Harvey’s Specialty Shop is a popular spot that specializes in international gour

ID: 354559 • Letter: H

Question

Harvey’s Specialty Shop is a popular spot that specializes in international gourmet foods. One of the items that Harvey sells is a popular mustard that he purchases from an English company. The mustard costs $10 a jar and requires a 2-month lead time for replenishment of stock. The replenishment time is almost constant. Harvey uses a 20% annual interest rate to compute holding costs. Bookkeeping expenses for placing an order amount to about $50. During the 2-month supply time, Harvey estimates that he sells an average of 100 jars but there is substantial variation. He estimates the standard deviation of demand for each 2-month period is 25. Assume that demand is described by a normal distribution. (3 + 3 + 4 + 8 + 12 + 20 = 50 points)

What is the optimal order quantity?

What will be the average time between transactions?

How much safety stock should be maintained for 98% cycle service level?

What should be the reorder point for 98% fill rate?

Now suppose that the English company is ready to send the mustard by a faster ship, which will reduce the replenishment lead time to 1-month and the standard deviation of demand during that period to 17.7, but increase the cost to $15 per jar. What will be the new reorder point for 98% fill rate and 98% cycle service level?

What will be the optimal total inventory cost (Ordering + Holding + Purchase) before and after the decrease of lead time (and resultant price increase)? What managerial insights can you get from this?

Explanation / Answer

Data given as follows:

Symbol

Value

Demand for 2 months

100

Annual Demand

100 x (12/2) = 600

units/year

Cost per order

$50

$/order

Unit cost

$10

Per unit

Annual holding charge

20%

Annual holding cost per unit

H = I*P

0.20*10

= $2

$/unit/year

1 and 2

EOQ units

Q* = ?(2AS/(H))

?(2*600*50/(2.00))

Q* = 173

No. of Orders per year

N = A/Q

600/173

= 3.46

Average time between orders

1/N

1/3.46

= 0.289 year

Or 0.289*12= 3.468 months

Time between order = 3.468 months

2-month demand during lead time = d = 100

2-month standard deviation = ? = 25 units

Lead time = L = 2 months

z-score for 98% CSL is 2.0537

Safety Stock = z?d?L = 2.0537 x 25 x ?2 = 72.61

Safety stock = 72.61 units

Reorder Quantity level for Q-model:

R = monthly demand during lead time + Safety stock

R = 100 + z?d?L

R = (100) + 72.61

R = 172.61

Reorder point = 172.61 units