OR is a very versatile science and has many tools/techniques, which can be used for problem solving.However, it is not possible to list all these techniques as everyday new methods in the use of OR are being developed. Some of the tools of OR are discussed in the succeeding paragraphs :-

**1. ****Linear Programming (LP)**

Most of the, industrial and business organisations have the objectives of minimizing costs and maximizing the profits. LP deals with maximizing a given objective. Since the objective function and boundry conditions are linear in nature, this mathematical model is called Linear Programming

Model. It is a mathematical technique used to allocate limited resources amongst competing demands in an optimal manner. The application of LP requires that there must be a well-defined objective function ‘(like maximizing profits and minimizing costs) and there must be constraints on the amount and extent of resources available for satisfying the objective function.

**2. ****Queuing Theory**

In real life situations, the phenomenon of waiting is involved whether it is the people waiting to buy goods in a shop, patients waiting outside an OPD (Out Patient, Department), vehicles waiting to be serviced in a garage and so on. Because in general, customers arrival and his service time is not known in advance; a queue is formed. Queuing or waiting line theory aims at minimizing the overall cost due to servicing and waiting. How many servicing facilities can be added at what cost to. minimize the time in queue is the aim in the application of this theory.

**3. ****Network Analysis Technique**

A network can be used to present or depict the activities necessary to complete a project. This helps us in planning, scheduling, monitoring and control of large and complex projects. The project may be developing a new battle tank, construction of dam or a spaceflight. The project managers are interested in knowing the total project completion time, probability that a project can be completed by a particular time, and the least cost method of reducing the total project completion time. Techniques like Programme Evaluation and Reviewing Technique (PERT) and Critical Path Method (CPM) are part of network analysis. These are popular techniques and widely used in project management.

**4. ****Replacement Theory Model**

All plants, machinery and equipment needs to be replaced at some point of time, either because there is deterioration in their efficiency or because new and better equipment is available and. the old one has become obsolete. Sooner or later the equipment needs to be replaced. The decision to be taken by the management involves consideration of the cost of new equipment which is to be purchased and what can be recovered fr.om the old equipment through its sale, or its scrap value, the residual life of the old equipment and many other related aspects. These are important decisions involving investment of capital and need to be taken very carefully.

**5. ****Inventory Control**

Inventory includes all the stocks of material, which an organization buys for production/manufacture of goods and services for sale. It will include raw material ; semi-finished and finished products, spare parts of machines etc. Managers face the problems of how much of raw material should be purchased, when should it be purchased and how much should be kept in stock. Overstocking will result in locked capital not available for other purposes, whereas under-stocking will mean stock-out and idle manpower and machine resulting in reduced output. It is desirable to have just the right amount of inventory at the right time. Inventory control models can help us in finding out the optimal order size, reorder level etc so that the capital resources are conserved and maximum output ensured.

**6. ****Integer Programming**

Integer programming deals with certain situations in which the variable assumes non-negative integer (complete or whole number) values only. In LP models the variable may take e.ven a fraction value and the figures are rounded off to the nearest integer to get the solution i.e., number of vehicles available in a problem cannot be in fractions. When such rounding off is done the solution does not remain ‘an optimal solution. In integer programming the solution containing unacceptable and fractional values are ruled out and the next best solution using whole numbers is obtained. An integer programming may be called mixed or pure depending on whether some or all the variables are restricted to integer values.

**7. ****Transportation Problems**

Transportation problems are basically LP model problems. This model deals with finding out the minimum transportation cost for transporting the single commodity from a number of sources to number of destinations. Typical problem involves transportation of some manufactured products (say cars in 3 different plants) and these have to be sent to the warehouses of various dealers in different parts of country. This may be understood as a special case of simplex method developed for LP problems, allocating scare resources to competing demands. The main purpose of the transportation is to schedule the dispatch of the single product from different sources like factories to different destinations as total transportation cost is minimized.

**8. ****Decision Theory and Games Theory**

Information for making decisions is the most important factor. Many models of OR assume availability of perfect information which is called decision-making under certainty. However, in real life situations, only partial or imperfect information is available. In such a situation we have two cases, either decision under risk or decision under uncertainty. Hence from the point of view of availability of information, there are three cases, certainty and uncertainty, the two extreme cases and risk is the “in-between” case.

Games theory is concerned with decision-making in a conflict situation where two or more intelligent opponents try to optimize their own decision. In Games theory, an opponent is referred to as a player and each player has a number of choices. The Games theory helps the decision maker to analyse the course of action available to his opponent. In decision theory, we use decision tree which can be graphically represented to solve the decision-making problems.

**9. ****Assignment Problems**

We have the problem of assigning a number of tasks to a number of persons who may use machines. The objective is to assign the jobs to the machines in such a way that the cost is least. This may be considered a special case of LP transportation model. Here jobs may be treated as ‘services’ and machines may be considered the ‘destinations’. Assignment of a particular job to a particular person so that all the jobs can be completed in shortest possible time hence incurring the least cost, is the assignment problem.

**10.****Markov Analysis **

Markov analysis is used to predict future conditions. It assumes that the occurrence of a future state depends upon the immediately preceding state and only on it. It is based on the probability theory and predicts the change in a system over a period of time if the present behaviour of the system is known. Predicting market share of the companies in future as also whether a machine will function properly or not in future are examples of Markov Analysis.

**11.****Simulation Techniques **

Since all real life situations cannot be represented mathematically, certain assumptions are made and dynamic models which act like the real processes are developed. It is very difficult to develop simulation models, which can give accurate solutions to the problems, but this is a good method of problem solving, when the problems are very complex and cannot be solved otherwise. .

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