A drugstore uses fixed-order cycles for many of the items it stocks. The manager

Question

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 14 days, and lead time is 3 days. Average demand for one item is 63 units per day, and the standard deviation of demand is 2 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 46 2 12 3 104 Determine the order quantities for cycles 1, 2, and 3: (Round your answers to the nearest whole number) Cycle Units 1 2 3

Explanation / Answer

Following to be noted :

Protection period = Order interval + Lead time = 14 + 3 = 17 days

Standard deviation of daily demand = 2 units

Therefore , standard deviation of demand during protection period = 2 x square root ( 17 ) = 2 x 4.123 = 8.246

Z value for service level of 0.98 = NORMSINV ( 0.98) = 2.0537

Therefore , Safety stock = Z value x Standard deviation of demand during protection period – 2.0537 x 8.246 = 16.938 ( 17 rounded to nearest whole number )

Therefore ,

Reorder point = Average daily demand x Protection period + Safety stock = 63 x 17 + 17 = 1071 + 17 = 1088

It is to be noted that :

Order quantity = Reorder point – Quantity at hand

Therefore ,

Order quantity when quantity on hand is 46 = 1088 – 46 = 1042

Order quantity when quantity on hand is 12 = 1088 – 12 = 1076

Order quantity when quantity on hand is 104 = 1088 – 104 = 984

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