Introduction to Operations Research

History of OR Operations Research

•      The name (OR) probably came from a programme under taken by Great Britain during world war II “research in military operations”.

•      In 1885, Ferderick W. Taylor gave importance to the application of scientific analysis to methods of production.

•      Firstly , Operations Researches applied on the military defence of the Great Britain.

•      Because of the success of OR in military operations, it quickly spread to all phases of industry and Government.

•      In 1951, OR had taken its place as a distinct science in the United States.

•      After that , OR was considered as the “art of winning war without actually fighting it”.

Operations Research in INDIA

•      In India OR society founded and became a member of international Federation of OR societies in 1959.

•      The Journal OPSEARCH was published for the first time in 1963.

•      Some of the Indian organisations, those are using OR techniques are as follows :

•      Indian Airlines

•      Defence Organisations

•      TATA

•      TELCO

Definition of Operations Research

•      Operations Research is scientific approach to problem solving for executive management.

•      It can also be defined as : OR is an aid for the executive in making his decision by providing him with the needed quantitative information based on the scientific method of analysis.

•      In other simple words “Operations research is the art of giving bad answers to problems which otherwise have worse answers”.

Features of Operations Research

1.      System orientation :  OR study the situation or problem as a whole. This means that any action or activity has same effect on the other part of the organization. The optimum result of one part of a system may not be the optimum for some  other part. Therefore to evaluate any decision one must identify all possible interactions and derermine their impact on the organization as a whole.

2.      Inter-Disciplinary team approach: OR is inter-disciplinary in nature, and is performed by a team of scientists whose individual members have been drawn from different scientific and engineering disciplines. No single individual can have a through knowledge of all aspects of the undertaking. Managerial problems have economic, physical, psychological, biological, sociological and engineering aspects.

3.      Scientific Approach :  OR uses the scientific methods to solve the problems. Most of the science studies such as Chemistry, Physics , biology etc can be carried out in the laboratories without much interference from the outside world.

4.      Decision Making :  OR increases the effectiveness of a management decisions. Management is most of the time making decisions. It is thus a decision science which helps management to make better decisions. It is thus a decision science which helps management to make better decisions. So, the major premise of OR is the decision making, irrespective of the situation involved. So decision making is a systematic process.

5.      Use of computer :  Operations research often requires a computer to solve the complex mathematical model or to perform a large number of computations that are involved.

6.      Objectives :  Operations research always attempts to find the best and optimal solution to the problem. For this purpose objectives of the organization are defined and analysed. These objectives are then used as the basis to compare the alternative courses of action.

7.      Quantitative solution : Operations research provides the managers with a quantitative basis for decision making. OR attempts to provide systematic and rational approach for quantitative solution to the various managerial problems.

8.      Human factors : In deriving quantitative solution we do not consider human factors, which doubtlessly play a great role in the problems. So study of the OR is incomplete without a study of human factors.

Types of Operations Research Models :

A model is a representation of the reality. Most of our thinking of operations research in business take place in the context of models. A model is general term denoting any idealized representation or abstraction of a real life system or situation. The objective of the model is not to indentify all aspects of the situation but to identify significant factors and their inter relationship. A model can be helpful in decision making as it provides a simplified description of complexities and uncertainties of a problem in hand in logical structure.

A broad classification of operations research models is given below :-

(a)   Physical Models :  These models include all forms of diagrams, drawings graphs and charts. Most of which are designed to deal with specific types of problems. By presenting significant factors and inter-relationships in pictorial term, physical models are able to indicate problem in a manner that facilitates analysis. For example a BAR chart can be used effectively as a summary presentation of a company’s monthly production forecast.

(i)                 Iconic models : An icon is an image or likeness of an object or system it represents. An iconic model the least abstract physical replica of a system, is usually based on a smaller scale than the original. The range of management usually based on a smaller scale than the original. The range of management problem areas where these models can be used effectively in extremely narrow. However, it consists largely of these fields that are oriented towards engineering to train their pilots and members of the crew.

(ii)              Analog models : Analog models are closely associated with iconic models. However they are not replicas of problem situations. Rather, they are small physical systems that have similar characteristics and work like an object or system it represents. E.g. children’s toys model of rail, roads etc.

(b)   Mathematical Model or Symbolic model : symbolic model employ a set of mathematical symbols to represent the decision variable of the system under study. These variables are related together by mathematical equations. In other words equations are mathematical model commonly used in operations research. Simple demand curve in economics is a symbolic model predicting buyer’s behavior at different price levels. Similarly profit and loss statement and budget for next year and both symbolic models. Profit and loss account is just reproduced on one sheet of paper and it summarizes the result of a year but does not recreates every action, which took place during the year.

(c)    By Nature environment

(i)                 Determine models : In this model everything is defined and the results are certain. Certainty is the state of nature assumed in these models. For any given input variable there shall be same output variables e.g. in EOQ models, one can easily determine economic lot size, one can apply sensitivity analysis, where change of one variable shall cause certain change in the outcome.

(ii)               Probabilistic model : In cases of risk and uncertainty , the input and output variables take the form of probability distribution. In fact such models are semi-closed model and reveal the probability of occurrence of an event. In fact they reveal the complexity of the real world and uncertainty prevailing in it.

(D)    By the extent of generality :

(i)  General models : General model is one which does not apply one situation only rather it has got general applications. For example linear programming model is known as a general model since it can be used for product mix, production scheduling, marketing, transportation, assignment problems.

(ii)  Specific Model : Specific model is applicable under specific condition only e.g. sales response curve or equation as a function of advertising is applicable in the marketing function alone.

Applications of Operations Research / Scope of Operations Research

In the field of industrial management, there is a chain of problems starting from the purchase of raw materials to the dispatch of finished goods. The management is interested in having an overall view of the method of optimizing profits. In order to take decision on scientific basis, operation research team will have to consider various alternative methods of producing the goods and the return in each case. Operation research study should also point out the possible changes in the overall structure like installation of a new machine, introduction of more automation, etc. OR has been successfully applied in industry, in the field of production, repair and maintenance, scheduling and sequencing, planning, scheduling and control of projects and scores of other associated areas.

Operation research approach is equally applicable to big and small organizations. For example, whenever a departmental store faces a problem like employing additional sales girls, purchasing an additional van etc, techniques of operation research can be applied to minimize cost and maximize benefit  for each such decision

1.      Finance, Budgeting and Investments :  Cost flow analysis , long-range capital requirements, investment portfolios, dividend policies etc.

2.      Purchasing procurement and Exploration : (a) Determining the quantity and timing of purchase of raw materials, machinery etc. (b) Rules of buying and supplies under varying prices. (c) Bidding policies (d) Equipment experiment policies. (e) Determination of quantities and timings of purchase. (f) Strategies for exploration and exploitation of new material sources.

3.      Production Management :

(i)                  Project Planning : (a) Location and Size of warehouse , distribution centers , retail outlets etc.

(b) Distribution Policy

(ii)   Manufacturing and Facility Planning :

(a) Production scheduling and sequencing.

(b) Project scheduling and allocation of resources

(c) Selection and location of factories, warehouses and their sizes

(d) Determining the optimal production Mix

(e) Maintenance policies and preventive maintenance

(f) Maintenance crew sizes.

(g) scheduling arid sequencing the production run by proper allocation of machines.

4. Marketing Management : (a) Product selection, timing, competitive actions.

(b) Advertising strategy and choice of different media of advertising.

(c) Number of salesmen, frequency of calling of accounts. Etc.

(d) Effectiveness of market research.

(e) Size of the stock and meet the future demand.

5. Personnel Management :  (a) Recruitment policies and assignment of jobs

(b) selection of suitable personnel with due consideration for age and skills.

(c) Establishing equitable bonus systems.

6. Research and Development :  (a) Determination of areas of concentration of research and development

(b) Reliability and evaluation of alternatives designs.

(c) Control of development projects.

(d) Co-Ordination of multiple research projects

(e) Determination of time and cost requirements.

Methodology of Operations Research : Given that OR represents an integrated framework to help make decisions, it is important to have a clear understanding of this framework so that  it can be applied to a generic problem. The approach or methodology of O.R. comprises the following seven consequential steps.

(a)   Orientation :  The first step in the O.R. approach is referred to as problem orientation. The primary objective of this step is to have a clean picture of the relevant issues. This phase also involves a study of documents and literature relevant to the problems.

(b)   Problem Definition : This is the second and most important and difficult step of O.R. process. The objective here is to have a clear definition of the problem in terms of its scope and the results desired.

(c)    Data collection : In the third phase of the O.R. process data is collected with the objective of translating the problem defined in the second phase into a model that can then be objectively analysed. Data typically comes from two sources. Data collection can have an important effect on the previous steps mentioned. Now we have ready access to data that was previously very hard to obtain. Even though the data is all present somewhere and in some form, extracting useful information from these sources is often very difficult.

(d)   Model formulation : In this fourth phase of O.R. process, modeling is the process of defining characteristics of all operations. A model may be defined formally as a selective abstraction of reality which helps in the working of original system.

(e)   Solution Results : After formulating an appropriate model, collection of data, the next stage is to find the solution to the model and then interpreting the solution. In this stage, we arrive at the answer to the variable and the objective function.

(f)     Analysis and interpretation of results : This stage requires determining whether the model can adequately and reliably predict the behavior of the real system. It involves testing the structural assumptions of the model. Analysis and interpretation of the performance of the model gives no assurance that the future performance of the system will continue to be in the same manner as in the past.

(g)   Implementation and Monitoring : It is the last process of implementing solution in the organization, implementation of solution is often more difficult as it does not assures that the solution obtained would automatically implemented. The impact of decision may effect various segments of the organization which needs proper monitoring the various changes and taking the suitable measures.

Techniques of Operations Research :

1.      Linear Programming : Linear programming techniques solve product mix and distribution problems of enterprises. LPP techniques used to allocate scarce resources in an optimum manner in problems of scheduling product mix etc.

2.      Inventory Control Models : Inventory may be defined as a useful idle resource which has economic value by raw materials, spare parts, finished products etc.

3.      Sequencing : Models have been developed to find a sequence for processing jobs so that the total elapsed time for all the jobs will be minimum.

4.      Assignment Problems : It deals in allocating the various resources or items to various activities on a one to one basis in such a way that the time or cost involved in minimizes one; sale or profit is maximized e.g. Manager may like to know which job should be assigned to which person so that all jobs can be completed in the shortest possible time.

5.      Transportation Problems : Transportation problem deals with the transportation of a product from a number of sources with limited supplies. The main objective of transportation is to schedule shipments from sources to destination in such a way as to minimize the total transportation cost.

6.      Decision Theory and Games Theory : Decision theory is primarily concerned with decision making under the conditions of risk and uncertainty

7.      Dynamic Programming : When we are faced with the problem of multi faced solution which are inter-related and almost similar in nature, differing any in time and space like solution of suitable product mix, inventory planning control.

Limitations  of Operations Research :

The previous sections have brought out the positive side of O.R. only. However there is also the need to point out the negative side.

1.      Magnitude of Computations :  O.R. tries to find out optimal solution taking into account all the factors. In the modern society these factors are enormous and expressing them in quantity and establishing relationships among these required complicated calculations which can only be handled by machine.

2.      Non – Quantifiable Factors : O.R. provides solution only when all elements related to a problem can be quantified. All relevant variables do not lend themselves to quantifications.

3.      Gap between manager and operations researcher : O.R. being specialist’s job requires a mathematician or stastician.

4.      Money and time costs : when the basic data are subjected to frequent changes, incorporation them into the O.R. models is a costly affair. Moreover, a fairly good solution at present may be more desirable than a perfect O.R. solution available after conventional thinking.

5.      Implementation : Implementation of decisions is a delicate task. It must take into account the complexities of human relations and behavior.

6.      Selection of Technique : Operations research techniques are very usefull but they cannot be used indiscriminately. Choice of technique depends upon the nature of problem.

7.      Not a substitute of Management : Operations research only provides the tools and cannot be a substitute of management. It only examines the results of alternative courses of action and final decision is made by management within its authority and judgement.