Simulation

Many problems which cannot be solved as linear programming method by its requirements of linearity of the function in the objective and constraints, can be solved by simulation. For some of the problems of queuing theory, inventory control and reliability theory etc., it is necessary that the inputs to the problem has to follow certain standard statistical distributions to apply some of the available models. A minor change in these standard form will prohibit the use of the available theory existing in that particular area of application.

Simulation can take care of all the changes and intricacies of problems which cannot be solved by other methods. There are many examples of simulation which are performed without incorporating the mathematical aspects of it. When we make an aircraft, a prototype of that is made and trials are run at different attitudes, pressure etc. in a wind tunnel and we take the best out of it for the design. Before making the final design of a boat or ship we always test a small size of it in pond or water tank. This idea of simulation can be extended to business systems also in a refined way to solve complicated problems. 

When we have complete information about the phenomenon, we can solve the problem very easily. But if we have partial information, simulations is a powerful method which can be applied. Similarly, we require a mechanism which provides equal chance for all the values of parameters to occur in equal probability. For this, we use random number table, In statistical terminology random numbers follow a rectangular distribution which gives equal chance (probability) for all the values of the parameter. 

Each problem will be different from the other and one has to analyse the problem in the proper perceptive such that the analysis leads to the results require.. We cannot take the results after one run. Several runs are to be repeated and the average values of parameter are the solution to the problem. The exact solution to the problem is obtained when the values of the parameter stabilizes. This will decide the number of runs required for simulation. The value of the parameters will be oscillating around the actual values as we increase the number of runs. After some runs the values will not change. Therefore, there are special computer languages and packages available exclusively for simulation. GPSS, SIMCRIP and DYNAMO are some of the languages specially used for simulation. 

Simulation need not give optimal solution but definitely very close to the optimal value. The closeness to the solution depends upon how closely we are taking the points for simulation. In this process, if we happen to take the optimal value for simulation, our solution will lead to optimal solution. If the points are taken very close by, we will not be far out from the optimal solution.