Greenhill Human Society of Eugene provides shelter and care for rescued pets available for adoption. They maintain a stock of kitty litter to meet the daily needs of the cats residing in the facility. While the overall demand for kitty litter remains relatively stable over time, the specific consumption can vary from day to day. Greenhill procures employs a Continuous Review inventory system to manage the orders for kitty litter. Greenhill operates 6 days a week and 52 weeks per year (total 312 days a year). Below, weve gathered information of Greenhill's inventory operations: Expected demand rate = 15 bags/day Standard deviation of demand rate = 6.124 bags/day Ordering cost = $54/order The variable cost of purchase = $11.70 per bag Annual holding cost = 27% of purchase cost Desired cycle-service level = 80% Lead time = 18 days

Problem 3: Periodic Review (P) System (Use problem statement and data above)

Suppose that Greenhill wants to apply a Periodic Review inventory system instead of a Continuous Review system.

1. Greenhill wants to approximate the cost trade-offs of the EOQ. What order cycle (in working days) they should use? (Hint: From Problem 2, calculate time between orders under EOQ. Round the result to the closest whole number and use it as the value for .) 2. What target inventory position should be used to achieve the service level of 80%? 3. It is time for reordering. There are 240 bags currently on hand and 50 bags scheduled receipt. How many bags of kitty litter should be ordered? 4. If Greenhill sets the target inventory position to be = 740 bags. Whats the probability of experiencing no stockout in a cycle?

Hint: i. Calculate the needed safety stock using: = ( + ) + (Safety Stock), ii. Calculate the corresponding Z score using: (Safety Stock) = + , (keep two decimal places after the dot in your result), iii. Using the Normal Distribution table to find the probability.