## INTRODUCTION TO OPERATIONS RESEARCH – PREVIOUS YEAR QUESTIONS GNDU

**“Operations research is a bunch of mathematical techniques aiming to solve industrial problems.” Elucidate.**

**Answer:**

“Operations research is a bunch of mathematical techniques aiming to solve industrial problems.” This statement shows the nature of the Operations research.

Operations research is that approach that uses various mathematical and scientific tools to solve the various problems like production planning and production management, finance, budgeting and investment decisions, personnel management decisions etc.

##### The various mathematical techniques are as follows:

Linear programming deals with the optimization (maximization or minimization) of a linear function called objective function, involving number of variables, subject to a set of linear equalities or inequalities called constraints and variables should be non-negative.__Linear programming:__

Linear programming has its applicability in the field of agriculture, military, production management, financial management, marketing management, personnel management etc.

2. ** Queuing theory: **This theory deals with the situations in which queue is formed. There are different types of situations in which queue is formed. Example: Customers waiting for service, machines waiting for landing stripes etc. This theory aims at minimising the overall cost due to serving and waiting. Queuing problems can be solved by using mathematical and simulation technique.

** 3. Inventory control models: **Inventory control models helps the managers to decide the reordering time and reordering level and optimal ordering quantity etc. Inventory planning answers two questions viz:

- How much to buy?
- When to buy?

The approach is to prepare a model of the situation that expresses total inventory costs in terms of the demand, size of order, possible overstocking or understocking and other relevant factors and then to determine optimal order size, reorder level etc. using inventory control models.

4. ** Network analysis: **Network models are a very popular and widely used quantitative technique. This model helps the manager to plan, schedule, monitor and control large projects such as construction of building, making a ship or planning for a space flight. The network analysis helps the manager to determine total project completion time, probability that a project will be completed by a certain date, least cost by way of shortening total project completion time etc.

Some common network analysis techniques are PERT (Programme evaluation and review technique and CPM (Critical Path Method)

5. ** Replacement theory: **The study of replacement is concerned with situation that arise when job performing units need replacement due to their deteriorating efficiency, failure or breakdown. Replacement theory helps in identifying the period when the replacement of job performing unit is most economical in terms of operating and depreciation etc.

6. ** Sequencing: **A sequence may be defined as the order in which jobs are to be processes. The sequencing problem may be defined as to determine the optimum sequence of performing a number of jobs by number of available facilities according to some pre-assigned order so as to optimize the output in terms of profit, cost or time.

The sequencing problems arise at the number of situations eg:

- ‘n’ jobs to be processed on ‘k’ machines on manufacturing plant.
- Customers arrive at the bank to get loans.
- Aircrafts waiting for the landing and clearance.
- Maintenance, scheduling in the factory.

7. ** Assignment theory: **The assignment problems deal in the allocation of ‘n’ resources to ‘n’ activities on one-to-one basis in such a manner that the resulting effectiveness is optimized.It is a special type of linear programming problem. Assignment theory is used when 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.

** 8. Transportation problem: **The transportation problems are special type of Linear programming problems in which objective is to transport various quantities of homogeneous products to different destinations in such a way that the total transportation cost is minimum. The transportation problems can be solved by the simplex method, but algorithms is laborious because it involves largen number of variables and constraints. However, MODI method and stepping stone method have been developed to solve transportation problems in much easy way.

9. ** Game theory: **Game theory is the body of knowledge which is concerned with the study of decision making in a situation where two or more rational opponents are involved under the condition of competition and conflicting interests. Game theory is the type of decision-making theory which is based on a type of reasoning in which the choice of action is determined after considering the possible alternatives available to the opponents playing the same game. The aim is to choose the best course of action because every player has got alternative course of action.

10. ** Simulation: **In many cases, the goals has been to determine optimal solution. All real-life problems cannot be states in mathematical form because of complexity i.e. Such situation can be tackled by simulations. Hence, simulation is a general technique that allows us to develop a dynamic model that acts like a real problem. Developing a good simulation model can be difficult but simulation allows us to solve problems that are difficult or impossible to solve other wise.