Building a Monte Carlo Simulation

IT Experts has received a consulting engagement from Lakeshore Service Station to design a system (simulation) that would help them predict gasoline demand, order quantity, and profits. Lakeshore is a service station that sells gasoline to boat owners. The demand for gasoline depends on weather conditions and fluctuates according to the following distribution.

Weekly Demand	Probability
1000	.09
2000	.12
3000	.23
4000	.38
5000	.18

Shipments arrive once a week. Since Lakeshore is in a remote place, it must order and accept a fixed quantity of gasoline every week for 10 weeks before the order quantity can be changed. Joe, the owner, faces the following problem: If he orders too small a quantity, he will lose, in terms of lost business and goodwill, 15 cents per gallon demanded and not provided. If he orders too large a quantity, he will have to pay 10 cents per gallon shipped back due to lack of storage. For each gallon sold he makes 95 cents profit. Now, Joe receives 3,600 gallons at the beginning of each week before he opens for business. He feels that he should receive more, maybe 3,700 or even 3,800 gallons. The tanks current capacity is 4,000 gallons. The problem is to find the best order quantity (you must answer this question at a minimum). Assume, Joe starts the first week off with 1000 gallons in beginning inventory.

EOQ can not be used due to the unpredictability of the weather. This problem can be solved by trial and error over time. That is, the service station must order each quantity for approximately 10 weeks, then compare the results. However, a simulation can give an answer in a few minutes (this is a Monte Carlo simulation and requires random numbers). Furthermore, the results of the simulation will be much more accurate, since years of operations can be simulated rather than only 10 weeks. Also, the losses are not real, they are only on paper (modified from Turban, MIS/Database texts).