Question

Dunstreet's Department Store would like to develop an inventory ordering policy of a 90 percent probability of not stocking out. To illustrate your recommended procedure, use as an example the ordering policy for white percale sheets.

     Demand for white percale sheets is 3,000 per year. The store is open 365 days per year. Every four weeks (28 days) inventory is counted and a new order is placed. It takes 11 days for the sheets to be delivered. Standard deviation of demand for the sheets is four per day. There are currently 180 sheets on hand.

How many sheets should you order? (Use Excel's NORMSINV() function to find the correct critical value for the given ?-level. Do not round intermediate calculations. Round "z" value to 2 decimal places and final answer to the nearest whole number.)

Answer 1

Annual demand (D) = 3000 sheets

Number of days per year = 365 days

Average daily demand (d) = D/number of days per year = 3000/365 = 8.22 units

Review period (R) = 28 days

Lead time (L) = 11 days

Standard deviation of daily demand (d) = 4 sheets

On hand inventory (I) = 180 sheets

At 90% service level value of Z = 1.28

Order quantity = [d(L +R)] + [Z x d x sqrt of (L+R) - I

= [8.22(11+28)] + [1.28 x 4 x sqrt of (11+28)] - 180

= (8.22 x 39) + [1.28 x 4 x sqrt of 39] - 180

= 320.58 + (1.28 x 4 x 6.24) - 180

= 320.58 + 31.95 - 180

= 352.53 - 180

= 172.53 or rounded to 173 sheets