Simulation - 6 - Simulation of Sales and Profit on different Production Levels

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Simulation

Case/Problem:
A company manufactures 30 units per day now. The sale depends upon demand the probability distribution of which is as follows:
Units: 27 28 29 30 31 32
Prob: 0.10 0.15 0.20 0.35 0.15 0.05
The selling price is Rs. 50 per unit while the production cost amounts to Rs. 40 per unit. Any unsold unit at the end of the day is to be disposed off at a loss of Rs. 15 unit. There is a penalty of Rs. 5 per unit, if the demand is not satisfied. Using the following random numbers, simulate the profit/loss of the company for the next 10 days:
10, 99, 65, 99, 95, 01, 79, 11, 16, 20
If the company decides to produce 29 units, instead of 30 as at present, per day, what can be the advantage or disadvantage of the company?

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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