A company manufactures hair dryers. It buys some of the components, but it makes

Question

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 853 per day. Hair dryers are assembled daily, 249 days a year, at a rate of 320 per day. Because of the disparity between the production and usage rates, the heating elements are periodically produced in batches of 2,133 units.

a. Approximately how many batches of heating elements are produced annually?

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?

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?

Explanation / Answer

Production rate of heating element = 853 units per day.

Batch size of heating element = 2,133 units.

Number of hair dryers assembled annually = 320 x 249 = 79,680.

So, number of heating elements produced annually = 79, 680 (since each hair dryer will require one heating element).

a. Number of batches of heating elements produced annually = 79,680/2,133 = 37.36 units.

b. Inventory on hand after 4 days = 4 x (853 – 320) = 2,132 units.

c.

Production rate, p = 853 units per day.

Usage rate, u = 320 units per day.

Batch size, i.e., economic production quantity, Q0 = 2,133 units.

Average inventory = {[(p – u) / p] x Q0} / 2= {[(853 – 320) / 853] x 2,133} / 2 = 666.41 units.      

d. One batch of heating element will require 2.5 days of equipment and if we include setup time of 0.5 day, total time taken by equipment to produce heating element will be 3 days. But production of job in another department by the same equipment will take 4 days.

Hence, there is not enough time to do this job between production of batches of heating elements.

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