Answer Happy

Operations Management
BACKGROUND An auto maintenance shop suddenly
has more customers than it can handle in a given day. The shop
currently has one maintenance bay and is considering adding
additional bays. The current options are to continue operations
with 1 bay or expand to 2, 3, or 4 bays. Each additional bay costs
$10,000 per day. There is no cost for the existing bay. Each day a
random number of cars arrive and the single bay serves as many cars
as possible. The number of cars the bay can handle each day is also
random. If there are 10 or more cars waiting to be served, the
night crew is hired for $12,000 to work on cars overnight. 10 of
the cars are sent to the overnight crew, all cars above 10 are sent
to a competitor resulting in no cost or revenue. Any of the 10 cars
the night crew cannot handle are added to the list for the next
day. Revenues are generated for each car served by the day crew and
the night crew. Example: 45 cars arrive, the bay services 20 cars
resulting in 25 cars waiting to be serviced. 15 of the 25 are sent
away and the remaining 10 are left for the night crew. If the night
crew works on 7, the final 3 cars are left for the next day.
DATA The attached Excel file contains
historical data for the auto shop for the past 60 days. Use the
data supplied to determine the best distributions to use to model
the system. The data includes the following:
1. Tab1: The number of cars that arrived each day for 60
days
2. Tab2: The number of cars serviced by the day crew for 60
days
3. Tab3: The number of cars the night crew serviced each night
for 60 days
4. Tab4: The average revenue per car per day for 60 days
5. For the data given in tabs 1-4, your team will have to fit
the distribution using analytic solver>simulation
models>distributions>distribution wizard. Use the wizard to
fit the data to determine the appropriate distribution to use. If
given the option, use the Kolmogorov-Smirnov tab.
6. The auto shop estimates that all new bays will service cars
based on a uniform distribution with a low value of 20 and a high
value of 30.
7. You will have to limit the use of “psi” formulas for
distributions due to the size of the simulation Replace psinormal
with norm.inv(rand(),mean,stdev) (input mean and stdev) Replace
psiuniform with randbetween(low,high) (input low and high)
GOAL
a. Use the supplied data and information above to create a
simulation to find the optimal number of additional bays the
company should build. The answer will be 0, 1, 2 or 3 additional
bays for a total of 1, 2, 3 or 4 bays. Please include the overall
profit the company would make for each of the four options and
clearly identify which option your team suggests based on the
optimal solutions. Your report should include charts or graphs to
support your decision.
b. Using your answer in part a, evaluate how the system will
perform with the number of bays your team suggests if the number of
cars that arrived each day was based on a normal distribution with
a mean that ranged from 100 to 125 and a standard deviation of 10.
Show how the profit will change over the range of the mean for the
fixed number of bays you chose in part a.