CS177 Assignment 1 Spring 2003
Cutting Costs in Building Maintenance?
Due: 11:59pm Sunday April 13
I. Summary
Help the building maintenance department assess a
possible change in operating policy designed to reduce their costs of maintaining
proper lighting throughout the building. Their definition for proper lighting
in a room is that no more than 10% of light bulbs in that room are burnt
out at any time. Their goal is to meet that standard at minimum cost.
Your job is to tell them whether they will save money by replacing all
the light bulbs in a light fixture (whether or not they are burnt out)
while they have it open, instead of just the burnt-out ones.
II. Some Details
Consider a large building, in which there are 50
rooms. Each room has 20 light fixtures, and inside each light fixture there
are 2 light bulbs. Assume that the average life expectancy for a light
bulb is 2,000 hours, and that the length of time that each light bulb
lasts can be calculated independently using the exponential
distribution
with a mean of 2,000 hours. Also assume that the lights in the building
are turned on for 15 hours per day, 5 days per week, and are turned off
at all other times. Ignore changes to this routine because of holidays,
power failures, leap-seconds, etc.
One person is responsible to maintaining the lighting
in this building. Every morning, he spends one hour travelling around the
building, checking each room to see how many of its light bulbs are burnt
out. If the number is greater than 4 (i.e., the 10% limit on the number
of burnt out light bulbs), he adds the room to his list of lighting repair
jobs for the end of the day. Assume that he starts his lighting repair
jobs one hour before the end of the day. Assume it takes about 5
minutes (actually a uniform time between 4 and
6 minutes) to carry his ladder and tools from its storage area to a room,
from one room to the next, or back to its storage area. Also assume that
for each lighting fixture that contains burnt-out light bulbs, it takes
a uniform time between 2 and 4 minutes to set up his ladder, open up the
light fixture, close up the light fixture and take down his ladder. While
his ladder is set up and the light fixture is open, it takes him exactly
1 minute to change a single light bulb. If, on any day, it takes him more
than 1 hour to finish his lighting repair jobs, he is paid overtime at
$40.00 per hour, rounded up to the nearest half hour.
Under the current scheme, only those light
bulbs that are burned out are changed when the light fixture is open for
repair. In the alternative scheme that you must evaluate, all
light bulbs in the fixture are changed whenever it is open for repair.
The idea behind this new scheme is that light bulbs are cheap (only $1.00
each), so we may as well replace the ``partly used'' ones along with the
``completely used'' ones, to increase the time until we need to return
to the same room again.
III. Measurements
Run your program for 1 year (i.e., 52 weeks, 260
non-consecutive days, or 3900 non-consecutive hours) starting from an initial
condition where all light bulbs in the building are brand new. For each
strategy, calculate: (i) the total cost of new light bulbs installed over
the year; (ii) the cost of the maintenance worker at $25.00 per hour +
overtime; and (iii) what percentage of the time the lighting satisfies
the guidelines of no more than 10% of the light bulbs burnt out. Also calculate
how much longer on average the working light bulbs that get changed under
the alternative scheme would have continued to function before they requiring
replacement under the current scheme.
You should also make other measurements to help you
determine that your program is working correctly, such as: the average
length of time that a light bulb lasts before burning out; the average
time spent on a lighting repair job; the average number of light bulbs
changed in a lighting repair job; and the average number of lighting repair
jobs carried out in a day.
IV. Questions
-
Is there a significant cost savings using the new
strategy? (You may need to calculate confidence intervals using the output
from several ``runs'' using different random number seeds to answer this
properly.) Use your measurements to explain what you found.
-
In designing this simulation program, you have a
choice of what to put in the event list: the time at which each individual
light bulb fails or the time that the lighting level in a room falls below
the guideline. Briefly describe how would you change your program to implement
the other choice.
-
Explain why it is important to use a heap
data structure (instead of a simple linked list) for the event list in
this program? Also explain how a cross-linked data structure can be used
to speed up the event list updates in the case of the alternative scheme
when you change a working light bulb.
-
Subtract the fixed cost of the morning inspection
tours from the cost of the maintenance worker, and then divide by the number
of light bulbs replaced to produce the average cost to change a light bulb
under each scheme. How does this compare to the cost of the light bulb
itself?