Question

There is a retailer called "The Coop", which carries a wide variety of products with MIT's name and logo: shirts, caps, keychains, pens... you name it! Anything from golf balls and teddy bears to pocket protectors and jewelry. With a store inside MIT's Student Center, and another one in the popular Kendall Square, across the street from MIT campus, The Coop is a favorite stop for casual MIT visitors, current students and their relatives, and nostalgic alumni.

The Coop carries a line of products that feature MIT's official seal cast in a jewelry-grade steel. The same seal (about the size of a coin) is used in multiple finished goods, such as necklaces, tie pins, cufflinks, and paperweights. The Coop is considering introducing in 2018 a new line of products featuring MIT's seal cast in 18 karat gold. These seals would be used in upscale jewelry, and as an ornament in the diploma frames that sell especially during commencement season.

Based on their experience with similar products in the past, The Coop has projected the following demand for gold MIT seals for each month of 2018.

January	February	March	April
1300	300	600	500

May	June	July	August
2000	5500	1800	1400

September	October	November	December
600	500	1000	2500

The seals would be produced, under license, by Seventh Seal, a specialty manufacturer of commemorative seals cast in precious metals, located in Syracuse, New York. Seventh Seal has offered to produce the gold MIT seals exclusively for The Coop. Seventh Seal has explained to The Coop that there is a cost to setting up the equipment to produce the gold MIT seal. Because of this, Seventh Seal will charge The Coop a set-up cost of $1417.5 every time the MIT seal is produced.

Because of the high set-up cost, one of the managers at The Coop proposes doing all the seals that will be needed for 2018 in a one-time production batch. "This will save us a lot of money in set-up costs", he says.

Another manager, however, warns that - because the gold seals are expensive - there is an associated holding cost. The Coop estimates that the holding cost will be about $0.21000000000000002 per seal per month (the dot is a decimal mark).

Because of the high holding costs, that manager proposes doing monthly batches in the amount of seals that will be required that month, according to the demand projection. "This will save us a lot of money in holding costs", she says.

What are the total costs (e.g. the sum of set-up costs and holding costs) of producing the gold seals using a fixed economic order quantity (FOQ) vs periodic order quantity (POQ)?

Answer 1

2018 Seal demands projection
Month	Qty	Average Monthly Inventory on periodic order basis=Monthly demand/2
Jan	1,300	650
Feb	300	150
Mar	600	300
Apr	500	250
May	2,000	1,000
Jun	5,500	2,750
Jul	1,800	900
Aug	1,400	700
Sep	600	300
Oct	500	250
Nov	1,000	500
Dec	2,500	1,250
Yearly Demand	18,000	9,000

A .EOQ Ordering
EOQ
Details
Annual usgae	18,000
Set Up cost per Production order	$     1,417.50
Holding cost per unit per year=0.210*12	$             2.52

EOQ = Sq Root of [(2*Set up cost*Annual usage)/(Annual Holding cost per unit]

EOQ= Sq Rt [(2*1417.5*18000)/2.52]
EOQ =4500
So no of Orders in a year=18000/4500=4
Total Set up cost in a year =4-1417.5=		$5,670
EOQ =4500
So average annual Inventory =4500/2=		2250
Annual Inventory Holding cost =2250*2.52=		$5,670
Total annual set up and holding cost =		$11,340

B. Periodic Order
No of orders in a year=	12
Yearly Set Up cost=12*1417.5=	$        17,010
Average monthly Inventory holding =9000 units
Monthly holding cost/unit=	$0.21
Annual Holding cost=9000*0.210=	$1,890.00
Total Annual Cost =Set Up +Holding cost=	$18,900