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. (30 points)  Your company can deliver its products using either leased trucks or a courier service.  You do not know in advance the exact number of orders you will need to deliver, but in the past it has followed the following pattern:

Each leased truck has a 94% chance, independent of all other trucks, of being serviceable on any given day, in which case it can deliver up to 5 orders at a cost of $20 per order. If a truck is not serviceable, it cannot deliver any orders. Each truck also costs $80 per day to lease, but only on the days it is serviceable. Orders not delivered by leased truck are delivered by courier at a cost of $95 each. How many trucks should you lease in order to minimize your average total daily leasing and delivery cost? Simulate  3, 4, 5, and 6 trucks.  With the optimal number of trucks, what is the average number of orders per day that have to be shipped by courier?
 

Q2. (30 points)   Your company has 200 personal computers.  Each computer has a 5% probability, independent of all other computers, of encountering a hardware problem on any given day.  Most hardware problems require 3/4 of an hour of attention from a computer support technician (CST).  Each problem that occurs, however, has a 30% chance (independent of all other problems) of developing into a more serious problem requiring an extra 2 hours of attention from a CST.

Each CST can spend up to 6 hours per day fixing problems, and costs the company $300 per day.  Every CST hired must be paid their full salary each day, whether or not they have sufficient work to keep them busy.  If the company does not have enough CST's to solve all the problems occurring on a given day, it hires an outside firm that charges $95 per hour.

You are trying to decide whether to hire 1, 2, 3, or 4 CST's.  Which option gives the lowest average cost per day?  With this number, what is the average number of hours of support per day you must buy from the outside firm?
 

Q3.  (40 points)  Your firm processes mediation requests from companies with minor labor relations disputes.  The number of requests received per day is well-modeled by a Poisson random variable with an average value of 45.  All requests are processed by "primary adjudicators", who can process up to 10 requests per day, and make $400 per day.  If too many requests are received for the number of primary adjudicators on staff, the extra requests are sent to be processed at another firm at a cost of $200 each.  Each request that undergoes primary adjudication internally has a 40% chance, independent of all other requests, of requiring attention from a "secondary adjudicator".  Secondary adjudicators make $600 per day and can process up to 5 request per day.  If there are more requests for secondary adjudication than your staff is able to handle, the extra requests are sent for secondary adjudication at another firm, at a cost of $150 each.

You are considering having 3, 4, 5, or 6 primary adjudicators on staff, and 1, 2, or 3 secondary adjudicators.  Of all 12 possible combinations of these options, which would give you the lowest average cost?