The demand for a certain product has shown to be relatively stable; its sales are not subject to any seasonal influence, and demand is not expected to change in the future. In fact, during the last 10 lead times, the following demand was observed:

64 51 48 32 93 21 47 57 41 46 Assuming that this demand is a good representative of total demands in future lead times and a reorder point of 51 is used, compute:

a. The various possible shortage sizes and their probabilities of occurrence (HINT: Assume that these are the only values that the demand can take, each with a 0.1 probability of occurring).

b. The expected (or average) shortage.

c. What reorder point would you use if the average shortage was to be no larger than 5 units? What is the associated probability of a stockout?