Operations research- introduciton
- 2. Operations Research is a ‘war baby’. It is because, the first problem attempted to solve in a systematic way was concerned with how to set the time fuse bomb to be dropped from an aircraft on to a submarine. In fact the main origin of Operations Research was during the Second World War. At the time of Second World War, the military management in England invited a team of scientists to study the strategic and tactical problems related to air and land defense of the country. The problem attained importance because at that time the resources available with England was very limited and the objective was to win the war with available meager resources. The resources such as food, medicines, ammunition, manpower etc., were required to manage war and for the use of the population of the country. It was necessary to decide upon the most effective utilization of the available resources to achieve the objective. It was also necessary to utilize the military resources cautiously. Hence, the Generals of military, invited a team of experts in various walks of life such as scientists, doctors, mathematicians, business people, professors, engineers etc., and the problem of resource utilization is given to them to discuss and come out with a feasible solution. These specialists had a brain storming session and came out with a method of solving the problem, which they coined the name “Linear Programming”. This method worked out well in solving the war problem. As the name indicates, the word Operations is used to refer to the problems of military and the word Research is use for inventing new method. As this method of solving the problem was invented during the war period, the subject is given the name ‘OPERATIONS RESEARCH’ and abbreviated as ‘O.R.’ After the World War there was a scarcity of industrial material and industrial productivity reached the lowest level. Industrial recession was there and to solve the industrial problem the method linear programming was used to get optimal solution.
- 3. CHARACTERISTICS OF OPERATIONS RESEARCH After considering the objective and definitions of Operations Research, now let us try to understand what are the characteristics of Operations Research. (a) 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. (b) 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. (c) 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.
- 4. SCOPE OF OPERATIONS RESEARCH The scope aspect of any subject indicates, the limit of application of the subject matter/techniques of the subject to the various fields to solve the variety of the problems. But we have studied in the objective, that the subject Operations Research will give scientific base for the executives to take decisions or to solve the problems of the systems under their control. The system may be business, industry, government or defense. Not only this, but the definitions discussed also gives different versions. This indicates that the techniques of Operations Research may be used to solve any type of problems. The problems may pertain to an individual, group of individuals, business, agriculture, government or defense. Hence, we can say that there is no limit for the application of Operations Research methods and techniques; they may be applied to any type of problems. Let us now discuss some of the fields where Operations Research techniques can be applied to understand how the techniques are useful to solve the problems. In general we can state that whenever there is a problem, simple or complicated, we can use operations research techniques to get best solution.
- 5. In Defense Operations In fact, the subject Operations research is the baby of World War II. To solve war problems, they have applied team approach, and come out with various models such as resource allocation model, transportation model etc.In any war field two or more parties are involved, each having different resources (manpower, ammunition, etc.), different courses of actions (strategies) for application. Every opponent has to guess the resources with the enemy, and his courses of action and accordingly he has to attack the enemy. For this he needs scientific, logical analysis of the problem to get fruitful results. Here one can apply the techniques like Linear Programming, Game theory, and inventory models etc. to win the game. In fact in war filed every situation is a competitive situation. More over each party may have different bases, such as Air force, Navy and Army. The decision taken by one will have its effect on the other. Hence proper co-ordination of the three bases and smooth flow of information is necessary. Here operations research techniques will help the departmental heads to take appropriate decisions.
- 6. In Industry After the II World War, the, Industrial world faced a depression and to solve the various industrial problems, industrialist tried the models, which were successful in solving their problems. Industrialist learnt that the techniques of operations research can conveniently applied to solve industrial problems. Then onwards, various models have been developed to solve industrial problems. Today the managers have on their hand numerous techniques to solve different types of industrial problems. In fact decision trees, inventory model, Linear Programming model, Transportation model, Sequencing model, Assignment model and replacement models are helpful to the managers to solve various problems, they face in their day to day work. These models are used to minimize the cost of production, increase the productivity and use the available resources carefully and for healthy industrial growth. An industrial manager, with these various models on his hand and a computer to workout the solutions (today various packages are available to solve different industrial problems) quickly& preciously.
- 7. In Planning For Economic Growth In India we have five year planning for steady economic growth. Every state government has to prepare plans for balanced growth of the state. Various secretaries belonging to different departments has to co- ordinate and plan for steady economic growth. For this all departments can use Operations research techniques for planning purpose. The question like how many engineers, doctors, software people etc. are required in future and what should be their quality to face the then problems etc. can be easily solved. In Agriculture The demand for food products is increasing day by day due to population explosion. But the land available for agriculture is limited. We must find newer ways of increasing agriculture yield. So the selection of land area for agriculture and the seed of food grains for sowing must be meticulously done so that the farmer will not get loss at the same time the users will get what they desire at the desired time and desired cost In Traffic control Due to population explosion, the increase in the number and verities of vehicles, road density is continuously increasing. Especially in peak hours, it will be a headache to control the traffic. Hence proper timing of traffic signaling is necessary. Depending on the flow of commuters, proper signaling time is to be worked out. This can be easily done by the application of queuing theory . In Hospitals Many a time we see very lengthy queues of patient near hospitals and few of them get treatment and rest of them have to go without treatment because of time factor. Some times we have problems non-availability of essential drugs, shortage of ambulances, shortage of beds etc. These problems can be conveniently solved by the application of operations research techniques. The above-discussed problems are few among many problems that can be solved by the application of operation research techniques. This shows that Operations Research has no limit on its scope of application.
- 9. Formulation of the Problem The Operations Research analyst or team of experts first have to examine the situation and clearly define what exactly happening there and identify the variables and constraints. Similarly identify what is the objective and put them all in the form of statement. The statement must include a) a precise description goals or objectives of the study, b) identification of controllable and uncontrollable variables and c) restrictions of the problem. The team should consult the personals at the spot and collect information, if something is beyond their reach, they have to consult duty engineers available and understand the facts and formulate the problem. A company manufactures two products X and Y, by using the three machines A, B, and C. Each unit of X takes 1 hour on machine A, 3 hours on machine B and 10 hours on machine C. Similarly, product Y takes one hour, 8 hours and 7 hours on Machine A, B, and C respectively. In the coming planning period, 40 hours of machine A, 240 hours of machine B and 350 hours of machine C is available for production. Each unit of X brings a profit of Rs 5/- and Y brings Rs. 7 per unit. How much of X and Y are to be manufactured by the company for maximizing the profit? Variables The Company is manufacturing two products X and Y. These are the two variables in the problem. When they are in the problem statement they are written in capital letters. Once they are entered in the model small letters (lower case) letters are used (i.e,. x and y). We have to find out how much of X and how much of Y are to be manufactured. Hence they are variables. In linear programming language, these are known as competing candidates. Because they compete to use or consume available resources. Objective of the Problem To maximise the profit how much of X and Y are to be manufactured? That is maximization of the profit or maximization of the returns is the objective of the problem. For this in the statement it is given that the profit contribution of X is Rs 5/- per unit and that of product Y is Rs. 7/- per unit
- 10. Resources and Constraints There are three machines A, B, and C on which the products are manufactured. These are known as resources. The capacity of machines in terms of machine hours available is the available resources. The competing candidates have to use these available resources, which are limited in nature. Now in the above statement, machine A has got available 40 hours and machine B has available a capacity of 240 hours and that of machine C is 350 hours. The products have to use these machine hours in required proportion. That is one unit of product X consumes one hour of machine A, 3 hours of machine B and 10 hours of machine C. Similarly, one unit of Y consumes one hour of machine B, 8 hours of machine B and 7 hours of machine C. These machine hours given are the available resources and they are limited in nature and hence they are constraints given in the statement. Maximise Z = 5x + 7y Subject to a condition (written as s.t.) Objective function. 1x + 1y ≤ 40 3x + 8y ≤ 240 Structural Constraints. 10x + 7y ≤ 350 and Both x and y are ≥ 0 non-negativity restrictions.
- 11. A company manufactures two products X and Y, which require, the following resources. The resources are the capacities machine M1, M2, and M3. The available capacities are 50,25,and 15 hours respectively in the planning period. Product X requires 1 hour of machine M2 and 1 hour of machine M3. Product Y requires 2 hours of machine M1, 2 hours of machine M2 and 1 hour of machine M3. The profit contribution of products X and Y are Rs.5/- and Rs.4/- respectively Machines Products Availability in hours X Y M 1 0 2 50 M2 1 2 25 M3 1 1 15 Profit in Rs. Per unit 5 4 he contents of the statement of the problem can be summarized as follows: Maximize Z = 5x + 4y OBJECTIVE FUNCTION. For Machine M1 0x + 2y ≤ 50 For Machine M2 1x + 2y ≤ 25 For machine M3 1x + 1y ≤ 15 Both x and y are ≥ 0 . NON -NEGATIVITY CONSTRAINT.