Table of Contents

# OPERATIONS RESEARCH

Operations research (OR) is an analytical method of problem-solving and decision-making that is useful in the management of organizations. In operations research, problems are broken down into basic components and then solved in defined steps by mathematical analysis.

The concept of OR arose during World War II by military planners. After the war, the techniques used in their operations research were applied to addressing problems in business, the government and society.

**ACCORDING TO THE OPERATIONAL RESEARCH SOCIETY OF GREAT BRITAIN **

“Operational Research is the attack of modern science on complex problems arising in the direction and management of large systems of men, machines, materials and money in industry, business, government and defense. Its distinctive approach is to develop a scientific model of the system, incorporating measurements of factors such as change and risk, with which to predict and compare the outcomes of alternative decisions, strategies or controls. The purpose is to help management determine its policy and actions scientifically.”

** ACCORDING TO RANDY ROBINSON **

“Operations Research is the application of scientific methods to improve the effectiveness of operations, decisions and management. By means such as analyzing data, creating mathematical models and proposing innovative approaches, Operations Research professionals develop scientifically based information that gives insight and guides decision making. They also develop related software, systems, services and products.”

**ACCORDING TO P.M. MORSE AND G.E. KIMBALL **

“O.R. is a scientific method of providing executive departments with a quantitative basis for decisions regarding the operations under their control”.

**ACCORDING TO T L SATTY **

“O.R. is the art of giving bad answers to problems which otherwise have worse answers”.

**ACCORDING TO MILLER AND STARR **

“O.R. is applied decision theory, which 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 problem”.

**ACCORDING TO POCOCK **

“O.R. is scientific methodology (analytical, mathematical, and quantitative) which by assessing the overall implication of various alternative courses of action in a management system provides an improved basis for management decisions”.

**ACCORDING TO AURTHER CLARKE**

“Operations Research is the art of winning wars without actually fighting”.

**ACCORDING TO J. STEINHARDT**

“Operations Research is Research into Operations”.

**ACCORDING TO EL ARNOFF and M J NETZONG**

“Operations research is the systematic method oriented study of the basic structure, characteristics, functions and relationships of an organization decision making to provide the executive with sound, scientific and quantitative basis for decision making.”

Operations Research takes tools from different discipline such as mathematics, statistics, economics, psychology, engineering etc. and combines these tools to make a new set of knowledge for decision making. Today, O.R. became a professional discipline which deals with the application of scientific methods for making decision, and especially to the allocation of scarce resources. The main purpose of O.R. is to provide a rational basis for decisions making in the absence of complete information, because the systems composed of human, machine, and procedures may do not have complete information.

## CHARACTERISTICS OF OR

The features of Operations Research are as follows:

**OPERATIONS RESEARCH
IS AN INTERDISCIPLINARY TEAM APPROACH:**

The problems an operations research analyst face is heterogeneous in nature, involving the number of variables and constraints, which are beyond the analytical ability of one person. Hence people from various disciplines are required to understand the operations research problem, who applies their special knowledge acquired through experience to get a better view of cause and effects of the events in the problem and to get a better solution to the problem on hand. This type of team approach will reduce the risk of making wrong decisions.

**OPERATIONS RESEARCH
INCREASES THE CREATIVE ABILITY OF THE DECISION MAKER:**

Operations Research provides manager mathematical tools, techniques and various models to analyse the problem on hand and to evaluate the outcomes of various alternatives and make an optimal choice. This will definitely helps him in making better and quick decisions. A manager, without the knowledge of these techniques has to make decisions by thumb rules or by guess work, which may click some times and many a time put him in trouble. Hence, a manager who uses Operations Research techniques will have a better creative ability than a manager who does not use the techniques.

**OPERATIONS RESEARCH
IS A SYSTEMS APPROACH:**

A business or a Government organization or a defense organization may be considered as a system having various sub-systems. The decision made by any sub-system will have its effect on other sub-systems. Say for example, a decision taken by marketing department will have its effect on production department. When dealing with Operations Research problems, one has to consider the entire system, and characteristics or sub- systems, the inter-relationship between sub-systems and then analyse the problem, search for a suitable model and get the solution for the problem. Hence we say Operations Research is a Systems Approach.

**WHOLISTIC
APPROACH TO THE SYSTEM:**

While evaluating any decision, the important interactions and their impact on the whole organisation against the functions originally involved are reviewed.

**OBJECTIVE
APPROACH:**

O.R. attempts to find the best or optimal solution to the problem under consideration, taking into account the goals of the organisation.

**SCIENTIFIC APPROACH:**

*ACCORDING TO P.M. MORSE AND G.E. KIMBALL *

“O.R. is a scientific method of providing executive departments with a quantitative basis for decisions regarding the operations under their control”.

So OR is a proper scientific approach to solve the complex business problems. The scientific methods in Operations Research consist of three phases:

**Judgement Phase:** This phase consists of:

- Determination of operations.
- Establishment of objective and values related to the operation.
- Determination of the suitable measures of effectiveness.
- Formulation of the problems relative to objectives.

**Research Phase: **This phase utilizes:

- Operations and data collection for a better understanding of the problem.
- Formulation of hypothesis and model.
- Observation and experimentation to test the hypothesis on the basis of additional data.
- Analysis of the available information and verification of the hypothesis using pre-established measures of effectiveness.
- Prediction of various results from the hypothesis.
- Generalization of the various result and consideration of alternative methods.

**Action Phase:** It consists of making recommendations for the decision process by those who first posed the problem for consideration or by anyone in a position to make a decision, influencing the operation in which the problems occurred.

**USE OF COMPUTER**

Operations Research often requires a computer to solve the computer mathematical model or to perform a large number of computations that are involved. Use of a digital computer has become an integral part of the operations research approach to decision making.

**QUANTITATIVE SOLUTION**

*ACCORDING TO EL ARNOFF and M J NETZONG*

“Operations research is the systematic method oriented study of the basic structure, characteristics, functions and relationships of an organization decision making to provide the executive with sound, scientific and quantitative basis for decision making.”

The above definition clearly states that the solutions derived by applying the OR methods and techniques are quantitative in nature as the all techniques applied are mathematical. Operations research attempts to provide a systematic and rational approach for quantitative solutions to the various managerial problems.

## METHODOLOGY OF OPERATIONS RESEARCH

The systematic methodology developed for O.R. study with problems involving conflicting multiple objectives policies and alternatives. OR in the final analysis is a scientific methodology which is applied to the study of the operations of large complex organizations or activities with a view to assessing the overall implications of various alternative courses of action thus providing an improved basis for management decisions.

**STEP 1.
PROBLEM FORMULATION**

This is a major phase in which the OR team should formally formulate the management problem and then transform it into a research problem. For purposes of formulating the management problem in the first instance, the OR team makes a thorough analysis of organizational structure and function the communication and control systems the objectives and policies of the organization and so on

In O.R. approach problem formulation has a different meaning than what is understood in common parlance. The major components of a problem are:

– A group or an individual decision maker who faces a problem.

– The environment wherein the problem is supposed to lie. It is not unlikely that the roots of problem are traced to a different area. Therefore it is wise to call the entire organization as the second component.

– Objectives

– Alternative courses of action that affect the objectives. The outcomes are not known beforehand and the decision makers are in a dilemma as to which courses of action is to be chosen.

– Constraints

**STEP 2. ANALYSIS AND DEFINING THE PROBLEM**

After analyzing the problem of the environment, the researcher should analyse the problem and define it in clearer terms. All the factors affecting the problems directly and indirectly should be taken into consideration. The in depth analysis of the problem helps in its proper understanding and their contribution towards finding the best solution for the problem.

Example: Suppose a manager notices that a reduction in sales volume is causing fall in the profit of the current year. The operations researcher has been asked to analyse the problem.

Now the Operations researcher analyses company’s products prices and promotions. He discovers that promotion is the main problem area. He must investigate the various variables responsible for reduced sales. The culprit could be:

- Amount of money spent.
- The media used.
- The timings of sale.
- Or any combination of these.

**STEP 3.
COLLECTING DATA REQUIRED BY THE MODEL**

‘Garbage In and Garbage Out’ is the famous saying. It means if the data is inappropriate then the model built on the basis of that data will also be inappropriate. So the data should be collected very cautiously. The data may be collected from either primary or secondary source. This means the researchers should conduct a fresh research to get the data or should approach the historical records.

**STEP 4.
CONSTRUCTING A MATHEMATICAL MODEL**

The next stage in the O.R process is to try to express the relevant features of the system under study in terms of a mathematical model. The general form a mathematical model is:

E = f (x_{i, }y_{i})

Where f represents a system of mathematical relationships between
the measure of effectiveness of the objectives sought (E) and the variables.
Both controllable (x_{i}) and
uncontrollable (y_{i}).

**STEP 5.
DERIVING SOLUTIONS FROM THE MODEL**

Once the mathematical model is formulated the next step is to determine the value of decision variables that optimize the given objective function. The various mathematical techniques for arriving at such solutions comprise much of the contents of this text.

In addition to the solution of the model, it is also sometimes essential to perform sensitivity analysis, i.e., determine the behavior of the system changes in the system parameters and specifications. This is done because the input data (parameters) may not be accurate or stable and the structural assumptions of the model may not be valid. Thus sensitivity analysis is an essential part of this phase of the methodology and must not be overlooked.

**STEP 6.
TESTING THE MODEL**

Since in once a model is only a partial and simplified representation of reality, the results are to be tested against the real word experience in order to establish the model’s credibility. Several simplifying assumptions are made while initiating the model building. These assumptions can be relaxed one by one to see the reaction of the model results to such relaxation.

Similarly inclusion of some inappropriate variables in the model and exclusion of some appropriate variables from the model, just for purposes of abstraction and simplification may require review so that their impact on the model vis-à-vis reality is analysed form a proper perspective. Model distortion through simplification intentional or otherwise has to be properly assessed with the help of previous experience judgment actual test data and similar devices.

**STEP 7.
ESTABLISHING CONTROLS OVER THE SOLUTION**

Complex models of specific problems produce decision rue ties which could be used a procedures to take care of repetitive situations without having to build a model ever time. This naturally calls for incorporation of controls into the model so that they are adaptable for a range of problem. In the dynamic business world, values of parameters keep changing; some parameters become outdated new parameters emerge unless taken care of will leave the model solution utterly useless for later similarly problems. A conscious control procedure is to be established for detecting significant changes in the parameters and relationships and for specifying the action to be taken or adjustments to be made in the solution when a significant change occurs.

**STEP 8.
IMPLEMENTING THE SOLUTION.**

This is certainly the most important phase of the study, because it is only after a proposal has been implemented that the benefits accrue. When an operationally feasible solution has been decided upon, stage is set to put that solution into practice. This is often far from straight forwardness as solutions which look feasible on paper may conflict drastically with the ideas and capabilities of the people involved in the system. Many perfectly sound (theoretically) OR recommendations do not reach implementation because they prove unworkable in practice.

Finally no system is even completely static and it is always necessary to monitor the environment within which a system operates to ensure that changing conditions do not render a solution inappropriate. It is important to ensure that any solution implemented is continuously reviewed and (if necessary) updated and modified in the light of a changing environment. 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.

**SCOPE OF OPERATIONS
RESEARCH**

The scope of OR is not only confined to any specific agency like defense services but today it is widely used in all industrial organizations. It can be used to find the best solution to any problem be it simple or complex. It is useful in every field of human activities, where optimization of resources is required in the best way. Thus, it attempts to resolve the conflicts of interest among the components of organization in a way that is best for the organization as a whole. The main fields where OR is extensively used are given below:

**NATIONAL PLANNING AND
BUDGETING**

OR is used for the preparation of Five Year Plans, annual budgets, forecasting of income and expenditure, scheduling of major projects of national importance, estimation of GNP, GDP, population, employment and generation of agriculture yields etc.

**DEFENSE SERVICES**

Basically formulation of OR started from USA army, so it has wide application in the areas such as:

- Development of new technology
- Optimization of cost and time
- Tender evaluation
- Setting and layouts of defense projects
- Assessment of “Threat analysis”
- Strategy of battle
- Effective maintenance and replacement of equipment
- Inventory control
- Transportation and supply depots etc.

**R & D AND
ENGINEERING**

Research and development is the heart of technological growth. OR has wide scope in this field also. It can be applied in

- Technology forecasting and evaluation
- Technology and project management
- Preparation of tender and negotiation
- Value engineering
- Work/method study and so on.

**AGRICULTURE AND
IRRIGATION**

In the area of agriculture and irrigation also OR can be useful for project management, construction of major dams at minimum cost, optimum allocation of supply and collection points for fertilizer/seeds and agriculture outputs and optimum mix of fertilizers for better yield.

**EDUCATION AND
TRAINING**

OR can be used for obtaining optimum number of schools with their locations, optimum mix of students/teacher student ratio, optimum financial outlay and other relevant information in training of graduates to meet out the national requirements.

**TRANSPORTATION**

Transportation models of OR can be applied to real life problems to forecast public transport requirements, optimum routing, forecasting of income and expenses, project management for railways, railway network distribution, etc. In the same way it can be useful in the field of communication.

**HOME MANAGEMENT AND
BUDGETING**

OR can be effectively used for control of expenses to maximize savings, time management, work

study methods for all related works.

**MANUFACTURING **

OR’s success in contemporary business pervades manufacturing and service operations, logistics, distribution, transportation, and telecommunication.

Operations research is used to for various activities which include

- Scheduling
- Routing,
- Workflow improvements
- Elimination of bottlenecks
- Inventory control
- Business process re-engineering
- Site selection
- Facility and general operational planning.

**REVENUE MANAGEMENT**

The application of OR in revenue management entails first to accurately forecasting the demand, and

secondly to adjust the price structure over time to more profitably allocate fixed capacity.

**SUPPLY CHAIN
MANAGEMENT**

In the area of Supply Chain Management, OR helps in taking decisions that include the who, what, when, and where abstractions from purchasing and transporting raw materials and parts, through manufacturing actual products and goods, and finally distributing and delivering the items to the customers. The primary objective here is to reduce overall cost while processing customer orders more efficiently than before. The power of utilizing OR methods allows examining a rather complex and convoluted chain in a comprehensive manner, and to search among a vast number of combinations for the resource optimization and allocation strategy that seem most effective, and hence beneficial to the operation.

**RETAILING**

In supermarkets, data from store loyalty card schemes is analyzed by OR groups to advice on merchandising policies and profitability improvement. OR methods are also used to decide when and where new store developments should be made.

**FINANCIAL SERVICES**

In financial markets, OR practitioners address issues such as portfolio and risk management and planning and analysis of customer service. They are widely employed in Credit Risk Management—a vital area for lenders needing to ensure that they find the optimum balance of risk and revenue. OR techniques are also applied in cash flow analysis and capital budgeting.

**MARKETING MANAGEMENT**

OR helps marketing manager in making the apt selection of product mix. It helps them in making optimum sales resource allocation and assignments.

**HUMAN RESOURCE
MANAGEMENT**

OR techniques are being applied widely in the functional area of Human Resource Management by helping the human resource managers in activities like

- Manpower planning
- Resource allocation
- Staffing and scheduling of training programs.

**GENERAL MANAGEMENT**

OR helps in designing Decision Support System and management of information systems, organizational design and control, software process management and Knowledge Management.

**PRODUCTION SYSTEMS **

The area of operations research that concentrates on real-world operational problems is known as production systems. Production systems problems may arise in settings that include, but are not limited to, manufacturing, telecommunications, health-care delivery, facility location and layout, and staffing.

**REAL LIFE EXAMPLES OF OPERATIONS RESEARCH**

- In 2013, Dutch Delta program Commissioner used mixed integer programming to derive an optimal investment strategy for strengthening dykes for protections against high water and keeping fresh water supplies upto standard, resulting in savings of 8 billion Euros in investment costs.
- In 2012, TNT Express developed a portfolio of multi- commodity and vehicle routing models for package and vehicle routing and scheduling, planning of pickup and delivery and supply chain optimization for its operations across 200 countries using 2,600 facilities, 30,000 road vehicles and 50 aircraft resulting in savings of 207 million euros over the period 2008-2011 and reduction in Carbon-dioxide emissions by 283 million kilograms.

- In 2010, Mexico’s central security depository, INDEVAL used linear programming to develop a secure and automatic clearing and settlement engine to determine the set of transactions that can be settled to maximize the number of traded securities, thereby efficiently processing

**MATHEMATICAL TECHNIQUES IN OPERATIONS RESEARCH**

The significant mathematical techniques of OR which has been successfully applied to decision making are the following:

**LINEAR PROGRAMMING **

Linear Programming (LP) is a mathematical technique. It is the process of taking various linear inequalities relating to some situation, and finding the “best” value obtainable under those conditions. In “real life”, linear programming is part of a very important area of mathematics called “optimization techniques”. It takes all kinds of factors into consideration to determine the best combination of a purchasing or manufacturing process, to either maximize profit, minimize cost or some other goal. Therefore, LP is a very important part of any business.

**TRANSPORTATION PROBLEM**

The transportation problem is a special type of linear programming problem, where the objective is to minimize the cost of distributing a product from a number of sources to a number of destinations. Transportation helps shape an area’s economic health and quality of life.

**ASSIGNMENT PROBLEM**

In a few words, when the problem involves the allocation of n different facilities to n different tasks, it is often termed as an assignment problem. Assignment deals with the question how to assign n object to m other object in an injective fashion in the best possible way. An assignment problem is specified by its two component:

- The assignment which represent the underlying combinatorial structure
- The objective function to be optimized which model “the best possible way”

**QUEUING THEORY**

The queuing problem is identified by the presence of a group of customers who arrive randomly to receive some service. Queuing theory deals with problems which involve queuing (or waiting). This theory helps in calculating the expected number of people in the queue, expected waiting time in the queue, expected idle time for the server, etc.

**GAME THEORY**

Game theory is the formal study of decision-making where several players must make choices that potentially affect the interests of the other players. It is used for decision making under conflicting situations where there are one or more opponents (i.e., players). In the game theory, we consider two or more persons with different objectives, each of whose actions influence the outcomes of the game. Game theory is a mathematical method for analyzing calculated circumstances, such as in games, where a person’s success is based upon the choices of others.

**INVENTORY CONTROL MODELS**

The literal meaning of inventory is “idle but usable resources. Thus, this model is concerned with the acquisition, storage, handling of inventories so as to ensure the availability of material whenever needed and minimize wastage and losses.

**GOAL PROGRAMMING**

It is a powerful tool to tackle multiple and incompatible goals of an enterprise. Goal programming models are very similar to linear programming models but whereas linear programs have one objective goal programs can have several objectives.

**SIMULATION**

It is a technique that involves setting up a model of real situation and then performing experiments. Simulation is used where it is very risky, cumbersome, or time consuming to conduct real experiment to know more about a situation.

**NONLINEAR PROGRAMMING**

These methods may be used when either the objective function or some of the constraints are not linear in nature. Non-Linearity may be introduced by factors such as discount on price of purchase of large quantities.

**INTEGER PROGRAMMING**

These methods may be used when one or more of the variables can take only integral values. The Integer Programming problem (IP) is that of deciding whether there exists an integer solution to a given set of m rational inequalities on n variables. E.g. the number of trucks in a fleet, the number of generators in a power house, etc.

**DYNAMIC PROGRAMMING**

Dynamic programming is a methodology useful for solving problems that involve taking decisions over several stages in a sequence. One thing common to all problems in this category is that current decisions influence both present & future periods.

**SEQUENCING THEORY**

It is related to Waiting Line Theory. It is applicable when the facilities are fixed, but the order of servicing may be controlled. The scheduling of service or sequencing of jobs is done to minimize the relevant costs.

**REPLACEMENT MODELS**

These models are concerned with the problem of replacement of machines, individuals, capital assets, etc. due to their deteriorating efficiency, failure, or breakdown.

**NETWORK SCHEDULING-PERT AND CPM**

Network scheduling is a technique used for planning, scheduling and monitoring large projects. Such large projects are very common in the field of construction, maintenance, computer system installation, research and development design, etc.

**INFORMATION THEORY**

It is an analytical process transferred from the electrical communications field to operations research. It seeks to evaluate the effectiveness of information flow within a given system and helps in improving the communication flow.

**IMPORTANCE OF OPERATIONS RESEARCH**

Operations research is important because it is a helpful tool used to solve complex problems under uncertainty. In business, very few things are certain, and managers must often make decisions based on their instincts instead of being able to use reliable data. Operations research techniques fill this void with methods that quantify issues and give business managers a better basis for making decisions.

**IMPROVED DECISION MAKING**

As the above example shows, operations research techniques can take a muddle of factors and numbers and reduce them to simple formulas. These formulas will find the optimal solutions within the constraints of the problem.

**BETTER
CONTROL**

OR techniques give managers the tools that provide better direction and control over subordinates. A manager can use OR methods to set up performance standards for employees and identify areas that need improvement.

**HIGHER
PRODUCTIVITY**

A significant use of OR is the ability to identify optimal solutions. A few examples are finding the best inventory mix, optimal utilization of manpower, most desirable use of plant machinery and highest-producing marketing campaigns.

**BETTER
DEPARTMENTAL COORDINATION**

When the optimal results from OR analysis are shared with all departments, everyone works together toward the same goal. For example, the marketing department might coordinate their efforts with the schedules laid out by the production supervisor.

**EFFECTIVE
SYSTEMS**

Operational research techniques are to analyze the problem of decision making such as good site for plant, whether to open a new storehouse, etc. It also helps in assortment of cost-effective means of transportation, jobs sequencing, production scheduling, replacement of old machinery, etc.

**MAXIMIZE
PROFITS & MINIMIZE LOSSES**

The operational Research techniques provide the quantitative data to take the decision which help the analyzer to take the appropriate decision which lead to maximize the profit and minimize the losses.

**ROLE OF OPERATIONS RESEARCH IN DECISION MAKING**

Operations research plays an important role in almost all areas of decision making. Some areas where operational research (OR) techniques can be used as listed below:

**FINANCING
AND INVESTMENT POLICES**

This category includes the analysis of credit and loan policy, fund flow and cash flow and also considers the dividend, share and bonus policy. It reflects the portfolio of investment too.

**SELLING,
PROMOTION, MARKETING & PUBLICITY **

It emphasis on selection of the product and timing which means what type of commodity should be manufactured at the proper passage of the time. It focuses on the media of publicity like print media and electronic media may be chosen. It also used to know about how many number of sales persons are required to some specific area. More over OR also use to select the product mixed which include product, price, place and promotions.

**ACQUISITION,
INVESTIGATION, MANUFACTURING AND PERSONNEL MANAGEMENT **

The operational research techniques being used to purchase, substitute and reorganize the most advantageous policies. These techniques also include location and manufacturing size of retail outlets, factories and warehouses, loading and unloading facilities for trucks, allocation and scheduling of resources and optimum to merge the products, recruitment and selection of best suitable employee for a company and job assignments etc.

**RESEARCH
AND DEVELOPMENT **

The methods currently available in literature for numerically solving operational research problems may be broadly classified as deterministic methods and probabilistic methods. The deterministic methods try to guarantee that a neighborhood of the solution of a problem is attained. Such methods do not use any stochastic techniques, but rely on a thorough search of the feasible domain. They are applicable, however, to a restricted class of problems only. On the other hand the probabilistic methods make use of probabilistic or stochastic approach to search for the solutions for the problems. Although probabilistic methods do not give an absolute guarantee of the exact solution having been obtained, these methods are sometimes preferred over the deterministic methods because they are applicable to wider class of problems.

**LIMITATIONS OF OPERATIONS RESEARCH**

OR has some limitations. However, the limitations are related to the problem of model building and

the time and money factors involved in application rather than its practical utility. Some of them are

as follows:

**MAGNITUDE OF COMPUTATION**

The models of OR strive to find out optimal solutions taking into account all the factors. These factors may be huge and state them in quantity and establish relationships among the factors require ample calculations which can be effectively solved by computers.

**NON-QUANTIFIABLE FACTORS**

OR provides solution only when all elements related to a problem can be quantified. All relevant variables do not lend themselves to quantification. Factors which cannot be quantified find no place in OR study.

**DISTANCE BETWEEN USER AND ANALYST**

OR being specialist’s job requires a mathematician or statistician, who might not be aware of the business problems. Similarly, a manager fails to understand the complex working of OR. Thus there is a gap between the User and Analyst.

**TIME AND MONEY COSTS**

OR models are a costly proposition as they require time and money for scientific application. The computational time increases depending upon the size of the problem and accuracy of results desired.

**IMPLEMENTATION**

Implementation of any decision is a delicate task. It must take into account the complexities of human relations and behavior. Sometimes, resistance is offered due to psychological factors which may not have any bearing on the problem as well as its solution.

**DIFFICULT TO BALANCE THE REQUIREMENT**

It is often difficult to balance the requirement of reality and those of simplicity.

**POOR AND/OR INACCURATE DATA**

The quality of data collection may be poor and/or inaccurate.

**LACK OF SUITABLE SOLUTION TECHNIQUES**

In many cases, the solution of Operations Research problem is restricted by the lack of suitable solution techniques. As example, the derived solution may be sub-optimal i.e. the boundaries of the problem may be open.

**CONFLICT**

An Operations Research model is static but the solution it imitates is dynamics. Conflict between conclusion reached by the Operations Research analyst and the opinion of time managers as to the best course of action.

**NOT A SUBSTITUTE FOR
MANAGEMENT**

Operations research only provides the tools and techniques and cannot be a substitute of management. It only examines the results of alternatives course of action and final decision is made by management within its authority and judgment.

**SUB-OPTIMIZATION
**Sub-optimization is deciding in respect of a relatively narrow aspect of
the whole business situation or optimization of a sub-section of the whole.
Functional heads sometimes, without taking care of wider implications,
sub-optimize their functions. This may cause loss in that part of the
organization which is left out of the exercise and as such should be avoided.

**NOT REALISTIC**

Operations research experts make very complex models for solving problems. These models are/ may not be realistic. Hence, they may not be useful for real life situations.

**CONCLUSION**

The OR profession was for a time the centre of managerial attention. It had its golden era. It is now a small professional grouping which has found its niche. Few people realize that OR lies behind many every day events, providing the algorithms for airline reservation systems, checking the credit worthiness of loan applicants, and calculating the replenishment quantities required by supermarkets. Despite its important role in today’s society OR lacks self-importance, it includes many, diverse interests and has demonstrated a certain capacity for survival.