Question

your dorm has decided to go in together on a communal shelter for dogs. dog food can be kept for a long time when stored properly. because you stop by the shelter every day to check on the dogs, you have a continuous review system. dogs eat 15 bags of dog food every day at a constant rate. every time you place an order for bulk dog food from the manufacturer, it takes 5 days for delivery and costs 3 dollars (independent of the number of bags). thanks to ordering in bulk, each bag of dog food only costs 1 dollar. the annual cost of storing dog food is 0.25 dollars per bag per year. assume 300 days per year. dogs start to eat more or less depending on how much they play outside. demand now becomes variable. after a few months, you find that the demand is normally distributed with an average demand of 15 bags per day and a standard deviation of 3 bags per day. assume a service level of 95%. questions what is the standard deviation of bags per day? with this variable demand, assuming a service level of 95%, what is the reorder point (rop) in units? what is the

Answer 1

The standard deviation of bags per day is 1. The reorder point (ROP) in units is approximately 77 bags.

Step-by-step explanation:

The standard deviation of bags per day can be calculated using the formula:

Standard deviation = (Maximum demand - Minimum demand) / 6

Given that the average demand is 15 bags per day and the standard deviation is 3 bags per day, we can calculate the maximum demand by adding the average demand to the standard deviation: 15 + 3 = 18 bags per day. The minimum demand can be calculated by subtracting the standard deviation from the average demand: 15 - 3 = 12 bags per day. Plugging these values into the formula, we get: (18 - 12) / 6 = 1 bag per day. Therefore, the standard deviation of bags per day is 1.

The reorder point (ROP) in units can be calculated using the formula:

ROP = Average demand × Lead time + Safety stock

Given that the lead time is 5 days and the service level is 95%, we can calculate the safety stock using the formula:

Safety stock = (Z-score × Standard deviation) × √Lead time

Using a Z-score of 1.645 (corresponding to a 95% service level), the standard deviation of 1 bag per day, and the lead time of 5 days, we can calculate the safety stock as: (1.645 × 1) × √5 = 3.667 bags. Plugging these values into the ROP formula, we get: 15 × 5 + 3.667 = 76.667 bags. Therefore, the reorder point (ROP) in units is approximately 77 bags.