Question

Using the fixed-time period inventory model, and given an normally

distributed daily demand of mean 120 units and standard deviation 10 units,
1 week between inventory reviews, 3 days for lead time, 113 units of
inventory on hand, a target service level of 98%, what is the optimal order
quantity?

Answer 1

The optimal order quantity in the fixed-time period inventory model is 940 units.

Step-by-step explanation:

The optimal order quantity in the fixed-time period inventory model can be calculated using the formula:

Order Quantity = (Average Daily Demand x Review Period) + Safety Stock - Inventory on Hand

Where:

• Average Daily Demand = 120 units
• Review Period = 7 days
• Lead Time = 3 days
• Safety Stock = (Z-value x Standard Deviation of Daily Demand x Square Root of Review Period)
• Z-value for 98% service level = 2.05
• Standard Deviation of Daily Demand = 10 units
• Inventory on Hand = 113 units

Plugging in the values:

• Safety Stock = (2.05 x 10 x sqrt(7)) = 48.32 units (rounding up to 49 units)
• Order Quantity = (120 x 7) + 49 - 113 = 940 units

Therefore, the optimal order quantity is 940 units.