An Industrial Engineer is designing a procurement process for Spinney’s Supermarket and after studying the demand for cereals, he concludes that the demand for cereals follows a normal distribution and falls between 200 to 230 boxes per week. Therefore, the demand of the cereal is a random variable because the demand can fluctuate between 200 and 230 boxes however; the demand will not decrease or increase tremendously unless some unusual event occurs. Using this estimate, the industrial engineer can decide how much cereal to procure in a certain week so that demand can be fulfilled without storing extra inventory.
During his study, he also finds out that the mean demand for cereal is 217 boxes per week and the standard deviation (which is the difference of the actual demand from the projected demand) is 15 boxes per week then he can find out the percentage of actual demand that is above 230 boxes per week since this will help him to decide whether to store extra inventory or not because if the probability of demand to exceed 230 is low then he might decide not to fulfill those orders since their chance of occurrence is low and holding cost is high.
To determine the percentage of times the demand exceeds 230 boxes per week, the engineer will use the formula: P (X > 230) = P [X > (230 – 217) / 15] P (Z > 0. 8667) = 1- 0. 8078 = 19. 22% Using this figure, the procurement department has to decide whether they should keep extra inventory or should they not be worrying about the 19. 22% of times when they might be having lost sales.