Operation Research is a very resourceful branch of science which is used for solving problems with numerous techniques and tools.As with every passing day new methods of operation research applications are being developed, listing every technique is not possible. Although it is a difficult task, few of the important operation research tools are explained below.

**Network Analysis Technique**

For a successful completion of a project, a network is extremely helpful in presenting the activities which are required in this respect. In a complicated project, this technique helps in preparing, organising, observing and supervising the activities. The developing project may be of anything. It may be about a spaceflight construction, creation of a dam or development of a battle tank.

The area of interest the project managers intend to know are divided into 3 parts.

- Estimated time required for the entire project completion.
- The project completion expectation rate

- Costing methodology and the different ways to reduce the prices involved in the entire project.

There are 2 techniques which serve as important parts of network analysis.

- Critical Path Method (CPM)
- Programme Evaluation and Reviewing Technique (PERT)

Used extensively in project management, these techniques are the very popular.

**Linear Programming**

Usually, an increase in profit and a decrease incost is considered as one of the key objectives by most of the business organisations and firms.To maximise the ratio of a given objective, linear programming is used. This mathematical model is stated as linear programming model as its boundary conditions as well as the objective functions are linear in nature.

Used for the assignment of limited resources, this mathematical technique is utilised in a favourable manner amongst the competing demands. A well-defined objective function is a mandatory requirement in the application of linear programming. The objective functions are like reduction in costs and increase in profits. Also, these functions emphasise on the fact that to satisfy the requirements; there should be limitations on the quantity and its extent of the available resources.

**Inventory Control**

When a company purchases commodities and services on sale for their manufacturing process,stock of these materials is called inventory. The goods which are included in it are:

- Raw materials
- Spare parts of equipment
- Semi-finished and completed products

The issues that managers usually have to face in this aspect are:

- The quantity of raw materials that are required to be bought.
- The appropriate purchase time of those materials.
- Quantity that should be kept as stock.

The manager also has to look for overstocking as well as undestocking. This is because overstocking locks funds which cannot be used for another business purpose. Also understocking means problems when required materials will be out of stock, and there will be idle manpower and less machine usage. This results in minimal output.

The best option is to have a balanced amount of inventory which can be utilised at the right time. For conserving capital resources, for the generation of maximum output and to find out ideal order size and reorder level, the help of Inventory control models are taken.

**Transportation Problems**

Transportation problems are basically associated withlinear programming model problems. To find out the least transportation cost to carry goods from various resources to different destinations this model is used. There are predictable problems which occur during the transportation of few manufactured goods.

For example, there are 3 cars (products) which are needed to be transported in 3 different plants that too in different parts of the country.

From this example, it can be clearly seen that this is a case of simple method developed for linear programming problems who assigns inadequate resources to compete demand. The aim of transportation is to programme and dispatch products from various sources like firms, factories, organisations to the require destinations at minimal cost.

**Assignment Problems**

It is very difficult to allocate a number of tasks to the people who use machineries. The main objective of work assignment is to strategically allocate work to equipment so that the costing involved in it is the lowest. This objective is considered as an exceptional case of linear programming transportation model.

The machines are represented as adestination and the work is deemed as services. When a certain work is assigned to certain people so that in the least possible duration and with lowest costing the entire work gets completed, it is called assignment problem.

**Simulation Techniques**

Not all real life circumstances can be used for depicting a situation mathematically.There are few specific assumptions which are required to be made. Due to this, few dynamic models are also developed which represents real life processes. Although simulation models are extremely hard to be developed, these models are the accurate solution provider. This method has been termed as an outstanding problem solving method to those complicated procedures which cannot be solved by any other models.

**Queuing Theory**

Queuing Theory is basically based on the concept of waiting. If seen in real life situation, there are circumstances where patients wait to meet doctors in a hospital, vehicles in garageswait to be serviced,people waiting for buyingcommodities, and many other instances. If to be stated in simplified words, a queue is only formed when customer arrival and the time required for their service is unknown.

In order to reduce the overall cost caused because of servicing and waiting, this theory of queuing is utilised. The aim of applying this theory is to calculate the number of facilities required to be added and the cost associated with it for reducing the waiting time.

**Replacement Theory Model**

The replacement of machineries depends on time, its condition and its requirement. When machineries become inefficient, or the condition of equipmentdeteriorates or latest and better instruments become available, the old and obsolete ones are discarded by plants.

There are multiple decisions which the managements are required to take in this aspects. Few of these involves:

- Cost consideration required for the purchase of the new machineries.
- Any recovering price from the sale of old machineries.
- The scrap value of any equipment in respect to its residual life.

When the involvement of capital investment is the foremost aspect, these decisions come to great help which should be taken carefully.

**Integer Programming**

In certain circumstances when the variables assume whole number values (non-negative integers), those situations are dealt by Integer programming. Other models like linear programming models even consider fractional values and round it off to thenearest complete number. But in this programming, it cannot be done. It can be explained by the fact that vehicles or machinery in a problem cannot be counted in fractions.

An ideal solution cannot be stated to one where the solution is calculated as a round off figure. This method of solution finding is deemed incorrect and unacceptable as the fractional values here are ruled out. The best solution which is considered and is acquired are those with whole numbers.An integer programming is described as pure or mixed when few or all its variables are minimalised to integer values.

**Decision Theory and Games Theory**

The most important factor required for effective decision making is information. There are certain models of operation research which are used by management bodies to avail ideal information. These assumptions are termed decision making under uncertainty.

Nevertheless, imperfect or limited information is only available in actual situations. In these situations, there are 2 cases.

- Decision which is under risk
- Decision which is uncertain

If seen from the point of view of informationavailability, there are 3 cases.

- Certainty
- Uncertainty
- In-between

The first two are the extreme cases, and the last one comes in between both cases.

Games theory affects the effective decision-making which is taken during conflict situations where there are more than 2 brilliant competitors who try to elevate their decisions. Referred as players, the competitors have a number of choices in this game theory.Helping to take a correct and effective decision, game theory guides the decision makers to study the course of action accessible to his opponent. The use of decision tree for graphical representation for solving decision-making problems is used in decision theory.

**Markov Analysis**

As a prediction to future conditions,Markovanalysis is relied upon. The development of future state stands on the support of the current preceding situation and only on it is the speculation of this analysis. Based on probability theory, if the current behaviour of a system is already known, it can easily predict any periodical change in the system.Markov analysis can be exemplified as the market share prediction of a company or by predicting whether any equipment will function properly or not.