- 1. Operations Research – Session 1
- 2. Course Introduction • Operations Research (OR) may be defined as the science that aims for the application of analytical and numerical techniques along with information technology to solve organizational problems. • OR is a field of applied mathematics that makes use of analytical tools and mathematical models to solve problems and aid the management in decision making. • The goal of OR is to help select the alternative that will maximize the use of available resources and lead to the best possible outcome.
- 3. Session Plan Sr. No. Contents 1 Basics of Operations Research 2 OR Models and Modelling 3 Introduction to Linear Programming. 4 Liner Programming : The mathematical formulation of a business problem 5 Liner Programming : Graphic Solution 6 Liner Programming : Simplex Method 7 Liner Programming : Problem solving using excel solver 8 Transportation Problem: Finding an Optimal Solution 9 Assignment Problem 10 Project Network Analysis With Critical Path Method 11 Project Evaluation and Review Technique (PERT)
- 4. 1. Basics Of Operations Research
- 5. Index Topic Particulars Learning Objectives 1 Concept of Operations Research 2 Operations Research: A Quantitative Approach for Decision Making 3 Applications and Uses of Operations Research in Management Let’s Sum Up
- 6. Learning Objectives • Explain the concept of operations research • Discuss the history of operations research • List the tools and techniques of operations research • Gain an insight into operations research as a quantitative approach for decision making. • Discuss the applications and uses of operations research
- 7. 1. Concept of Operations Research • Decision making is not a simple task in today’s socio economic environment. Complex problems such as transportation, queuing, etc. are routinely presented and dealt with at the operational level. • Decision makers cannot afford to take decisions by simply taking their personal experiences or intuitions into account. • Decisions made in the absence of suitable information can have serious consequences. Being able to apply quantitative methods to decision making is, therefore, vital to decision makers. • OR helps in making informed decisions, allocating optimal resource and improving the performance of systems.
- 8. Concept of Operations Research History of Operations Research • The beginning of OR as a formal discipline can be traced back to 1937 when A P Rowe, Superintendent of the Bawdsey Research Station in British Royal Air Force, sought British scientists to assist military leaders in the use of the recently developed radar system to detect enemy aircrafts. • Once World War II ended, several British operations researchers relocated to government and industry By the 1950 s, the United States government and industry also incorporated OR programmes. • In India it was in 1949 when an Operation Research unit was set up at Regional Research Laboratory, Hyderabad, that OR came into being.
- 9. History Of Operations Research
- 10. Concept of Operations Research Definitions of Operations Research • O.R. is the art of winning wars without actually fighting. - Aurther Clarke • It is concerned with scientifically deciding how to best design and operate man-machine systems usually under conditions requiring the allocation of scarce resources. -O.R. Society of America • O.R. is the art of giving bad answers to problems which otherwise have worse answers. - T.L. Saaty • O.R. is applied decision 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 thorough-going rationality in dealing with his decision problems. -D.W. Miller and M.K. Starr • Operational research is a scientific approach to problems solving for executive management. -H.M. Wagner • O.R. is the application of scientific methods, techniques and tools to problems involving the operations of a system so as to provide those in control of the system with optimum solution to the problem. -Churchman, Ackoff and Arnoff
- 11. Concept of Operations Research Definitions of Operations Research Operations Research (OR) may be defined as the science that aims for the application of analytical and numerical techniques along with information technology to solve organizational problems.
- 12. What is Operations Research?
- 13. Concept of Operations Research Characteristics of Operations Research Some of the important characteristics of OR are • OR as a Decision making Approach • OR as a Problem solving Approach • OR as a Scientific Approach • OR as an Interdisciplinary Approach • OR as a Systems Approach • OR as a Computer Based Approach
- 14. OR as a Decision making Approach: • All organizations are faced with situations where they need to select the best available alternative to solve a problem. • OR techniques help managers in obtaining optimal solutions for their problems. Additionally, OR techniques are also used by managers to understand the problems at hand in a better manner and make effective decisions. • It is important to note that OR techniques help in improving the quality of decisions. • OR helps in finding bad answers to problems having worse answers. It means that for many problems, OR may not be able to give perfect replies but can help in improving the quality of decisions.
- 15. OR as a scientific approach: • OR uses multiple scientific models along with tools and techniques to resolve complex problems while eliminating individual biasness. The scientific method involves observing and defining a problem, formulating and testing the hypothesis and analyzing the results of the test. The results of the test determine whether the hypothesis should be accepted or rejected. OR as an interdisciplinary approach: • Since OR focuses on com plex organizational problems, it includes expertise from different disciplines such as mathematics, economics, science and engineering. • Having different experts ensures that the problem is analyzed from different perspectives and alternative strategies are evolved for the selected problem. • Some of the complex problem. that can be solved using OR include deciding or choosing optimal dividend policies, investment portfolio management, auditing, balance sheet and cash flow analysis, selection of product mix, marketing and export planning, advertising, media planning and packaging, procurement and exploration, optimal buying decisions, trans- portation planning, facilities planning, location and site selection, production cost and methods, assembly line, blending, purchasing and inventory control, etc.
- 16. OR as a systems approach: • In OR, important interactions and their influence on the organization as a whole are considered for decision-making. OR looks at problems from the perspective of the organization: • To determine potential for enhancing the performance of the system as a whole. • To measure the impact of alterations in variables on the whole System. • To find reasons for malfunctioning of the system as a whole, OR as a computer-based approach: • OR solves business problems using mathematical models, manipulating large amount of data and performing computations on these large data sets. • It is almost impossible to do such computations and manipulations manually. Therefore, most OR-based problems are solved using computers..
- 17. Concept of Operations Research Objectives of Operations Research OR is basically a problem solving and decision making tool used by organizations for enhancing their productivity and performance Apart from this, certain other objectives of OR are as follows: • Solving operational questions. • Solving queries related to resources’ operations such as human. • resource scheduling, machine and material scheduling, utilization of funds, etc. • Making informed decisions. • Improving the current systems. • Predicting all possible alternative outcomes • Evaluating risks associated with each alternative
- 18. Concept of Operations Research Tools of Operations Research •OR is widely used in industries, businesses, governments, military establishments and agriculture Most importantly, OR techniques are used by organizations. •OR uses a variety of tools to solve different business problems The most commonly used tools of OR are: 1. Linear Programming 2. Simulation 3.Statistics 4.Assignment 5.Queuing Theory 6.Game Theory 7. Nonlinear Programming 8. Dynamic Programming 9. Goal Programming 10. Integer Programming 11. Network Scheduling
- 19. LINEAR PROGRAMMING Organizations use the Linear Programming (LP) technique to determine the optimal solutions that may be defined as either most profitable or least cost solutions. Businesses use LP techniques to assign jobs to machines, select product mix, select advertising media, select an investment portfolio, etc. SIMULATION Simulation is another important OR tool wherein an expert constructs a model that replicates a real business scenario. Simulation is extremely useful in cases where actual market testing is risky or impossible due to various reasons such as high expenditure. It has widely been used in a variety of probabilistic marketing situations. For example, finding the Net Present Value (NPV) distribution of the market introduction of a product.
- 20. STATISTICS Statistics allows an organization to evaluate the risks present in all the domains of the business. It enables an organization to predict future trends and thus make informed business decisions. The OR team compares different trade-offs and chooses the best alternative. For example, statistics is used in solving various real-life problems such as deterministic optimization. Some of the problems where statistics serves as the primary vehicle for OR include decision theory, optimal strategies for search engine marketing, credit scoring, queuing theory, stochastic programming and inventory management. ASSIGNMENT Assignment method deals with the issue of how to allocate a fixed number of facilities to different tasks in the most optimal manner. The aim is to minimize the cost/time of completing a number of tasks by a number of agents (person or equipment). For example, assigning method can be used to assign specific workers to specific tasks.
- 21. QUEUING THEORY If a problem involves queuing, the Queuing or Waiting Line theory is used. Using this tool, the expected number of people waiting in line, expected waiting time, expected idle time for the server and so on can be calculated. Queuing theory can be used to solve problems related to traffic congestion, repair and maintenance of broken machines, air traffic scheduling and control, scheduling bank counters, etc. GAME THEORY Game theory is useful in decision-making in cases where there are one or more opponents (or players) with conflicting interests. Just as in a game, where the success of one person is influenced by the choices made by the opponent, in the game theory, the actions of all the players influence the outcomes. For example, game theory is used for selecting war strategies and military decisions, bidding at auctions, negotiations, product pricing, stock market decisions, etc.
- 22. NON-LINEAR PROGRAMMING Non-linear problems are similar to linear problems except that they have at least one non-linear function or constraint. Non-linear models beco1ne useful in cases where the objective function of some of the constraints is not linear in nature. For instance, non-linear programming is used for 1naking optimal decisions in production process, optimizing fractionated protocols in cancer radiotherapy, training recur rent neural networks in ti1ne series prediction problems, etc. DYNAMIC PROGRAMMING Dynamic programming models deal with problems in which decisions need to be made over multiple stages in a sequence and the current decisions affect both present and future stages. For example, dynamic programming is used by Google Maps to find the shortest path between a source and destination. It is also used in networking to sequentially transfer data from one sender to various receivers.
- 23. GOAL PROGRAMMING Goal programming tools allow organizations to handle multiple and incompatible objectives. These models are quite similar to linear programming models with the difference being that goal programming can have multiple objectives whereas linear programs have only one. For example, goal programming can be applied to corporate budgeting, financial planning, working capital management, financing decisions, co1nmercial bank management, accounting control, etc. NETWORK SCHEDULING Network scheduling methods are useful in planning, scheduling and monitoring projects of large scales common in construction industry, information technology, etc. For example, network scheduling is used for assembly line scheduling, inventory planning and control, launching new advertisement campaign, installing new equipment, controlling projects, etc.
- 24. Concept of Operations Research Advantages of Operations Research • The field of OR contains robust tools that can be applied in a variety of fields such as transportation, warehouse, production management assignment of jobs, etc. Application of OR tools and techniques help in making best decisions with the available data The advantages of OR as follows: Increased productivity Optimized outcomes Better coordination Lower failure risk Improved control on the system
- 25. Increased productivity: OR helps in increasing the productivity of organizations to a huge eident. The use of OR for effective control of operations allows the managers to take informed decisions. Effective and precise decision-making leads to improve1nent in the productivity of an organization. OR tools also help increase the efficiency of various routine tasks in an organization such as inventory control workforce related business expansion, technology upgrades, installation etc. All these ultimately contribute towards productivity improvement. Optimized outcomes: Management is responsible for making various important decisions about the organization. OR tools can be used by the management to find out various alternative solutions to a problem and selecting the best solution. Selection is based on the profits accrued and costs incurred.
- 26. Better coordination: OR can be used to synchronize the objectives of different departments which results in achieving the goals of all departments. Managers belonging to different departments become aware of the common objectives of the organization, which ensures that different departments coordinate towards achievement of the said goals. For example, OR helps in coordinating the goals of marketing department with the production department schedule. Lower failure risk: Using OR tools and techniques, managers can find all the alternative solutions and risks associated with a given problem. Prior information with respect to all the possible risks helps in reducing the risks of failure.
- 27. Improved control on the system: Managers can apply OR to take better control of the work since it provides comprehensive information about any given course of action. Since OR informs managers about the expected outcome, they can determine what standards of performance need to be expected from employees. They can compare the actual performance of the employees with the standard performance and, therefore, control them in a better manner. It also enables managers to priorities tasks in terms of their importance.
- 28. Concept of Operations Research Limitations of Operations Research •There is no doubt with respect to the practical utility and usability of OR and its applications in real life However, OR also suffers from several limitations which are as follows: High costs Dependence on technology Reliance on experts Unquantifiable factors
- 29. High costs: High cost is one of the biggest limitations of OR. It not only needs expensive technology to create mathematical equations, but also experts to perform simulations. Therefore, while OR does provide effective solutions to a particular problem, it comes with a high cost attached. Dependence on technology: OR is heavily reliant on technology. Computers are generally needed to model and analyze OR problems. Since technology is quite costly a well as subject to failure, its use is severely restricted.
- 30. Reliance on experts: OR requires a team of experts from different fields to perform the assessments. Hiring multiple experts can be costly. In addition, maintaining good communication and coordination among experts and making all experts work together is a critical task. Unquantifiable factors: It is known that OR tools are based on mathematical models that include various information based on quantifiable factors. It means that the efficacy of a solution provided by OR tool depends on quantifiable factors. However, there are certain important unquantifiable factors that cannot be included in the models. When this happens, solutions can often be inexact, inaccurate and therefore, inefficient.
- 31. Operations Research –A Quantitative Approach for Decision-making • Quantitative approach refers to the practice of collecting and analyzing numerical or ‘ data using statistical, mathematical, or computational techniques. • This approach helps in detecting patterns and means forecasting, testing causal relationships, and drawing conclusions for wider populations OR provides managers with a quantitative basis for decision making. • It enables managers to make long term plans and resolve organizational problems in a systematic and logical manner. • In qualitative analysis, the manager’s past experiences and judgment play a key role, while in a quantitative analysis, real quantifiable data deemed to be relevant to the problem) is given primary emphasis.
- 32. Operations Research –A Quantitative Approach for Decision-making • As a quantitative approach OR must follow certain steps as shown in the following Figure: Formulating the Problem Obtaining a Solution from a Model Testing the Model and Solution Establishing Controls over the Solution Implementing the Solution
- 33. 1. Formulating the problem : An important requirement for OR study is that the problem must be clearly defined at the start. Usually, the OR study starts with tentatively formulating the problem, with reformulation occurring during the course of the study. For this step, analysis of the following components is a must: Environment: Environment refers to the physical and socio-economic factors that can influence the problem in question. Some examples of these include materials, equipment: workforce, vendors, customers, competitors, the government, etc. Decision makers: It is important for the analyst to assess the decision- makers and their relationship to the given problem. Objectives: The objectives need to be defined, considering the problem as a whole. Alternatives: The OR study examines which strategy among.st the alternatives is moat suitable to achieve the de sired objectives. It is important to keep in mind the expected reactions of the stakeholders to each alternative. Constraints: Constraints refer to the conditions that can limit the achievement of the objectives. Constraints arise due to limited resources in terms of money, space, manpower, materials, equipment, etc.
- 34. 2. Obtaining a solution from a model: The next step in the OR study is to develop a model for the system. Models demonstrate correlations and causal relationships. Models are used to determine the solution either by simulation or by mathematical analysis. The operation researcher constructs a model that is able to predict how crucial factors impact the solution. 3. Testing the model and solution: In this phase, the suggested model is tested to work under given environmental constraints. If a model is formulated and manipulated properly, it should be able to forecast how fluctuations in control variables impact the efficiency of the overall system. This analysis is generally called a 'sensitivity analysis', The usefulness and validity of the solution is tested by comparison of results achieved with or without using the model.
- 35. 4. Establishing controls over the solution: For the solution to be efficient and stable, the uncontrolled variables need to maintain their values and interrelationships. Fluctuations in one or more variables or their interrelationships can render the solution unmanageable. In these situations, the models require alterations to account for any changes. Once this has been done, the response of the system to the modifications needs to be monitored. 5. Implementing the solution: The last phase in the OR methodology is to implement the solution obtained from the above steps. The solution obtained from the OR study has to be translated into operating procedure so that the concerned persons can understand and apply the solution to the system. The operations researcher and the implementing authority need to close any communication gaps between them and play positive roles.
- 36. Applications and Uses of Operations Research in Management Following are some areas where OR may be applied • Resource distribution in projects • Project scheduling, monitoring and control • Production and facilities planning • Marketing • Personnel management • Finance and accounting • Supply chain management
- 37. Resource distribution in projects: Various OR tools are used to determine which resources are to be allocated to which activities. For instance, OR can help in determining the allocation of 'n’ number of jobs among two machines. Similarly, OR can also be applied to determine and allocate materials workforce, time and budget to projects . Project scheduling, monitoring and control: OR is applied to activities involving scheduling, inventory control, improvement of workflow, elimination of bottlenecks, business process re-engineering, capacity planning and general operational planning. OR tools such as Critical Path Method (CPM) and Project Evaluation and Review Technique (PERT) are used for scheduling the different activities involved in a project. In addition, these tools are also used for continuous monitoring and control of the project.
- 38. Production and facilities planning: OR can be applied for activities involving cite selection factory size, facility planning, inventory forecasts, calculation of economic order quantities, computing reorder levels, maintenance policies, replacement policies, man power planning, assembly line scheduling, etc. All the important decisions and planning work related to facilities, manufacturing and maintenance can be completed using OR tools. Marketing: Application of OR can be done in budget allocation for advertising choice of advertising media and product launch timing. For instance, how should a company allocate its budget for advertising a newly launched product on two TV channels, TV1 and TV2 within a given budget. A company may also use OR techniques to find out how many units of each product in a product mix should be produced to maximize demand.
- 39. Personnel management: OR also finds application in manpower planning, scheduling of training programs, wage administration, etc. Finance and accounting: The application of OR in finance is concerned with effective capital planning, cash flow analysis, capital budgeting, credit policies, investment analysis and decisions establishing Cots for by-products and developing standard costs portfolio management, risk management, etc. Supply chain management: The application of OR in Supply Chain Management involves decision- making regarding the transportation of goods for the purpose of manufacturing and distribution. This further involves the selection of shortest optimal routes so that the goods can be transported to maximum locations at minimum costs.
- 40. Let’s Sum Up • Operations Research (OR) may be defined as the science that aims for the application of analytical and numerical techniques along with information technology to solve organizational problems. • Decision making problems arise when there are two or more alternative courses of action, with each resulting in a different outcome. • OR allows decision makers to compare all possible courses of action understand the likely outcomes and test the sensitivity of the solution to modifications or errors. • OR as a discipline, first developed in the late 1930 s and has evolved continuously since. • The salient features of operations research are that it is a decision making problem oriented, scientific, interdisciplinary systems approach relying heavily on the use of computers.
- 41. Let’s Sum Up • The key objectives of OR are to enable organizations to achieve comprehensive datasets, identify suitable tools and techniques to solve a given problem, weigh all available options, predict all possible alternative outcomes and assess risks associated with each. • OR is needed when the problem is very complex, where no individual bias can be afforded, where the problem has no precedence or where the problem is a recurring one. • The most commonly used tools of OR are linear programming simulation statistics, assignment problem, queuing theory, game theory information theory, non linear programming, dynamic programming goal programming, integer programming, and network scheduling.
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