Question

JC Manufacturing (JCM) has a policy for its raw materials to keep 1 week’s (or ¼ month’s) supply as safety stock for every item it carries. For one item, it uses an average of 200 units per month. The item has a value of $24, ordering costs are $175, and holding costs are $6/item/year. The item is ordered in batches of 200, the lead time is 0.5 months and the standard deviation of lead time demand is 25 units. a) How many shortages are expected per year? (5 points) b) If the cost of a stockout is $200, what is the expected cost of this policy (holding, ordering and shortage)? (10 points total; 1 for setup, 3 each for holding, ordering and shortage)

Answer 1

Given:

Monthly demand = 200 units per month

D= annual demand = 12*200 = 2400 units per year

P = Unit cost = $24/unit

I = holding costs per unit per year = %6/item/year

S = ordering cost = $175 per order

Q = order quantity = 200 units per order

L = lead time = 0.5 months

Safety stock = ¼ months supply of demand

SS = Safety stock = ¼ x 200/month = 50 units

σL =Standard deviation of lead time demand is 25 units

a. Expected shortages per year

To determine the shortages, we require determining the cycle service level (CSL) from safety stock

Safety stock = (z)( Standard deviation of lead time demand) = z*σL

SS = z(25) = 50

Z = 2

From normal distribution table, the probability relative to z=2 is 0.9773

Cycle service level = 97.73%, the probability of not stocking out

Probability of stocking out = 1 – probability of not stocking ut = 1 – 0.9773 = 0.0227

Expected shortages per year = annual demand x probability of stocking out = 2400 x 0.0227 = 54.48 units

Expected shortages per year = B = 54.48 units

Part b.

G = cost of stockout = $200

Total Cost = Annual (ordering + inventory carrying + shortage costs)

Total Cost = (D/Q)S + [(Q/2) + SS]*(H) + G*B

Total Cost = (2400/200)$175 + [(200/2) + 50]($6) + (54.48)($200)

Total Cost = 2100 + 900 + 10896

Total cost = $13,896