In Section 9.1 we developed an approximation model based on the assumption that demand in excess of supply is backordered. Suppose now that demand is lost when inventory is not available to meet demand. The goal now is to find the values of Q and r that minimize the average annual fixed ordering costs, holding costs and lost sales costs. Using the notation found in Section 9.1, develop a model and a solution procedure for finding Q∗ and r∗. In the model π now represents the cost of a lost sale.

As you develop the model you will have to determine the expected cycle length and the expected number of orders placed per year. Observe that this latter quantity is no longer λ

Q , since some demand is lost. Thus during a cycle, demand equals Q units plus possibly some lost sales. Hence the expected demand during a cycle is equal to Q plus the expected lost sales. You will have to make some assumption as to how to deal with this observation as you construct your model and solution methodology. Remember, as you develop your solution methodology that you are assuming that lost sales will be a small fraction of total sales and that Q is sufficiently large so that no more than one order is outstanding at any point in time.