The cost of keeping a unit of inventory is a.
The cost of being short a unit is b.
The expected demand is normally distributed with mean m and std. dev. c.
I'm trying to find a formula for the optimum amount of inventory.
I'm currently plugging in values for q in the following formula:
aq+b*Integral of(normal distribution*(x-q)) from q to infinite
q is the inventory in excess of the expected demand.
Is this correct? If so, what would the derivative of this formula be so I can find the maximum.