Question

The annual demand of cameras at Machey's department store is normally distributed with mean 1,200 and standard deviation 70. The store pays a setup cost of $35 per order, and the holding cost is $10 per camera per year. Machey's wants to place order from its supplier at an optimal frequency (or periodically). It takes one week for an order to arrive once it is placed. The store's management has specified its target service level as 95%. Machey operates all 52 weeks in a year.

a) What should be the optimal review period?

b) What should be the target inventory position of Machey for the above review period when the target service level is maintained?

c) Calculate the average inventory level for the above periodic review policy.

d) Calculate the total annual inventory cost of Machey.

Answer 1

Answer:

a)

Requesting cost = A = $35 per request

Holding cost = h = $10 per camera every year

Normal interest during lead time = Mean * Lead time

substitute qualities

= 1200/52 * 1

= 23.07 units

Variance of interest during lead time = 1*(70/52)*(70/52)

= 1.82 units

Standard deviation of interest during lead Time = Sqrt(variance)

= Sqrt (1.82)

= 1.34 units

EOQ = sqrt (2*AD/h)

= sqrt(2*35*1200/10)

= 91.65

= 92 units

Survey period = 92/1200*52

= 4 weeks i.e., 1 month

b)

Reorder level comparing to 95% help level is determined as follows:-

z = (X-u)/s

z value for 95% is 1.645

1.645 = (X - 23.07)/1.34

X = 25.27

Target Inventory for 95% help level = 26 units

c)

Normal stock during audit period = Reorder level + EOQ/2

substitute qualities

= 26 + 92/2

= 72 units

d)

All out yearly stock expense = Ordering cost + Holding cost

substitute qualities

= 1200/92*35+72*10

= $1176.5