Problem 13-31 A drugstore uses fixed-order cycles for many of the items it stock
ID: 446503 • Letter: P
Question
Problem 13-31
A drugstore uses fixed-order cycles for many of the items it stocks. The manager wants a service level of .98. The order interval is 15 days, and lead time is 2 days. Average demand for one item is 68 units per day, and the standard deviation of demand is 3 units per day. Given the on-hand inventory at the reorder time for each order cycle shown in the following table.
Determine the order quantities for cycles 1, 2, and 3: (Round your answers to the nearest whole number)
A drugstore uses fixed-order cycles for many of the items it stocks. The manager wants a service level of .98. The order interval is 15 days, and lead time is 2 days. Average demand for one item is 68 units per day, and the standard deviation of demand is 3 units per day. Given the on-hand inventory at the reorder time for each order cycle shown in the following table.
Use Table.Explanation / Answer
order quantity Q = D * (T+L) +z * st. dev. of (T+L) - I
where D = average daily demand = 68 units
T = order interval = 15 days
L = lead time = 2 days
Standard deviation of demand = 3 units per day
z = 2.055 at 98% services level
I = current inventory levels = 46 for cycle 1, 10 for cycle 2 and 103 for cycle 3
let calculate the st. deviation for order interval and lead time as we have st.dev. for demand
st. dev. (T+L) = sqrt [(T+L) * (st. dev. for demand)2]
= sqrt [ (15+2) * 32 ) = sqrt ( 17 * 9) = sqrt (153) = 12.37
now calculate order quantity for cycle 1
Q1 = 68 * (15+ 2) + 2.055* 12.37 - 46
= 1135 units
Q2 = 1171 units
Q3 = 1078 units
Answer
Cycle Units 1 1135 2 1171 3 1078