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Example for lost sales cases
For the lost sales case minimization of annual cost is equivalent to the maximization of the annual profit. The only difference between lost sales and back order models is in evaluating the safety stock expression.
In case  represents the marginal distribution of lead time demand, and in case we consider that to be normally distributed then the annual variable cost  is given by the following expression (9.3).
where:
 = Cost of placing an order = Average annual demand = Inventory carrying cost = Unit cost of the item = Per unit back order cost = Optimal order quantity = Expected value of demand distribution, which is denoted by   = Standard deviation of demand distribution, which is denoted by 
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