Problem 10 18a: Production Process Consists Of Three Steps
Problem 10 18a Production Process Consists Of A Three Step Operation
The production process consists of a three-step operation. The scrap rate is 15 percent for the first step and 8 percent for the other two steps. a. If the desired daily output is 470 units, how many units must be started to allow for loss due to scrap? (Do not round intermediate calculations. Round up your final answer to the next whole number.)
b. If the scrap rate for each step could be cut in half at every operation, how many units would this save in terms of the scrap allowance? (Do not round intermediate calculations. Round up your final answer to the next whole number.)
c. If the scrap represents a cost of $10 per unit, how much is it costing the company per day for the original scrap rate (i.e., the Part a scrap rate)? (Round your final answer to the nearest whole number. Omit the "$" sign in your response.)
Paper For Above instruction
The production process described involves a three-step operation with specific scrap rates at each stage, necessitating calculations to determine the initial number of units to start, potential savings from process improvements, and associated costs due to scrap. This scenario exemplifies key principles in operations management, particularly in process efficiency, waste reduction, and cost control, which are critical to optimizing manufacturing productivity and profitability.
Calculating the Required Starting Units
To ensure a daily output of 470 usable units after accounting for scrap at each stage, it is essential to work backward through the process. The scrap rates at each step create cumulative losses, and understanding these allows for accurate planning of initial production volume. The first step has a 15% scrap rate, while the subsequent two steps each have an 8% scrap rate.
Initially, recognize that the effective yield after each step is (1 - scrap rate): 85% at step one, and 92% at steps two and three. The total process yield combines these losses as follows:
- Yield after step one: 1 - 0.15 = 0.85
- Yield after step two: 1 - 0.08 = 0.92
- Yield after step three: 1 - 0.08 = 0.92
Calculating the overall yield:
Overall yield = 0.85 × 0.92 × 0.92 ≈ 0.7192
To find the number of units needed at the start (denoted as X):
X × 0.7192 = 470
X = 470 / 0.7192 ≈ 654.1
Rounding up, the company must start with 655 units daily to produce 470 good units.
Impact of Halving Scrap Rates
If the scrap rates are reduced by half, the new rates become 7.5% for the first step and 4% for the second and third steps. Their corresponding yields:
- Step one: 1 - 0.075 = 0.925
- Steps two and three: 1 - 0.04 = 0.96
The combined yield now:
0.925 × 0.96 × 0.96 ≈ 0.8525
To meet the same output, the new starting units (Y) are:
Y = 470 / 0.8525 ≈ 551.9
Rounding up, 552 units are needed. The savings in units:
Original start: 655 units; new start: 552 units; savings: 655 - 552 = 103 units.
Cost Analysis of Scrap
Scrap cost per day at the original scrap rate involves calculating the total units scrapped at each stage and multiplying by the cost per unit ($10). Total scrap units are derived as follows:
Scrap at step one:
Number of units sliced off: 655 × 0.15 = 98.25 units
Remaining units after step one: 655 - 98.25 = 556.75 units
Scrap at step two:
Units before step two: 556.75
Scrapped at step two: 556.75 × 0.08 ≈ 44.54 units
Remaining units after step two: 556.75 - 44.54 ≈ 512.21 units
Scrap at step three:
Units before step three: 512.21
Scrapped at step three: 512.21 × 0.08 ≈ 40.98 units
Total scrap units per day:
98.25 + 44.54 + 40.98 ≈ 183.77 units
Cost of scrap per day:
183.77 units × $10 ≈ $1,837
Rounding to the nearest dollar, the company incurs approximately $1,837 daily in scrap costs under the original process.
Application in Industry
An illustrative example is a manufacturing firm in the electronics industry that produces printed circuit boards (PCBs). This company implements rigorous quality controls and tracks scrap rates at each production stage to enhance efficiency. By analyzing their process yields, they have optimized their machinery settings and material selection, leading to a reduction in scrap rates that aligns with the scenario described. These improvements have resulted in significant cost savings and higher output efficiency—mirroring the calculations above. The firm’s management continuously evaluates scrap costs and process yields, emphasizing waste reduction and process optimization, which reflect core concepts from operations management, such as process control, quality assurance, and cost efficiency (Heizer, Render, & Munson, 2017).
Conclusion
Understanding and managing scrap rates in production processes is vital for operational efficiency and cost control. The calculations derived demonstrate the importance of process yield analysis in planning and decision-making. Reducing scrap rates not only increases practical output but also significantly lowers associated costs, directly impacting profitability. Industry examples, such as electronics manufacturing, show how process improvements grounded in principles from operations management can generate tangible benefits. This scenario underscores the essential role of process analysis and waste minimization strategies within manufacturing industries.
References
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