Question

A drugstore uses fixed-order cycles for many of the items it stocks. The manager wants a service level of .99. The order interval is 12 days, and lead time is 4 days. Average demand for one item is 63 units per day, and the standard deviation of demand is 6 units per day. Given the on-hand inventory at the reorder time for each order cycle shown in the following table.

Cycle	On Hand
1	38
2	10
3	93

Determine the order quantities for cycles 1, 2, and 3.

Answer 1

Given values:

Service level = 0.99

Daily demand (d) = 63 units per day

Time between orders (T) = 12 days

Lead time (L) = 4 days

Standard deviation of demand, Sigma (d) = 6 units per day

Solution:

Using NORMSINV function in MS Excel, value of Z can be determined.

Z = NORMSINV (Service level)

Z = NORMSINV (0.99)

Z = 2.33

Order Quantity (Q) is calculated as,

Q = d (T + L) + Z Sigma (T + L) - I

where,

I = On-hand inventory

Sigma (T + L) = Sigma (d) x SQRT (T + L)

Sigma (T + L) = 6 x SQRT (12 + 4)

Sigma (T + L) = 24

Putting the given values in the above formula, we get,

Q = d (T + L) + Z Sigma (T + L) - I

Q = [63 x (12 + 4)] + [2.33 x 24] - I

Q = 1008 + 55.92 - I

Q = 1063.92 - I

Order quantity for period 1:

Order quantity (cycle 1) = 1063.92 - 38

Order quantity (cycle 1) = 1025.92 or 1026 (Rounding off to the nearest whole number)

Order quantity (cycle 1) = 1,026 units

Order quantity for period 2:

Order quantity (cycle 2) = 1063.92 - 10

Order quantity (cycle 2) = 1053.92 or 1054 (Rounding off to the nearest whole number)

Order quantity (cycle 2) = 1,054 units

Order quantity for period 3:

Order quantity (cycle 3) = 1063.92 - 93

Order quantity (cycle 3) = 970.92 or 971 (Rounding off to the nearest whole number)

Order quantity (cycle 3) = 971 units