METHODS FOR SOLVING OPERATIONS RESEARCH MODELS
In general, the following three methods are used for solving OR models, where values of decision variables are obtained that optimize the given objective function (a measure of effectiveness).
Analytical (or deductive) method
In this method, classical optimization techniques such as calculus, finite difference and graphs are used for solving an OR model. The analytical methods are noniterative methods to obtain an optimal solution of a problem. For example, to calculate economic order quantity (optimal order size), the analytical method requires that the first derivative of the mathematical expression
TC = (D/Q) C0 + (Q/2) Ch
Numerical (or iterative) method
When analytical methods fail to obtain the solution of a particular problem due to its complexity in terms of constraints or number of variables, a numerical (or iterative) method is used to find the solution. In this method, instead of solving the problem directly, a general algorithm is applied for obtaining a specific numerical solution
The numerical method starts with a solution obtained by trial and error, and a set of rules for improving it towards optimality. The solution so obtained is then replaced by the improved solution and the process of getting an improved solution is repeated until such improvement is not possible or the cost of further calculation cannot be justified.
Monte Carlo method
This method is based upon the idea of experimenting on a mathematical model by inserting into the model specific values of decision variables for a selected period of time under different conditions and then observing the effect on the criterion chosen. In this method, random samples of specified random variables are drawn to know how the system is behaving for a selected period of time under different conditions. The random samples form a probability distribution that represents the real-life system and from this probability distribution, the value of the desired random variable can then be estimated.