Operational research (operations research in USA) is the application of scientific methods to problems of management
decision-making.
It relies very much on mathematical modelling.
Its techniques provide *optimal solutions* to problems, concerned with complete systems as well as components of a system.

OR has its roots in the Second World War when teams of scientists and mathematicians worked on strategic and tactical problems which included the development of radar and battle strategies.

Data for the problem under consideration is analysed and the most appropriate tool is selected for its solution. Some of these are now summarized.

The elements of the problem are analysed into mathematical models or decision matrices and trees. Once the variables have been quantified these can then be processed using appropriate computer software. There are many uses in both business and military areas. Probability theory or Game Theory has an important role in these models. During WWII the probable strategy of the Japanese navy in the Battle of the Coral Sea was successfully predicted by the American navy using OR, resulting in a successful outcome for the US Navy.

LP can solve problems concerned with the allocation of finite resources or capacities.
Clearly, there are limitations (known as *constraints*) on how such resources *can* be allocated and these are taken into
account in the resulting mathematical models.
Simple LP problems can be solved algebraically or graphically but computer programs are available for more complex situations.

An example of a transportation problem is in commodity distribution. A supermarket chain would have several warehouses throughout the country and hundreds of outlets. The problem is which warehouses should serve which outlets in the most efficient pattern of distribution. Again this can be solved by using mathematical matrices but the computer is more convenient and suitable software is readily available.

As plant and equipment ages the probability of it failing increases so replacement strategies are vital to avoid breakdowns.
These range from programmes of *planned maintenance* i.e. doing maintenance at predetermined times before the
predicted times for breakdowns are reached, to more comprehensive tasks of complete replacement of plant.

Stock (or inventory) control uses a set of techniques designed to avoid 'outages' i.e. running out of stock. A model of usage of components and stock items is built and from this the date for the re-ordering is deduced, allowing 'lead time' for the supplier to deliver.

One technique is to calculate the Economic Batch Quantity (EBQ), models for which can be found in many textbooks on applied statistics.

OR solves problems of investment such as sale and leaseback decisions, break-even levels, net present value and other related issues.

Regression analysis can be used to create mathematical computer models from data collected from the situation under analysis.
Simple *linear* regression produces models of the form y = b + ax where y is the result (dependent variable) and x is the amount
of the independent variable. The values "a" and "b"
are constants derived from the computer analysis. A very simple example is:

*time (minutes) to paint a wall with a paint roller* = 12.4 + 1.02*(area in sq.m.).

Thus, for a wall with a total area of 40 sq.m. the time would be 12.4 + (1.02*40) = __53.2 minutes__.

Where more than one independent variable is evident recourse must be had to
**multiple regression analysis**, with a model in the general form:

*Y = b + a _{1}.x_{1} + a_{2}.x_{2} + a_{3}.x_{3} + a_{4}.x_{4} +
... ... ... ... ... a_{n}.x_{n}*

These are *linear* (straight line) models, but can also be *curvilinear*.

CPA or Network Analysis, describes a group of techniques designed to plan and schedule tasks in the correct order of performance using a network diagram. This allows consecutive and concurrent work to be plotted and by adding times for performing each task, the overall project time can be derived.

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