Question

Can you please explain the asnwer for #1 (parts A - D)

1) 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

This is a problem that is similar to Economic order quantity. However, this is about production and often known as Production order quantity (POQ) or economic production quantity (EPQ). Either ways, it applies same formulas and concept. Here, however, they have not provided and asked for economic production quantities. Nonetheless if you look this topic up on your textbook it will help you.

The set up to the problem is about manufacturing the hair dryers and the corresponding heating units (units). There is a demand for 300 units per day. This makes the annual demand (D) = 300*250 = 75000 units.

Now there is also production capacity to keep in mind. The company can produce at the rate of (p) = 800 units/day. Now in manufacturing process, there is something called setup time. This is the time and the money required to set the machinery up. During this time, the production does not take place but the machine gets ready. Once the machine is ready it usually runs continuously till the batch is completed. The continuous running could be in days, hours, months, etc.

These are basic concepts and the information. Now based on these we can answer the questions.

A)

We know the annual demand is 75000. We know that every batch for this company has 2000 units. This means the number of batches that will be required is 75000/2000 = 37.5

Most likely the batches will be complete and we can round it up to 38 batches per year.

B)

To answer this we need to think about the daily demand and daily production capacity. We need to use 300 units per day. However, when the production is running, we will produce 800 units per day. This mean on a daily level our utilization is 300/800 units. Since we are beginning with 0 inventory, we will produce 800 units on day 1 and use 300 units out of it. Next day we will have 500 units remaining.

Now on day 2 we produce another 800 units. This makes the total number of units in our stock as 500+800 = 1300. But we use 300 of them again as daily demand. This leaves us with 1000 units.

So after 2 days we will have 1000 units left on hand.

C)

The production quantity here is 2000. This is the batch size of the number of units that is produced continuously in one setup. Average inventory is denoted by averaging the beginning and ending inventory. The straight forward formula is Q/2 and for us that will be 1000 units.

D)

We need to determine the interval and how long does the production process run. In order to make 2000 units with a rate of 800 units per day, the amount of days required to run the process for heating units is 2000/800 = 2.5 days. Also the problem tells us that the heating element setup time is half a day. So each batch requires 3 days. Now the question is how often does it run?

From the earlier problem we know that the number of batches needed is 37.5. This is over 250 days a year. This means 250/37.5 = 6.67 days. Every 6.67 days we need to run the production batch for the heating unit. Once it begins it will take 3 days to complete the entire process. This means the time left in our hand between the finish of a batch and the beginning of a setup of the next batch is 6.67 – 3= 3.37 days.

Since the other product will take 4 days we cannot accommodate it in our time as we only have 3.37 days. So there is not enough time to do this.