Question

A drugstore uses fixed-order cycles for many of the items it stocks. The manager wants a service level of .95. The order interval is 10 days, and lead time is 2 days. Average demand for one item is 61 units per day, and the standard deviation of demand is 4 units per day. Given the on-hand inventory at the reorder time for each order cycle shown in the following table. Use Table. Cycle On Hand 1 36 2 8 3 91 Determine the order quantities for cycles 1, 2, and 3: (Round your answers to the nearest whole number) Cycle Units 1 2 3

Answer 1

Given values:

Service level = 0.95

Average demand (d) = 61 units per day

Time between orders (T) = 10 days

Lead time (L) = 2 days

Standard deviation of demand, (d) = 4 units per day

Solution:

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

Z = NORMSINV (Service level)

Z = NORMSINV (0.95)

Z = 1.645

Optimal Order Quantity (Q) is calculated as,

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

where, I = On-hand Inventory

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

Q = d (T + L) + [Z x (d) x SQRT (T + L)] - I

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

Q = 61 (10 + 2) + [1.645 x 4 x SQRT (10 + 2)] - I

Q = 732 + 22.79 - I

Q = 754.79 - I

(a) Cycle 1:

On-hand inventory = 36 units

Q = 754.79 - I

Q = 754.79 - 36 = 718.79 (Rounding off to the nearest whole number)

Order quantity = 719 units

(b) Cycle 2:

On-hand inventory = 8 units

Q = 754.79 - I

Q = 754.79 - 8 = 746.79 (Rounding off to the nearest whole number)

Order quantity = 747 units

(c) Cycle 3:

On-hand inventory = 91 units

Q = 754.79 - I

Q = 754.79 - 91 = 663.79 (Rounding off to the nearest whole number)

Order quantity = 664 units