# 14.7.1 Exercise: Capacity Determination

### Intended learning outcomes: Determine theoretical capacity, availability, rated capacity, demonstrated capacity, actual utilization, work center efficiency, etc.

The following exercise was developed on the basis of a communication from Barry Firth, to whom we extend many thanks.

A plant runs 10 * 8 hour shifts per normal week. A work center in the plant has 5 identical machines, each requiring one operator to run it. This is a machine-paced work center (a machine capacity). Operators get a total of 1 hour for breaks, and they usually take their breaks at the same time. Each machine requires one episode of planned maintenance per week of 3 hours, scheduled by the planner. During the last 6 weeks, the performance data in Figure 14.7.1.1 were recorded:

Fig. 14.7.1.1       Capacity performance data.

Questions:

a.    What is the theoretical capacity in machine hours per normal week (5 days)?

b.    Taking into account scheduled nonproduction events, what is the availability (as a percentage) of machine time per normal week, without considering operator constraints?

c.    What is the availability (as a percentage) of machine time per normal shift, taking into account the normal working conditions for operators?

d.    If the tactical utilization is targeted to be 90%, what value should be used for the utilization factor of machine time for capacity rating purposes?

e.    What is the demonstrated capacity per normal week of this work center? (Adjust the data for week 2 to correct for the short week.)

f.    What was the actual utilization (as a percentage) through the 6 weeks in review?

g.    What was the work center efficiency through the 6 weeks in review?

h.    If planned efficiency is targeted to be 85%, and taking into account your answer to question (d), what was the rated capacity per normal week?

i.     Compare your answers to questions (a), (e), and (h). What should we do now?

Solutions (see also the definitions in Section 14.1.1):

a.    Theoretical capacity = 400 hours per normal week
= (5 machines) * (10 shifts) * (8 hours per shift and machine).

b.    Downtime due to maintenance is 15 hours per week. Therefore, the availability factor is (400 – 15) / 400 = 96.25%.

c.    Downtime due to operator breaks is 1 hour per shift of 8 hours. Therefore, the availability factor is 7 / 8 = 87.5%.

d.    Assuming that maintenance cannot be effected during operator breaks, the utilization factor is 87.5% * 96.25% * 90% ≈ 75.80%.

e.    Demonstrated capacity is expressed as standard hours produced (row 4 in the table above). The adjusted output for week 2 is 160 * 5 / 4 = 200 hours. Over 6 weeks, the mean is (1340 + 40) / 6 = 230 standard hours per week.

f.    During the 6 weeks in review, production has run for 1600 machi­ne hours (row 2 in the table above) out of a possible 2320 hours (= 5*400 + 320). Therefore, actual utilization = 1600 / 2320 ≈ 69.0%.

g.    Actual efficiency = standard hours produced divided by actual hours worked
= 1340 / 1600 = 83.75%.

h.    Rated capacity = 400 hours * 75.8% * 85% ≈ 258 (standard) hours.

i.     Demonstrated capacity (230 hours) is too low compared to rated capacity (258 hours). However, in week 4, the output (280 hours) exceeded 258 hours. Check whether the measurements are still requi­red. If so, check for exceptional events, calculating actual utilization and efficiency for each week. Decide whether to make adjustments to planned utilization or efficiency.