Simulation - 3 Production and Transportation Capacity utilization

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Simulation

Case/Problem:
A company manufactures around 200 units of a product daily. Depending upon the availability of the resources, the daily production has been varying from 196 units to 204 units, the probability distribution of which is as follows:

Production-
Units/day: 196 197 198 199 200 201 202 203 204
Probability:0.05 0.09 0.12 0.14 0.20 0.15 0.11 0.08 0.06

The finished units are transported to a warehouse in a specially designed truck that cn accommodate only 200 units. Using these following 15 random numbers, 82, 89, 78, 24, 53, 61, 18, 45, 04, 23, 50, 77, 27, 54 and 10, simulate the units produced, transported and waiting in the factory: Also answer the following questions:
(i) What will be the average number of units waiting in the factory?
(ii) What will be the number of empty spaces in the truck?

Monte Carlo Method:
The ‘Monte Carlo’ simulation technique involves conducting repetitive experiments on the model of the system under study, with some known probability distribution to draw random samples (observations) using random numbers. If a system cannot be described by a standard probability distribution such as normal, Poisson, exponential, etc, an empirical probability distribution can be constructed. The Monte Carlo simulation technique consists of the following steps:
(1) Setting up a probability distribution for variables to be analyzed.
(2) Building a cumulative probability distribution for each random variable.
(3) Generating random numbers and then assigning an appropriate set of random numbers to represent value or range (interval) of values for each random variable.
(4) Conducting the simulation experiment using random sampling.
(5) Repeating Step – 4 until the required number of simulation runs has been generated.
(6) Designing and implementing a course of action and maintaining control.

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