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Problem 13-12 A company manufactures hair dryers. It buys some of the components, but it makes the heating element, which it can produce at the rate of 827 per day. Hair dryers are assembled daily, 250 days a year, at a rate of 310 per day. Because of the disparity between the production and usage rates, the heating elements are periodically produced in batches of 2,068 units.

a. Approximately how many batches of heating elements are produced annually? (Round your answer to 2 decimal places.)

b. If production on a batch begins when there is no inventory of heating elements on hand, how much inventory will be on hand four days later ?

c. What is the average inventory of elements, assuming each production cycle begins when there are none on hand? (Do not round intermediate calculations. Round your answer to the nearest whole number.)

d. The same equipment that is used to make the heating elements could also be used to make a component for another of the firm’s products. That job would require four days, including setup. Setup time for making a batch of the heating elements is a half day. Is there enough time to do this job between production of batches of heating elements?

Paper For Above instruction

The manufacturing process of a company producing hair dryers involves both assembly of finished units and the fabrication of key components, notably the heating elements. These heating elements are produced periodically in batches due to the disparity between their production rate and the rate of consumption for assembly. To analyze this process, we need to determine key inventory metrics and capacity constraints that inform production planning and resource utilization.

Production Rates and Batch Size

The company produces heating elements at a rate of 827 units per day. The assembly of hair dryers occurs at a rate of 310 units per day over 250 working days annually. As these rates differ significantly, the production of heating elements is conducted in batches of 2,068 units, rather than continuous production. Understanding the number of batches produced annually, the inventory dynamics, and the feasibility of additional utility processes is essential for optimizing operations and reducing costs.

Annual Number of Batches

To estimate the number of heating element batches produced annually, we first consider the total utilization of the heating elements required for assembling hair dryers. Since the production rate of heating elements exceeds the consumption rate, the total number required annually is determined by the total units assembled per year.

The company produces 310 hair dryers per day over 250 days, which totals 77,500 units annually (310 units/day * 250 days). Since each hair dryer requires one heating element, the total units needed are 77,500 annually.

The batch size is 2,068 units, so the approximate number of batches produced annually is the total units required divided by the batch size:

Number of batches = 77,500 / 2,068 ≈ 37.48

rounded to two decimal places, the company produces approximately 37.48 batches of heating elements annually.

Inventory After Four Days

If production on a batch begins when there are no heating elements on hand, the inventory buildup over four days can be calculated by considering the daily production rate and the consumption rate of 310 units per day.

In four days, production would be 827 units/day * 4 days = 3,308 units produced.

During this period, the number of units consumed for assembly would be 310 units/day * 4 days = 1,240 units.

The net inventory remaining after four days is thus:

Inventory = Units produced – Units consumed = 3,308 – 1,240 = 2,068 units.

This matches the batch size, indicating that, after four days, the inventory of heating elements on hand would be 2,068 units.

Average Inventory Level

Assuming each production cycle starts with zero inventory, the average inventory can be estimated based on the batch size and the cycle time.

The cycle time, that is, the duration to produce a batch of 2,068 units, is:

Batch production time = Batch size / Production rate = 2,068 / 827 ≈ 2.5 days.

The total cycle includes the setup time of half a day, so the total cycle length is approximately 3 days.

In a typical cycle, inventory ramps up from zero to a maximum at the end of production. If we assume a uniform distribution of inventory levels during production (which is reasonable for constant production rates), the average inventory is half the batch size:

Average inventory = Batch size / 2 = 2,068 / 2 = 1,034 units.

Thus, the average inventory of heating elements throughout the process is approximately 1,034 units (rounded to the nearest whole number).

Utilization of Equipment for Additional Tasks

The equipment used for producing heating elements can also be used for other jobs, which take four days including setup time. The setup for a batch requires half a day. To evaluate whether the equipment can handle both tasks, we review the available production time and the job durations.

Each production cycle takes about 3 days (including setup). The alternative task needs 4 days, which exceeds the available cycle duration if scheduled consecutively without overlap.

Assuming the manufacturing process operates continuously with one batch production cycle, there isn't sufficient idle or spare capacity to perform the extra job within the same cycle timeframe of approximately 3 days. Since the alternative task requires a full four days, it would not fit between the production of batches of heating elements without causing delays or requiring additional shifts.

Therefore, the answer is No, there is not enough time to do this job between production cycles of heating elements under current conditions.

Conclusion

Analyzing the production and inventory metrics reveals critical insights for manufacturing efficiency. The company produces roughly 37.48 batches annually, with a four-day inventory of 2,068 units, and an average inventory of approximately 1,034 units. Furthermore, the current production schedule does not afford the capacity to undertake additional tasks within the same cycle timeframe, emphasizing the need for careful scheduling or capacity expansion to optimize resource utilization and meet strategic objectives.

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