BUSI 3010 Week 3 CNC Capacity Calculation Example

Design Capacity of 20 Jobs a Week, Effective Capacity of 17 and Actual Output of 15.2: A Capacity Calculation for the CNC Edging Machine at a Stone Fabrication Shop, With Utilization and Efficiency Interpreted

Student Name

Walden University

BUSI 3010: Operations Management

Instructor Name

Month Day, Year

Design Capacity of 20 Jobs a Week, Effective Capacity of 17 and Actual Output of 15.2: A Capacity Calculation for the CNC Edging Machine at a Stone Fabrication Shop, With Utilization and Efficiency Interpreted

The Resource and Why It Was Chosen

This calculation measures how much the CNC edging machine can produce at Red River Stone & Surface (a composite Fargo fabricator). The CNC shapes the edge profile on each countertop piece and cuts the openings for sinks and cooktops. It was chosen because last week's process map showed that jobs wait longer in front of it than in front of any other machine, sometimes nearly three working days. Capacity here is measured in kitchen jobs per week, where a job is a typical kitchen of about 55 square feet. That unit was chosen because the shop sells, schedules and installs by the job.

Inputs

All inputs come from the shop's schedule, the machine's run log and the maintenance record for the 26 weeks from January 5 to July 3, 2028.

Table 1

Inputs for the CNC Capacity Calculation

Red River Stone & Surface and its records are composite.

Calculations

Design capacity is the most the machine could produce if it ran at its standard time for every scheduled hour.

Design capacity = 50 hours per week ÷ 2.5 hours per job = 20.0 jobs per week.

Effective capacity removes the time the shop plans to lose every week. The planned allowances are tool changes (2.0 hours), cleaning and maintenance (3.0 hours), first-piece checks (1.5 hours) and crane waits (1.0 hour), which total 7.5 hours.

Effective available time = 50.0 − 7.5 = 42.5 hours per week.

Effective capacity = 42.5 hours per week ÷ 2.5 hours per job = 17.0 jobs per week.

Actual output is the average over the 26 weeks.

Actual output = 395 jobs ÷ 26 weeks = 15.2 jobs per week.

Utilization compares actual output with design capacity.

Utilization = 15.2 ÷ 20.0 = 0.76, or 76.0 percent.

Efficiency compares actual output with effective capacity.

Efficiency = 15.2 ÷ 17.0 = 0.894, or 89.4 percent.

What the Figures Mean

The two percentages answer different questions. Utilization of 76 percent says the machine produces about three-quarters of what it could if nothing were ever lost. That figure looks modest, and it would lead a casual reader to conclude the CNC has spare capacity. It does not. Most of the gap between design and effective capacity, 3 jobs a week, is planned loss that the shop has chosen to accept: bits must be changed, the machine must be cleaned, and the first piece of each program must be checked.

Efficiency of 89.4 percent is the more useful measure for management, because it compares output with what the machine can realistically produce. The remaining gap, 1.8 jobs a week, comes from losses nobody planned: programs that had to be rerun, an operator called away to help unload a delivery and pieces that arrived at the CNC late in the day with too little shift left to finish them.

The figures matter because of demand. Over the same 26 weeks, the shop took orders for an average of 15.2 jobs a week, so output kept up with orders on average. But orders are seasonal. In May and June the shop sold about 17.3 and 18.2 jobs a week, above the CNC's effective capacity of 17. When demand exceeds effective capacity, the queue in front of the machine grows every week until demand falls, which is consistent with the carts seen there and with installation lead times that slipped from ten working days to fourteen.

Comparison With Other Stations

The same method applied to the other fabrication steps gives a rough sense of where the CNC stands. The bridge saw has a standard time of about 1.8 hours per job, for a design capacity near 27.8 jobs a week on the same 50 hours. The two polishers together have 100 scheduled hours and need about 2.2 hours per job, for about 45 jobs a week. The three installation crews have 150 crew hours a week and average about 6 hours per job including travel, for about 25 jobs a week. On these figures, the CNC has the lowest capacity of the fabrication and installation steps, which next week's bottleneck analysis will test with measured cycle times.

Assumptions and Limits

The calculation assumes that a typical kitchen job is a reasonable unit. Large jobs with islands take longer on the CNC, and small vanity tops take less, so a month with many large jobs would lower the real capacity. It also assumes that the standard time of 2.5 hours, taken from program averages, is accurate; if operators routinely slow the feed rate on dark quartz to prevent chipping, the true standard is higher. Stevenson (2021) notes that effective capacity depends on product mix, quality requirements and scheduling, all of which apply here. The queuing law proved by Little (1961) ties waiting to inventory: with output fixed, the time a job spends in the shop grows with the number of jobs ahead of it, so every extra job waiting in front of the CNC adds directly to the customer's lead time when output is fixed. Schmenner and Swink (1998) argue that productivity rises as material moves more swiftly and evenly through a process, and the CNC is where this shop's flow is least even.

References

Little, J. D. C. (1961). A proof for the queuing formula: L = λW. Operations Research, 9(3), 383-387. https://doi.org/10.1287/opre.9.3.383

Schmenner, R. W., & Swink, M. L. (1998). On theory in operations management. Journal of Operations Management, 17(1), 97-113. https://doi.org/10.1016/S0272-6963(98)00028-X

Stevenson, W. J. (2021). Operations management (14th ed.). McGraw Hill.