For each problem, make an Excel model, simulate via YASAI, and hand in the standard printouts for a simulation problem.  On the simulation output reports, be sure to indicate the answer to each question posed in the corresponding problem.  Use a sample size of 1000 for each problem.
 

Q1.  (40 points)   You manage a seaside resort complex consisting of 143 time-share condominiums.  On any given day, each condominium unit in the complex has an 87% chance of being occupied, independent of all other units.  Each occupied unit produces a random amount of wastewater with a mean of 23.4 gallons and a standard deviation of 22.1 gallons, independent of all the other condominiums units.  Vacant units do not produce any wastewater. 

You process the wastewater from condominiums in treatment devices, each of which leases for $39.00 per day and can process up to 500 gallons of water per day.  You are considering leasing 4, 5, 6, or 7 treatment devices.  If the condominiums produce more wastewater than you are able to process, you must pay for an emergency portable treatment unit, which costs $75 plus $0.10 per gallon processed.

Which number of treatment devices will give you the lowest daily cost?  Use a sample size of 1000
 

Q2.  (60 points)   Your store sells a product for which the daily demand is Poisson with an average value of 10.  The product sells for $50, and (because it requires special environmental conditions to store) the holding cost is $3.50 per unit per day.  Every time you order the product, you pay a $40 handling fee plus $32.50 per unit. There is a one day "lag" after an order is placed: for example, an order placed at the end of day 1 will arrive at the beginning of day 3.  If you run out of stock, sales are lost.

Your ordering policy is as follows, described by two parameters R and L:

• At the end of each day, let I be the ending inventory, and Y be the amount ordered yesterday (possibly zero)
• If I + Y > R, do not order anything
• If I + Y < R, order L - (I + Y) units, that is, try to bring the inventory up to L

On day one, you have a starting inventory of 43, and you have not ordered in the previous two days.  Using a period of 100 days and a sample size of at least 250, experiment with all combinations of 

• R = 10, 20, 30
• L = 30, 40, 50

Which gives the highest profit?  Give your answer both with and without a $25/unit "salvage" correction, applied to all units in inventory during the last day and ordered in the last two days.