Question

1. A bakery buys sugar from a big distributor to use in baking cakes. Typically, they use 24 pounds of sugar in a day. But depending on the day, they may use a little bit less or more. It is estimated that the standard deviation of demand for sugar is 4 lbs per day. It takes 9 days from the time the bakery orders sugar until the distributor delivers the sugar. The manager wants to have a service level of 0.92. Determine each of the following, assuming that demand is distributed normally.

1. Z value for the intended service level?
2. The safety stock that will provide the intended service level?
3. The ROP that will provide the intended service level?

Answer 1

Daily demand (d) = 24

Standard deviation of demand (sigmad) = 4

Lead time (L) = 9

Expected service level = 0.92 or 92%

a.

Corresponding z value for intended service level (from the standard normal table) = 1.41

b.

Safety stock formula

SS = z*sigmad*sqrt(L)

Thus safety stock is

SS = 1.41*4*sqrt(9) = 16.92 pounds

c.

ROP formula

ROP = d*L + SS

Thus reorder point will be

ROP = 24*9 + 16.92 = 232.92 pounds

Answer 2

Average daily demand (d) = 24 pounds

Standard deviation of daily demand ($\sigma$d) = 4 pounds

Lead time(L) = 9 days

Service level = 0.92 = 92%

a) At 92% service level value of Z = 1.41 (Derived from the standard normal table)

b) Safety stock = Z x $\sigma$d x √L = 1.41 × 4 × √9 = 1.41 × 4 × 3 = 16.92 pounds

C) Reorder point = d x L + safety stock

= 24 × 9 + 16.92

= 216 + 16.92

= 232.92 pounds