Question

The demand for a particular type of yogurt in a supermarket is normally distributed with a mean of 80 units per day and a standard deviation of 4 units per day. Lead time for delivery of the yogurt is 4 days. The supermarket uses a fixed order size of 92 units for yogurt orders. The ordering cost is $30 per order and the annual cost of holding inventory is $1/unit. Assume 300 days per year. if the manager wants a 98% annual service level, what is the total annual inventory cost of this policy?

a) $5,778.32

b)$6,556.28

c)$7,875.29

d)$8,775.32

Answer 1

May this helps you..

Average daily demand, μ = 80

StdDev of daily demand, σ = 4

Average lead time, L = 4 days

Order size, Q = 92

Unit carrying cost, h = $1 per annum

Fixed ordering cost, k = $40

So,

Average lead time demand, μLTD = μ*L = 80*4 = 320

StDev of lead time demand, σLTD = σ√L = 4√4 = 8

Annual service level = Fill rate = 1 - E(z)*σLTD / Q

or, 0.98 = 1 - E(z) * 8/92

or, E(z) = 92*0.02/8 = 0.23

Corresponding 'z' is 0.656

So, safety stock, SS = z * σLTD = 0.656*8 = 5.248

Total annual indentory cost = (300*μ/Q)*K + (Q/2)*h + SS*h + μ*h*L = (300*80/92)*40 + (92/2)*1 + 5.248*1 + 80*1*4= 10806

So, none of the answers matches. The method is correct and I have checked the calculations. So, please check the numbers in the question.

Please give thumb ?