Question

The field of Operations Research involves the use of statistics and simulation to make business decisions. If any of you would like to find an example of operations research in practice.

You would need to:

1. Find an example where operations research is being used in the real world.

2. Describe the statistical concepts and processes that are being used.

3. Describe the business situation you have found.

4. Analyze the solution that was reached and discuss the statistical validity of the solution

5. explore other possible solutions and statistical methods that might fit the situation.

Answer 1

Answer:

Given that:

1. Find an example where operations research is being used in the real world.

Example where operations research is being used in the real world:

Integer Programming At School

Every school is run on a master time-table. The pupils see only parts that affect them - the times, subjects and teachers and rooms. The teachers see a different time-table, with classes, subjects and rooms. Consider a school of say 1 000 pupils in about 40 classes ranging from year 7 to year 12, with about 80 staff and nearly sixty rooms counting special laboratories etc. Then think how you would allocate teachers and classes to rooms to maintain adequate supervision of all classes, to avoid clashes over rooms, to observe the working conditions for teaching staff, but primarily to provide a properly balanced teaching programme.

Linear Programming For Refinery Planning

Shell Australia operates two refineries, one at Geelong and the other at Clyde in the Sydney metropolitan area. The major inputs to these refineries are (-rude oil from Bass Strait and crude oil imported from Indonesia and the Middle East. The crude oil goes through a number of processes such as fractional distillation, which separates out the light components from the thicker heavier oils; cracking, which breaks down the heavy constituents of the crude oil into lighter components'. reforming which changes the chemical structure of other components in order to meet product specifications; and desulphurising which removes sulphur from the product in order to meet environmental and quality requirements. That list is far from complete, so it will be evident that an oil refinery is a very complex affair which can be operated with considerable variation mix of crude oil inputs. However, the job of the refinery economist is to work out the best way to run the refinery to decide how much of each crude to run through the distiller at each refinery: how much of the heavier fractions to run through the cracker, and so on, in order to find the most profitable way of meeting the expected market demand for:

petrol
diesel
kerosine (for jet aircraft)
fuel oil (for industry)
bitumen
lubricating oil and other products.

.2. Describe the statistical concepts and processes that are being used.

Operations research refers to a problem-solving toolset. Mainly it concerns the optimal allocation of limited resources. Mathematical programming is the most fundamental tool of operations research. Digital simulation of systems is probably the second most important tool.

3. Describe the business situation you have found.

EMPLOYMENT IN OPERATIONS RESEARCH

Many large firms have groups of OR analysts (commonly 4 to 12 people). These are located in the steel, mining, oil, gas, chemicals, paper and engineering industries; airlines, railways, banking and insurance. Within the public sector, OR analysts are also employed in health, education and electricity supply. Not all of these people have the formal title of Operations Research Analyst and may be located in departments such as Industrial Engineering, Management Services or Corporate Research.

PROFESSIONAL SOCIETY

THE AUSTRALIAN SOCIETY FOR OPERATIONS RESEARCH INC. ASOR Caters for all who are interested in, and are concerned about, Operations Research, and in particular for such person who are resident in Australia. ASOR operates as a professional society through Meetings, Conferences, Publications etc. Many of the Members have affiliations with other similar societies that serve their particular discipline. Accordingly, the ASOR strives to set very moderate subscription levels in order to foster this multi-discipline character.

4. Analyze the solution that was reached and discuss the statistical validity of the solution

Most operations research studies involve the construction of a mathematical model. The model is a collection of logical and mathematical relationships that represents aspects of the situation under study. Models describe important relationships between variables, include an objective function with which alternative solutions are evaluated, and constraints that restrict solutions to feasible values.

Although the analyst would hope to study the broad implications of the problem using a systems approach, a model cannot include every aspect of a situation. A model is always an abstraction that is of necessity simpler than the real situation. Elements that are irrelevant or unimportant to the problem are to be ignored, hopefully leaving sufficient detail so that the solution obtained with the model has value with regard to the original problem.

Models must be both tractable, capable of being solved, and valid, representative of the original situation.

5. explore other possible solutions and statistical methods that might fit the situation.

i) Operations research (OR) is a discipline explicitly devoted to aiding decision makers. This section reviews the terminology of OR, a process for addressing practical decision problems and the relation between Excel models and OR.

ii) A typical mathematical program consists of a single objective function, representing either a profit to be maximized or a cost to be minimized, and a set of constraints that circumscribe the decision variables. In the case of a linear program (LP) the objective function and constraints are all linear functions of the decision variables. At first glance these restrictions would seem to limit the scope of the LP model, but this is hardly the case. Because of its simplicity, software has been developed that is capable of solving problems containing millions of variables and tens of thousands of constraints. Countless real-world applications have been successfully modeled and solved using linear programming techniques.

iii) The term network flow program describes a type of model that is a special case of the more general linear program. The class of network flow programs includes such problems as the transportation problem, the assignment problem, the shortest path problem, the maximum flow problem, the pure minimum cost flow problem, and the generalized minimum cost flow problem. It is an important class because many aspects of actual situations are readily recognized as networks and the representation of the model is much more compact than the general linear program. When a situation can be entirely modeled as a network, very efficient algorithms exist for the solution of the optimization problem, many times more efficient than linear programming in the utilization of computer time and space resources.

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