Question

CASE
CASE 8.1 LOW NAIL COMPANY
After making some wise short-term investments at a
race track, Chris Low had some additional cash to invest
in a business. The most promising opportunity at the
time was in building supplies, so Low bought a business
that specialized in sales of one size of nail. The annual
volume of nails was 2,000 kegs, and they were sold to
retail
customers in an even flow. Low was uncertain how
many nails to order at any time. Initially, only two costs
concerned him: order-processing costs, which were $60
per order without regard to size, and warehousing costs,
which were $1 per year per keg space. This meant that
Low had to rent a constant amount of warehouse space
for the year, and it had to be large enough to accommodate
an entire order when it arrived. Low was not worried
about maintaining safety stocks, mainly because the
outward flow of goods was so even. Low bought his nails
on a delivered basis.

QUESTIONS
1. Using the EOQ methods outlined in the text, how many
kegs of nails should Low order at one time?
2. Assume all conditions in question 1 hold, except that Low’s
supplier now offers a quantity discount in the form of
absorbing all or part of Low’s order-processing costs. For
orders of 750 or more kegs of nails, the supplier will absorb
all the order-processing costs; for orders between 249 and
749 kegs, the supplier will absorb half. What is Low’s new
EOQ? (It might be useful to lay out all costs in tabular form
for this and later questions.)
3. Temporarily, ignore your work on question 2. Assume that
Low’s warehouse offers to rent Low space on the basis of
the average number of kegs Low will have in stock, rather
than on the maximum number of kegs Low would need
room for whenever a new shipment arrived. The storage
charge per keg remains the same. Does this change the
answer to question 1? If so, what is the new answer?
4. Take into account the answer to question 1 and the supplier’s
new policy outlined in question 2 and the warehouse’s
new policy in question 3. Then determine Low’s new EOQ.
5. Temporarily, ignore your work on questions 2, 3, and 4.
Low’s luck at the race track is over; he now must borrow
money to finance his inventory of nails. Looking at the situation
outlined in question 1, assume that the wholesale cost
of nails is $40 per keg and that Low must pay interest at the
rate of 1.5 percent per month on unsold inventory. What is
his new EOQ?
6. Taking into account all the factors listed in questions 1, 2, 3,
and 5, calculate Low’s EOQ for kegs of nails.

Answer 1

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Question 1: Using the EOQ methods outlined in the chapter, how many kegs of nails should Low order at one time?

The EOQ formula is:

    EOQ = √ 2 (annual use in units) (cost of placing an order) /

                 annual carrying cost per item per year

            = √ 2 (2000) (60) / 2

            = √ 120,000

            = 345 kegs per order

Note the 2 in the denominator. That is because, on average, the rented warehouse space is only half full, which, makes the average warehousing cost per keg be $2.

Question 2: Assume all conditions in Question 1 hold, except that Low’s supplier now offers a quantity discount in the form of absorbing all or part of Low’s order processing costs. For orders of 750 or more kegs of nails, the supplier will absorb all the order processing costs; for orders between 249 and 749 kegs, the supplier will absorb half. What is Low’s new EOQ? (It might be useful to lay out all costs in tabular form for this and later questions.)

Orders/year	Order size	Processing costs ($)	Warehousing costs ($)	Sum of processing and warehousing costs ($)
1	2,000	Free	2,000	2,000
2	1,000	Free	1,000	1,000
3	667	90	667	757
4	500	120	500	620
5	400	150	400	550
6	334	180	334	514
7	286	210	286	496
8	250	240	250	490
9	223	540	223	743

The new EOQ, based on the above information, is 250 kegs.

Question 3: Temporarily, ignore your work on Question 2. Assume that Low’s warehouse offers to rent Low space on the basis of the average number of kegs Low will have in stock, rather than on the maximum number of kegs Low would need room for whenever a new shipment arrived. The storage cost per keg remains the same. Does this change the answer to Question 1? If so, what is the new answer?

The relevant table is as follows:

Orders/year	Order size	Processing costs ($)	Warehousing costs ($)	Sum of processing and warehousing costs ($)
1	2,000	60	1,000	1,060
2	1,000	120	500	620
3	667	180	334	524
4	500	240	250	490
5	400	300	200	500

The new EOQ, based on the above information, is 500.

Question 4: Take into account the answer to Question 1 and the supplier’s new policy outlined in Question 2 and the warehouse’s new policy in Question 3. Then determine Low’s new EOQ.

The relevant table is as follows:

Orders/year	Order size	Processing costs ($)	Warehousing costs ($)	Sum of processing and warehousing costs ($)
1	2,000	Free	1,000	1,000
2	1,000	Free	500	500
3	667	90	334	424
4	500	120	250	370
5	400	150	200	350
6	334	180	167	347
7	286	210	143	353

The new EOQ, based on the above information, is 334.

Question 5: Temporarily, ignore your work on Questions 2, 3, and 4. Low’s luck at the race track is over; he now must borrow money to finance his inventory of nails. Looking at the situation outlined in Question 1, assume that the wholesale cost of nails is $40 per keg and that Low must pay interest at the rate of 1.5% per month on the unsold inventory. What is his new EOQ?

This answer can be done in tabular form as well, with the interest on inventory appearing as a new column. If one order is placed a year, the average inventory is 1,000 kegs, worth $40,000, with annual interest charges (1.5 x 12 = 18%) of $7,200. Other interest costs are calculated in a similar fashion, adjusted for average inventory.

The relevant table is as follows:

Orders/year	Order size	Processing costs ($)	Warehousing costs ($)	Interest costs ($)	Sum of processing, warehousing, and interest costs ($)
1	2,000	60	2,000	7,200	9,260
2	1,000	120	1,000	3,600	4,720
3	667	180	667	2,405	3,252
4	500	240	500	1,800	2,540
5	400	300	400	1,440	2,140
6	334	360	334	1,203	1,897
7	286	420	286	1,030	1,736
8	250	480	250	900	1,630
9	223	540	223	807	1,570
10	200	600	200	720	1,520
11	182	660	182	656	1,498
12	167	720	167	605	1,492
13	154	780	154	555	1,489
14	143	840	143	519	1,502

The new EOQ, based on the above information, is 154 kegs.

Question 6: Taking into account all the factors listed in Questions 1, 2, 3, and 5, calculate Low’s EOQ for kegs of nails.

The relevant table is as follows:

Orders/year	Order size	Processing costs ($)	Warehousing costs ($)	Interest costs ($)	Sum of processing, warehousing, and interest costs ($)
1	2,000	Free	1,000	7,200	8,200
2	1,000	Free	500	3,600	4,100
3	667	90	334	2,405	2,829
4	500	120	250	1,800	2,170
5	400	150	200	1,440	1,790
6	334	180	167	1,203	1,550
7	286	210	143	1,030	1,383
8	250	240	125	900	1,265
9	223	540	112	807	1,459

The new answer, based on the above information, is 250 kegs.

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