Optimal Order Quantity Calculation with Exponential and Normal Distribution
a) What is the optimal order quantity when demand for jumpers is exponentially distributed?
a) Once the item is sold below the breakeven cost the selling good will plan a second sale on.1
b) What is the optimal order quantity when demand for jumpers is normally distributed?
b) In the best-case scenario, the selling price of the jumper would allow the sale of the most items ordered to have the highest possible profit margin.1
a) Answer:
a) To find the optimal order quantity when the demand for jumpers is exponentially distributed, we can use the newsvendor model. The newsvendor model aims to balance the cost of ordering too many items (excess inventory) with the cost of ordering too few items (lost sales).
b) Answer:
b) To find the optimal order quantity when the demand for jumpers is normally distributed, we can use the newsvendor model with normal distribution assumptions.
a) To find the optimal order quantity when the demand for jumpers is exponentially distributed, we can use the newsvendor model. The newsvendor model aims to balance the cost of ordering too many items (excess inventory) with the cost of ordering too few items (lost sales).
Given:
- Unit cost of jumpers = $15
- Selling price of jumpers = $40
- Salvage value of unsold jumpers = $10
- Loss of goodwill cost = $7 per lost sale
- Demand is exponentially distributed with a mean of 50
The optimal order quantity can be calculated using the formula:
Q* = F^-1(1 - g/(p - s))
Where F^-1 is the inverse cumulative distribution function of the exponential distribution.
Plugging in the values, we get:
Q* = 34.657
Therefore, the optimal order quantity for jumpers is approximately 34 units when demand is exponentially distributed.
b) To find the optimal order quantity when the demand for jumpers is normally distributed, we can use the newsvendor model with normal distribution assumptions.
Given:
- Unit cost of jumpers = $15
- Selling price of jumpers = $40
- Salvage value of unsold jumpers = $10
- Loss of goodwill cost = $7 per lost sale
- Demand is normally distributed with a mean of 50 and standard deviation of 12
The optimal order quantity can be calculated using the formula:
Q* = F^-1(1 - g/(p - s))
Plugging in the values, we get:
Q* = 60.104
Therefore, the optimal order quantity for jumpers is approximately 60 units when demand is normally distributed with a mean of 50 and a standard deviation of 12.