A Manufacturer Of Printed Circuit Boards Has A Design Capaci

1 A Manufacturer Of Printed Circuit Boards Has A Design Capacity Of 1

A manufacturer of printed circuit boards has a design capacity of 1,000 boards per day. The effective capacity, however, is 704 boards per day. Recently, the production facility has been producing 915 boards per day. Compute the design and effective capacity utilization measures. (Round your answers to 1 decimal place, e.g., 3.5%.)

Utilization Effective = % Utilization Design = %

The town barber shop can accommodate 32 customers per day. The manager has determined that if two additional barbers are hired, the shop can accommodate 76 customers per day. What are the design and effective capacities for the barber shop?

Effective capacity = customers/day

Design capacity = customers/day

Demand has grown at Dairy May Farms, and it is considering expanding. One option is to expand by purchasing a very large farm that will be able to meet expected future demand. Another option is to expand the current facility by a small amount now and take a wait-and-see attitude, with the possibility of a larger expansion in two years. Management has estimated the following chances for demand: The likelihood of demand being high is 0.72. The likelihood of demand being low is 0.28.

Profits for each alternative have been estimated as follows: Large expansion has an estimated profitability of either $51,900 or $24,100, depending on whether demand turns out to be high or low. Small expansion has a profitability of $15,100, assuming that demand is low. Small expansion with an occurrence of high demand would require considering whether to expand further. If the company expands at that point, the profitability is expected to be $41,000. If it does not expand further, the profitability is expected to be $12,850.

(b) Calculate expected values for large and small expansions.

What should Dairy May Farms do? EV small expansion = $ EV large expansion = $ Company should opt expansion.

Paper For Above instruction

Capacity management is a critical aspect of operations in manufacturing and service industries, enabling organizations to optimize resource utilization, meet customer demand, and maximize profitability. This paper explores the concepts of capacity utilization, capacity planning, and decision-making under uncertainty, exemplified through real-world scenarios such as printed circuit board manufacturing, barber shop services, and farm expansion strategies. These scenarios illustrate how companies evaluate their current capacities, plan for future growth, and use probabilistic models to inform strategic decisions.

Capacity Utilization: Measurement and Significance

Capacity utilization measures how effectively a firm uses its installed productive capacity. It is calculated as the ratio of actual output to maximum possible output, expressed as a percentage. For instance, in the case of a printed circuit board manufacturer, the design capacity is 1,000 boards per day, while the effective capacity—considering realistic operating conditions—is 704 boards per day. If the actual production is 915 boards, the utilization rates can be computed as follows:

• Design capacity utilization = (Actual output / Design capacity) × 100 = (915 / 1000) × 100 = 91.5%
• Effective capacity utilization = (Actual output / Effective capacity) × 100 = (915 / 704) × 100 ≈ 130.1%

Notice that the effective capacity utilization exceeds 100%, indicating that the plant is operating beyond its average effective capacity—possibly through overtime, additional shifts, or efficiencies. Such insights help managers identify potential bottlenecks, assess operational efficiency, and plan capacity enhancements.

Capacity Planning in Service Settings

The barber shop example illustrates capacity planning in a service environment. The shop's original capacity accommodates 32 customers per day. Hiring two additional barbers increases capacity to 76 customers daily. The design capacity reflects the maximum theoretical service capability (76 customers), while the effective capacity might be lower during regular operations due to breaks, inefficiencies, or customer arrival variability. Calculating the utilization provides insights into how well the shop is performing relative to its capacity:

• Design capacity utilization = (Actual customers served / Design capacity) × 100
• Effective capacity utilization = (Actual customers served / Effective capacity) × 100

Understanding these metrics helps the management decide whether to expand facilities further or optimize existing resources through better scheduling and process improvements.

Decision-Making Under Uncertainty: Farm Expansion

Strategic expansion decisions often involve uncertainty and probabilistic outcomes. Dairy May Farms faces two expansion options: a large-scale purchase to meet full future demand or a small, earlier expansion with the possibility of further growth later. The probabilities associated with demand levels (high: 0.72, low: 0.28) influence expected profitability.

The expected value (EV) calculation provides a quantitative basis for decision-making. For the large expansion, the EV is computed as:

EV_large = (Probability of high demand × Profit in high demand) + (Probability of low demand × Profit in low demand)

= (0.72 × $51,900) + (0.28 × $24,100) = $37,368 + $6,748 = $44,116

For the small expansion, the EV takes into account the current profitability and options for further expansion if high demand materializes:

EV_small = (Probability of low demand × Profit assuming no further expansion) + (Probability of high demand × Profit if further expanded)

= (0.28 × $15,100) + (0.72 × $41,000) = $4,228 + $29,520 = $33,748

Comparison of EVs suggests that the large expansion strategy, with an expected value of approximately $44,116, is financially more advantageous than the small expansion, which has an EV of about $33,748. Therefore, based on expected monetary values, Dairy May Farms should pursue the large expansion. This decision aligns with maximizing expected profitability under uncertainty.

Conclusion

Effective capacity management and strategic expansion decisions are fundamental to competitive advantage. Regular assessment of capacity utilization ensures efficient resource deployment, while probabilistic decision models help organizations navigate uncertain markets. Dairy May Farms’ analysis demonstrates how quantitative methods can guide expansion choices, ultimately contributing to sustainable growth and profitability. Proper capacity planning often balances operational efficiency with strategic flexibility, ensuring organizations can adapt to demand fluctuations and seize opportunities for growth.

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