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

Hair Dryers are assembled at the rate of 320 per day for 249 days in a year.

Heating elements are produced in batches of 2,133 units.

a.   Therefore number of batches of heating elements in a year = (320*249)/2133 =38 approximately..

Number of heating elements required during four days = 320*4 =1280

b. Therefore inventory level after four days = 2133 - 1280 = 853 units

c. Average inventory = (maximum + minimum)/2, It is already mentioned that production starts when inventory level is 0 and the maximum is calculated as 1173 units as follows. Therefore average is approximately 587 units.

d. Production batch of 2133 units of heating elements at the rate of 853 units per day takes 2.5 days approx. With half day for setup, the total requirement is 3 days. Therefore remaining four days of the same equipment may be used for another component. But demand for the seven days is 2240 (320*7) more than the production of 2133 units meant for the seven days giving shortages of 107 units.

Days Production per day Opening Inventory Demand per day Closing Inventory 1 853 0 320 533 2 853 533 320 1066 3 427 1066 320 1173 4 0 1173 320 853 5 0 853 320 533 6 0 533 320 213

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