 2. Matrix 3. Determinants 4. Differentiation 5. Integration 6. Vestors 1. Collection of Data 2. Index Numbers 3. Time Series 4. Interpolation 5. Probability Theory 6. Sampling Analysis 1. Linear Programming 2. Assignment 3. Game Theory 4. Decision Theory 5. Simulation 6. Inventory Control Theory
9. I.  1. Permutation: 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.  Determine the number of possible arrangement.  Ex: 2 Pants (Red & Black) and 2 Shirts (Green & Blue)  2. Matrix: Matrix is an orderly arrangement of certain given numbers or  2. Matrix: 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.  An arrangement(array) of m rows and n columns is called matrix.  Number of rows and columns in a matrix is called its Dimention
10.  3. 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.  4. Differentiation: It is a mathematical process of finding out changes in the dependent variable with reference to a small change in the independent variable.  5. Integration: Integration is the reverse process of  5. Integration: Integration is the reverse process of differentiation.  6. Differential Equation: It is a mathematical equation which involves the differential coefficients of the dependent variables.
11. II STATISTICAL QT  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. 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.  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. given value of another.  4. Time series Analysis: Analysis of time series helps us to know the effect of factors which are responsible for changes.  5. Probability Theory: Theory of probability provides numerical values of the likely hood of the occurrence of events.  6. Ratio analysis: Ratio analysis is used for analyzing financial statements of any business or industrial concerns which help to take appropriate decisions.  7. Testing of hypothesis: Testing of hypothesis is an important statistical tool to judge the reliability of inferences drawn on the basis of sample studies.
12. III. PROGRAMMING QT  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.  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  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. Simulation: It is a technique of testing a model which resembles real life situations.  7. Sequencing: Sequencing tool is used to determine a sequence in which given jobs should be performed by minimizing the total efforts.
13. NATURE OF QT  QT is a very powerful tool by using this we judge our production, maximise profits, minimise costs and production methods can be oriented for the accomplishment of certain pre-determined objectives.  1. Decision Making: It is a support system in decision making process. It provides decision makers with appropriate tools of evaluation and presentation.  2. Deployment of Resources: QT, if properly applied, leads to optimal allocation of available limited resources. It avoids wastage and less efficient usage of resources and conservation of them.  3. Scientific Method: QT for decision making are examples for the use of scientific methods of management. It offers a systematic and objective experimentation, observation, and best evaluation of best strategies.  4. Network Programming: It is a technique of planning, scheduling, controlling, monitoring and coordinating large and complex projects comprising of a number of activities and events. It serves as an instrument in resources allocation and adjustments of time and cost up to the optimum level. It includes CPM, PERT etc.
14.  5. Branch and Bound Technique: It is a recently developed technique. This is designed to solve the combinational problems of design making where there are large number of feasible solutions, problems of plan location, problems of determining minimum cost of production etc are the examples of combinational problems.  6. 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 numeric form.  7. Numerical Analysis: Another basic feature of QT is numerical expression of variables and analysis there-on. Even qualitative characteristics or phenomenon can be transformed to numbers and symbols using QT. using QT.
15. SCOPE OF QT OR AREAS OF APPLICATION OF QT  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. scheduling.  Personnel Management: Manpower planning, Resource allocation, Staffing, Scheduling of training programmes.  General Management: Decision Support System and Management of Information Systems, MIS, Organizational design and control, Software Process Management and Knowledge Management.  Research and Development:
16. ROLE AND IMPORTANCE OF QT  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.  1. Provide a Tool for Scientific Analysis: These technique provides executives with a more precise description of the cause and effects, relationship and risks. Underlying business operations in measurable terms and this eliminates the subjective bias on which managements used to formulate their decisions decades ago.  2. Provides Solutions for Various Business Problems: QT used in the field of production, procurement, marketing finance and allied field. field of production, procurement, marketing finance and allied field. Problems like how best can be managers and executives allocate the available resources.  3. Helps in Minimising Waiting and Servicing Costs: This will the management in minimising the total waiting and servicing costs. This technique also helps to analyse the best feasibility of adding facilities.  4. Assists in Choosing Optimum strategy: Game theory is especially used to determine the optimum strategy in a competitive situation and enables the businessmen to maximise profits or minimise losses by adapting the profitable decisions.
17.  5. Enable proper deployment of resources: It render valuable help in proper deployment of resources. 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.  6. 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.  7. 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.  8. They facilitate the process of decision making: Decision theory enables  8. 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.  9. 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
18. LIMITATIONS OF QT  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 and such an equation 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 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. Thus, the use of quantitative techniques is a costlier affair and this in fact constitutes a big and important limitation of such techniques.
19.  3. 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. 4. Quantitative techniques are just the tools of analysis  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 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.
20. TYPES OF DECISIONS  1. Programmed and non-programmed decisions: Programmed decisions are concerned with the problems of repetitive nature or routine type matters.  These decisions are taken generally by lower level managers. Decisions of this type may pertain to e.g. purchase of raw material, granting leave to an employee and supply of goods and implements to the employees, etc.  Non-programmed decisions relate to difficult situations for which there is no easy solution.  These matters are very important for the organisation. For example, opening of a new branch of the organisation or a large number of employees absenting from the organisation or introducing new product in the market, etc., are the decisions which are normally taken at the higher level. which are normally taken at the higher level.  2. Routine and strategic decisions:  Routine decisions are related to the general functioning of the organisation. They do not require much evaluation and analysis and can be taken quickly. Ample powers are delegated to lower ranks to take these decisions within the broad policy structure of the organisation.  Strategic decisions are important which affect objectives, organisational goals and other important policy matters. These decisions usually involve huge investments or funds. These are non-repetitive in nature and are taken after careful analysis and evaluation of many alternatives. These decisions are taken at the higher level of management.
21.  3. Tactical (Policy) and operational decisions:  Decisions pertaining to various policy matters of the organisation are policy decisions. These are taken by the top management and have long term impact on the functioning of the concern. For example, decisions regarding location of plant, volume of production and channels of distribution (Tactical) policies, etc. are policy decisions.  Operating decisions relate to day-to-day functioning or operations of business. Middle and lower level managers take these decisions.  An example may be taken to distinguish these decisions. Decisions concerning payment of bonus to employees are a policy decision. On the other hand if bonus is to be given to the employees, calculation of bonus in other hand if bonus is to be given to the employees, calculation of bonus in respect of each employee is an operating decision.  4. Organisational and personal decisions:  When an individual takes decision as an executive in the official capacity, it is known as organisational decision. If decision is taken by the executive in the personal capacity (thereby affecting his personal life), it is known as personal decision.  Sometimes these decisions may affect functioning of the organisation also. For example, if an executive leaves the organisation, it may affect the organisation. The authority of taking organizational decisions may be delegated, whereas personal decisions cannot be delegated.
22.  5. Major and minor decisions:  Decision pertaining to purchase of new factory premises is a major decision. Major decisions are taken by top management.  Purchase of office stationery is a minor decision which can be taken by office superintendent.  6. Individual and group decisions:  When the decision is taken by a single individual, it is known as individual decision. Usually routine type decisions are taken by individuals within the  Usually routine type decisions are taken by individuals within the broad policy framework of the organisation.  Group decisions are taken by group of individuals constituted in the form of a standing committee.  Generally very important and pertinent matters for the organisation are referred to this committee. The main aim in taking group decisions is the involvement of maximum number of individuals in the process of decision making.
23. STEPS IN DECISION MAKING
25. METHODOLOGY OF QUANTITATIVE TECHNIQUES
26.  Step 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. Firstly, the key decision and the objective of the problem must be identified from the problem. Then, the number of decision variables and the relationship between variables must be determined.  Step 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 production of products A, B and C that should be manufactured by the company so as to maximize the profit?  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,  l Key decision : How many units of x1, x2 and x3 are to be manufactured  l Decision variables : x1, x2 and x3  l Objective : To maximize profit  l Constraint : Machine hours
27.  Step 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. TP = (SP – CP) x = (40 – 20) x TP = 20 x  The applications of models are wide, such as:  Linear Programming Model  Sensitivity Analysis  Sensitivity Analysis  Goal Programming  Non Linear Programming  Queuing Theory  Inventory Management Techniques  PERT/CPM (Network Analysis)  Decision Theory  Games Theory  Transportation and Assignment Models. Etc.  Step 4. Acquiring the Input Data: 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 will lead to wrong decisions.
28.  Step 5. Solving the Model:  Solving is trying for the best result by manipulating the model to the problem. This is done by checking every equation and its diverse courses of action. A trial and error method can be used to solve the model that enables us to find good solutions to the problem.  Step 6. 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 inaccuracies can be rectified by taking corrective actions, until the model is found to be fit.  Step 7. Implementing the Results: Once the model is tested and validated, it is ready for implementation. Implementation involves translation/application of solution in the company. Close administration and monitoring is required after the solution is implemented, in order to address any proposed changes that call for modification, under actual working conditions.
29. QUANTITATIVE ANALYSIS AND DECISION MAKING  1. Linear programming: 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. 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 and variables assumed to be linear.
30.  2. Waiting line: deals with mathematical study of queues. Queues are formed whenever the current demand for service exceeds the current capacity to provide that service.  Waiting line technique concerns 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  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 costs of both servicing and waiting.
31.  3. Inventory control/planning aims at optimizing inventory levels.  Inventory may be defined as a useful idle resource which has economic value, e.g., raw-materials, spare parts, finished products, etc.  Inventory planning, in fact, answers the two questions, viz., how much to buy and when to buy?  Under this technique, the main emphasis is on minimizing costs associated with holding inventories, procurement of inventories and shortage of inventories. and shortage of inventories.  4. Integrated production models aims at minimizing cost with respect to workforce, production and inventory.  This technique is highly complex 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.
32.  5. Dynamic programming refers to the 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.  6. Heuristic programming also known as discovery method, refers o step by step search toward an optimum when a problem cannot be expressed in the 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 solution and the search stops when a near optimum has been found.  7. The theory of replacement is concerned with the prediction of replacement costs and the determination of the most economic replacement policy.  There are two types of replacement models  one type of models deal with replacing equipment that deteriorate with time and  the other type of models helps in establishing replacement policy for those equipment which fail completely and instantaneously.
33. DIFFERENT TYPES OF MODELS AND THEIR USES  1. Physical Models: These models are usually used by engineers and scientists. In managerial research one finds the utilisation of physical models in the realm of marketing in testing of alternative packaging concepts.  2. Mathematical Models: The mathematical models use symbolic notation and equations to represent a decision-making situation. The system attributes are represented by variables and the activities by mathematical functions that interrelate the variables.  Ex. EOQ Sta4c models assume the system to be in  3. Static vs. Dynamic Models: Sta4c models assume the system to be in a balance state and show the values and relationships for that only. Dynamic models, however, follow the changes over time that result from the system activities. Obviously, the dynamic models are more complex and more difficult to build than the static models.  4. Descriptive model: Such Models are used to describe the behaviour of a system based on certain information. For example, a model can be built to describe the behaviour of demand for an inventory item for a stated period, by keeping the record of various demand levels and their respective frequencies.
34.  5. Explanatory model: Such models are used to explain the behaviour of a system by establishing relationships between its various components. For example, a model can be built to explain variations in productivity by establishing relationships among factors such as wages, promotion policy, education levels, etc.  6. Predictive model: Such models are used to predict the status of a system in the near future based on data. For example, a model can be built to predict stock prices (within an industry group), for given any level of earnings per share.  7. Prescriptive (or normative) model: A prescriptive model is one which provides the norms for the comparison of alternative solutions which result in the selection of the best alternative (the most preferred course of action). Examples of such models are allocation models.
35. MODEL BUILDING STEPS  The approach used for model building or model development for managerial decision-making will vary from one situation to another. However, we can enumerate a number of generalized steps which can be considered as being common to most modelling efforts. The steps are Step 1 • Identifying and formulating the decision problem Step 2 • Identifying the objective(s) of the decision maker(s) • System elements identification and block building Step 3 • System elements identification and block building Step 4 • Determining the relevance of different aspects of the system Step 5 • Choosing and evaluating the model form Step 6 • Model calibration (The measuring devise) Step 7 • Implementation
36. THE SEVEN-STEP MODEL-BUILDING PROCESS Step 1 •Formulate the problem Step 2 •Observe the system Step 3 •Formulate a mathematical model of a problem •Verify the model & use the model for prediction Step 4 •Verify the model & use the model for prediction Step 5 •Select a suitable alternative Step 6 •Present the results & conclusion of the study to the organisation Step 7 •Implement and evaluate recommendations
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