The concession stand at the Shelby High School stadium sells slices of pizza during boys’ and girls’ soccer games. Concession stand sales are a primary source of revenue for the high school athletic programs, so the athletic director wants to sell as much food as possible; however, any pizza not sold is given away free to the players, coaches, and referees or it is thrown away. As such, the athletic director wants to determine a reorder point that will meet the demand for pizza. Pizza sales are normally distributed with a mean of 6 pizzas per hour and a standard deviation of 2.5 pizzas. The pizzas are ordered from Pizza Beth’s restaurant, and the mean delivery time is 30 minutes, with a standard deviation of 8 minutes.
a. Currently the concession stand places an order when they have 1 pizza left. What level of service does this result in?
b. What should the reorder point be to have a 98% service level?