For each problem, make an Excel model, simulate the situation using YASAI, and hand in the
standard printouts for a
simulation problem.
Q1. (25 points) You have a business renting out specialized tools and equipment. For one particular kind of tool, you have observed the following historical daily demand pattern:
Demand | Probability | |
0 | 6% | |
1 | 16% | |
2 | 24% | |
3 | 21% | |
4 | 19% | |
5 | 9% | |
6 | 5% |
For example, you have observed that the demand is 0 about 6% of the days, 1 for about 16% of the days, and so forth. You have never seen a demand level above 6 in a single day. You are trying to decide how many units of the tool to keep on hand to rent to customers. You calculate that, including financing costs and maintenance, each unit costs you $125 per day to keep a tool unit on hand. You charge your customers $239 per day to rent a tools and the customers keep them for only one day at a time. Each time a customer requests a tool but you do not have one to rent, you undergo a loss of "good will" whose value you estimate at $50. What is the right number of tools to keep on hand
What is the best number of
tools to keep on hand? Try all values from 1 to 6, with a sample size of
1000.
Q2. (35 points) You manage a center that performs emergency walk-in mobile phone repairs for a major phone carrier. The table at the end of this problem shows the recent historical pattern for the number of phones that need to be repaired each day. For example, on 3% of the days you need to repair 10 phone, on 4% of the days, you need to repair 11 phones, and so forth. Each phone you receive has a 28% chance, independent of all other phones, of needing a "major" repair, which takes 75 minutes. Phones that do not need a "major" repair require only a "minor" repair, which takes 45 minutes. Repairs are performed by technicians who are paid $225 per day, and can work up to 7 hours. If you do not have enough technicians to perform all the work needed on a given day, you can pay overtime or bring in outside technicians -- either way, it costs you $85 per hour, but you can purchase fractions of hours.
How many technicians should you keep on staff to have the lowest average cost per day? Try the values 2, 3, 4, and 5, each with a sample size of 1000. The data on the number of phones that have to fixed each day follows below.
Phones | Probability |
10 | 3% |
11 | 4% |
12 | 4% |
13 | 7% |
14 | 6% |
15 | 7% |
16 | 9% |
17 | 5% |
18 | 3% |
19 | 4% |
20 | 2% |
21 | 3% |
22 | 4% |
23 | 6% |
24 | 6% |
25 | 7% |
26 | 7% |
27 | 5% |
28 | 4% |
29 | 3% |
30 | 1% |
Q3. (40 points) You manage a biotechnology plant that uses genetically-engineered microbes to produce pharmaceuticals. The microbes grow in large vessels called "incubators". You have 20 Type A incubators and 10 Type B incubators. On any given day, each Type A incubator has a 19% chance of needing to be serviced, independent of all other incubators. Each Type B incubator has a similar 8% chance of needing service. Servicing a Type A unit takes 2.1 hours of labor, and servicing a Type B unit takes 3.8 hours of labor.
Servicing can be done by in-house service people or by an outside contractor. Each in-house service person costs $550 per day. Each service person has a 92% chance of being able to work on any given day, independent of all other service people (the remaining 8% of the time comprises sick days, vacation, training, and paperwork; however, service people are always paid whether they are available to work or not). Each available service person can provide up to 7 hours of labor per day.
If you do not have enough in-house labor hours to service all the incubators that need attention on a given day, you must supplement your in-house service people with outside contractor labor, at a cost of $250 per hour.
By simulating 1000 days of operation, estimate whether it is best to hire 0, 1, 2, 3, 4, 5, or 6 in-house service people.