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In OR, we do not have a single general technique to solve all mathematical models that can arise in practice.

**SOLVING
THE OR MODEL**

In OR, we
do not have a single general technique to solve all mathematical models that
can arise in practice. Instead, the type and complexity of the mathematical
model dictate the nature of the solution method. For example, in Section 1.1
the solution of the tickets problem requires simple ranking of alternatives
based on the total purchasing price, whereas the solution of the rectangle
problem utilizes differential calculus to determine the maximum area.

The most
prominent OR technique is linear programming. It is designed for models with linear objective and constraint functions.
Other techniques include integer programming (in which the variables assume
integer values), dynamic programming (in which the original model can be
decomposed into more manageable subproblems), network programming (in which the
problem can be modeled as a network), and nonlinear programming (in which
functions of the model are nonlinear). These are only a few among many
available OR tools.

A
peculiarity of most OR techniques is that solutions are not generally obtained
in (formula like) closed forms. Instead, they are determined by algorithms. An
algorithm provides fixed computational rules that are applied repetitively to
the problem, with each repetition (called iteration) moving the solution closer
to the optimum. Be-cause the computations associated with each iteration are
typically tedious and voluminous, it is imperative that these algorithms be
executed on the computer.

Some
mathematical models may be so complex that it is impossible to solve them by
any of the available optimization algorithms. In such cases, it may be
necessary to abandon the search for the *optimal*
solution and simply seek a *good*
solution using heuristics or *rules of
thumb.*

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