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# Statewide Development Corporation: Monte-Carlo simulation

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Statewide Development Corporation

Statewide Development Corporation has built a very large apartment complex in Gainesville, FL. As part of the student-oriented marketing strategy that has been developed, it is stated that if any problems with plumbing or air conditioning are experienced, a maintenance person will begin working on the problem within one hour. If a tenant must wait more than one hour for the repairperson to arrive, a \$10 deduction from the monthly rent will be made for each additional hour of time waiting. An answering machine will take the calls and record the time of the call if the maintenance person is buy. Past experience at other complexes has shown that during the week when most occupants are at school, there is little difficulty in meeting the one hour guarantee. However, it is observed that weekends have been particularly troublesome during the summer months.

A study of the number of calls to the office on weekends concerning air conditioning and plumbing problems has resulted in the following distribution:

Time Between Calls (mins) Probability
30 0.15
60 0.30
90 0.30
120 0.25

The time required to complete the service call varies according to the difficulty of the problem. Parts needed for most repairs are kept in a storage room at the complex. However, for certain types of unusual problems, a trip to a local supply house is necessary. If a part is available on site, the maintenance person finishes one job before checking on the next complaint. If the part is not available on site and other calls have been received, the maintenance person will stop by the other apartment(s) before going to the supply house. It takes approximately one hour to drive to the supply house, pick up a part, and return to the apartment complex. Past records indicate that, on approximately 10% of all calls, a trip must be made to the supply house.

The time required to resolve a problem if the part is available on site varies according to the following:

Time For Repair (mins) Probability
30 0.45
60 0.30
90 0.20
120 0.05
It takes approximately 30 minutes to diagnose difficult problems for which parts are not on site. Once the part has been obtained from a supply house, it takes approximately one hour to install the new part. If any new calls have been recorded while the maintenance person has been away picking up a new part, these new calls will wait until the new part has been installed.

The cost of salary and benefits for a maintenance person is \$20 per hour. Management would like to determine whether two maintenance people should be working on weekends instead of just one. It can be assumed that each person works at the same rate.

Questions:

1. Use simulation to help you analyze this problem. State any assumptions that you are making about this situation to help clarify the problem.
2. On a typical weekend day, how many tenants would have to wait more than an hour, and how much money would the company have to credit these tenants?

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