The Three Hills Power Company provides electricity to a large metropolitan area through a series of almost 200 hydroelectric generators. Management recognizes that even a well-maintained generator will have periodic failures or breakdowns. Energy demands over the past 3 years have been consistently high, and the company is concerned over downtime of generators. It currently employs four highly skilled repairpersons at $30 per hour. Each works every fourth 8-hour shift. In this way, there is a repairperson on duty 24 hours a day, 7 days a week.

As expensive as the maintenance staff salaries are, breakdown expenses are even higher. For each hour that one of its generators is down, Three Hills loses approximately $75. This amount is the charge for reserve power that Three Hills must “borrow” from the neighboring utility company.

Stephanie Robbins has been assigned to conduct a management analysis of the breakdown problem. She determines that simulation is a workable tool because of the probabilistic nature of this problem. She decides her objective is to determine (1) the service maintenance cost, (2) the simulated machine breakdown cost, and (3) the total of these breakdown and maintenance costs (which gives the total cost of this system). Since the total downtime of the machines is needed to compute the breakdown cost, she must know when each machine breaks and when each machine returns to service. Therefore, a next-event-step simulation model must be used. In planning for this simulation, a flowchart, as seen in Figure 13.4, is developed.

Robbins identifies two important maintenance system components. First, the time between successive generator breakdowns varies historically from as little as 0.5 hour to as much as 3 hours. For the past 100 breakdowns, she tabulates the frequency of various times between machine failures (see Table 13.12). She also creates a probability distribution and assigns random number intervals to each expected time range.

Robbins then notes that the people who do repairs log their maintenance time in 1-hour time blocks. Because of the time it takes to reach a broken generator, repair times are generally rounded to 1, 2, or 3 hours. In Table 13.13, she performs a statistical analysis of past repair times, similar to that conducted for breakdown times.

Robbins begins conducting the simulation by selecting a series of random numbers to generate simulated times between generator breakdowns and a second series to simulate repair times required. A simulation of 15 machine failures is presented in Table 13.14. We now examine the elements in the table, one column at a time.

Column 5: Time Repairperson Is Free to Begin Repair

This is 02:00 hours for the first breakdown if we assume that the repairperson began work at 00:00 hours and was not tied up from a previous generator failure. Before recording this time on the second and all subsequent lines, however, we must check column 8 to see what time the repairperson finishes the previous job. Look, for example, at the seventh breakdown. The breakdown occurs at 15:00 hours (or 3:00 p.m.). But the repairperson does not complete the previous job, the sixth breakdown, until 16:00 hours. Hence, the entry in column 5 is 16:00 hours.

Figure 13.4 Full Alternative Text

One further assumption is made to handle the fact that each repairperson works only an 8-hour shift: when each person is replaced by the next shift, he or she simply hands the tools over to the new worker. The new repairperson continues working on the same broken generator until the job is completed. There is no lost time and no overlap of workers. Hence, labor costs for each 24-hour day are exactly $24 \text{hours}\times \$30 \text{per} \text{hour}=\$720.$

The simulation of 15 generator breakdowns in Table 13.14 spans a time of 34 hours of operation. The clock began at 00:00 hours of day 1 and ran until the final repair at 10:00 hours of day 2.

The critical factor that interests Robbins is the total number of hours that generators are out of service (from column 9). This is computed to be 44 hours. She also notes that toward the end of the simulation period, a backlog is beginning to appear. The thirteenth breakdown occurred at 01:00 hours but could not be worked on until 04:00 hours. The fourteenth and fifteenth breakdowns experienced similar delays. Robbins is determined to write a computer program to carry out a few hundred more simulated breakdowns but first wants to analyze the data she has collected thus far.

She measures her objectives as follows:

A total cost of $4,320 is reasonable only when compared with other, more attractive or less attractive maintenance options. Should, for example, the Three Hills Power Company add a second full-time repairperson to each shift? Should it add just one more worker and let him or her come on duty every fourth shift to help catch up on any backlogs? These are two alternatives that Robbins may choose to consider through simulation. You can help by solving Problem 13.25 at the end of the chapter.

As mentioned at the outset of this section, simulation can also be used in other maintenance problems, including the analysis of preventive maintenance. Perhaps the Three Hills Power Company should consider strategies for replacing generator motors, valves, wiring, switches, and other miscellaneous parts that typically fail. It could (1) replace all parts of a certain type when one fails on any generator or (2) repair or replace all parts after a certain length of service based on an estimated average service life. This would again be done by setting probability distributions for failure rates, selecting random numbers, and simulating past failures and their associated costs.

Building An Excel Simulation Model For Three Hills Power Company

Program 13.6 provides an Excel spreadsheet approach to simulating the Three Hills Power maintenance problem.

Figure 13.6 Full Alternative Text

13.5-22 Full Alternative Text