The concession stand at the Minnewa 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. 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 six 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 one pizza left. What level of service does this result in?
b. What should the reorder point be to have a 98% service level?