What is the optimal length of one inventory cycle for a firm that has an economic order quantity of 750 units, average daily demand of 68 units, and a price of $30 per unit?
A) 25 days
B) 11 days
C) 2.7 days
D) 331 days

Question

Quizplus · Accepted Answer

First, we need to calculate the annual demand of the firm: 
Annual demand = average daily demand x number of working days per year 
Number of working days per year = 365 days - 25 days (assuming weekends and holidays off) = 340 days 
Annual demand = 68 units/day x 340 days = 23,120 units 
Next, we can calculate the optimal length of one inventory cycle: 
Optimal cycle time = square root of (2 x annual demand x ordering cost / carrying cost per unit) 
Since the problem does not provide us with ordering cost or carrying cost per unit, we cannot calculate the optimal cycle time precisely. However, we can use the fact that the economic order quantity (EOQ) is 750 units to estimate the total annual cost of holding inventory: 
EOQ = square root of (2 x annual demand x ordering cost / carrying cost per unit) 
750 = square root of (2 x 23,120 x ordering cost / carrying cost per unit) 
We can simplify this equation to: 
Ordering cost / carrying cost per unit = (750^2 / 2 x 23,120) = 15.28 
Assuming a conservative 20% carrying cost per unit, we can estimate the ordering cost per order: 
Ordering cost / carrying cost per unit = 15.28 
Carrying cost per unit = 0.2 x $30 = $6 
Ordering cost per order = 15.28 x $6 = $91.68 
Using this estimated ordering cost per order, we can calculate the optimal cycle time: 
Optimal cycle time = square root of (2 x annual demand x $91.68 / $6) = 11.08 days 
Rounding up to the nearest whole number, we get the answer of 11 days.

What Is the Optimal Length of One Inventory Cycle for a Firm