Question

Part a

The Bogue High School Gift Shop purchases sweatshirts emblazoned with the school name and logo from a vendor in Montego Bay at a cost of $2,000 each. The annual holding cost for a sweatshirt is calculated as 1.5% of the purchase cost. It costs the Gift Shop $500 to place a single order. The Gift Shop manager estimates that 900 sweatshirts will be sold during each month of the upcoming academic year.

i) Determine the highest number of shirts that should be purchased by the Gift Shop in order to minimize stock administration costs.

ii) What is the number of orders to be placed each year?

iii)Compute the average annual ordering cost

iv) Compute the average annual carrying cost

v) Compute the total stock administration cost

Part b The maximum sale for the Gift Shop for any one week is 300 sweatshirts and minimum sales 150 sweatshirts. The vendor takes anywhere from 2 to 4 weeks to deliver the merchandise after the order is placed. Using the EOQ policy, determine the re-order level, minimum inventory level and maximum inventory level for the business

Answer 1

To minimise the administration cost we should purcahse the Economic order quantity.

(i) EOQ = Sqrt(2*Annual usage*ordering cost per order/carrying cost per unit for a year)

= Sqrt(2*900*12*500/(1.5%*2000))

= Sqrt(10800000/360000)

= Sqrt(360000)

= 600 shirts per order

(ii) No. of order placed in a year = shirts sold in a year/EOQ

= 900*12/600

= 18 orders

(iii) Total ordering cost = No, of order placed in a year * per order cost

= 900*12/600 *500

= 10800/600*500

= 18*500

= 9000

Average annual ordering cost = 9000/12*900

= 0.833/shirt

(iii) Average annual carrying cost = Annual per unit caryying cost*average inventory level

= 600/2*2000*1.5%

= 300*30

= 9000

(v) Total stock administration cost = Total ordering cost + Total carrying cost

= 9000+9000

= 18000

(b) max. sale for a week = 300 sweat shirts

min, sale for a week = 150 sweat shirts

average sale = (300+150)/2

= 225 sweat shirts

average time = 3 weeks, min. time = 2 week, max. time = 4 week

Re-order level = Max. usage * max. lead time

= 300*4

= 1200 sweat shirts

Min. inventory level = Reorder level - (Avg. usage * Avg. lead time)

= 1200 - (250*3)

= 1200 - 750

= 450

Max. stock level = Reorder level - (Min. usage * Min. lead time) + Reorder qty.(EOQ)(MAx. Usage*Avg. lead time)

= 1200 - (150*2) + (300*3)

= 1200 - 300+900

= 1800

Safety stock = Max. usage * max lead time - Average usage*avg. lead time

= 300*4 - 225*3

= 1200 - 675

= 525

Please comment in case of any clarification required.