Question: OuRx, a retail pharmacy chain, is faced with the decision of how much flu vaccine to order for the next flu season. OuRx has to place a single order for the flu vaccine several months before the beginning of the season because it takes four to five months for the supplier to create the vaccine. OuRx wants to more closely examine the ordering decision because, over the past few years, the company has ordered too much vaccine and too little. OuRx pays a wholesale price of $12 per dose to obtain the flu vaccine from the supplier and then sells the flu shot to their customers at a retail price of $20. Based on industry trends as feedback from their marketing managers, OuRx has generated a rough estimate of flu vaccine demand at their retail pharmacies. OuRx is confident that demand will range from 800,000 doses to 4,500,000 doses. The following table lists weights for demand values within this range.

Demand        1,000,000         2,000,000         3,000,000         4,000,000

Weight             .05                   .20                  .50                  .25

Because OuRx earns a profit on flu shots that it sells and it can't sell more than its supply, the appropriate profit computation depends on whether demand exceeds the order quantity or vice versa. Similarly, the number of lost sales and excess doses depends on whether demand exceeds the order quantity or vice versa.

a. Construct a spreadsheet model that computes net profit corresponding to a given level of demand and specified order quantity. Model demand as a random variable with ASP's custom general distribution.

b. Using simulation optimization, determine the order quantity that maximizes expected profit. What is the probability of running out of flu vaccine at this order quantity?

c. How many doses does OuRx need to order so that the probability of running out of flu vaccine is only 25 percent? How much expected profit will OuRx lose if it orders this amount rather than the amount from part b?