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 800 per day. Hair dryers are assembled daily, 250 days a year, at a rate of 300 per day. Because of the disparity between the production and usage rates, the heating elements are periodically produced in batches of 2,000 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 two 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? Explain.

Answer 1

Production rate, p = 800 per day
Demand rate, d = 300 per day
Batch size, Q = 2000 units

(a)

Number of batches produced annually = 300 * 250 / 2000 = 37.5 batches

(b)

Production in 2 days = 2 * 800 = 1,600 units
Sold in 2 days = 2 * 300 = 600 units.

So, inventory at the end of 2 days = 1,600 - 600 = 1,000 units

(c)

Average inventory = (Q/2) * (1 - d/p) = (2000/2) * (1 - (3/8)) = 625 units

(d)

Time to produce one batch = 2000 / 800 = 2.5 days. Time for one batch including the setup time = 2.5+0.5 = 3 days

Demand for these 3 days = 3 * 300 = 900 units

So, extra production = 2000 - 900 = 1100 i.e. 1100/300 = 3.67 days of demand which is less than 4 days. So, a four days job between two successive batches cannot be taken.