Chapter 9, Problem 13P

Sam’s Cat Hotel operates 52 weeks per year, 6 days per week, and uses a continuous review inventory system. It Purchases kitty litter for $11.70 per bag. The following information is available about these bags. $\begin{array}{l}\text{Demand}=\text{9}0\text{ bags}/\text{week}\\ \text{Order Cost}=\$\text{54}/\text{order}\\ \text{Annual holding cost}=\text{27 percent of cost}\\ \text{Desired cycle-service level}=\text{8}0\text{ percent}\\ \text{Lead time}=\text{3 weeks }\left(\text{18 working days}\right)\\ \text{Standard deviation of weekly demand}=\text{15 bags}\end{array}$

Current on-hand inventory is 320 bags, with no open orders or backorders.

1. What is the EOQ? What would be the average time between orders (in weeks)?
2. What should R be?
3. An inventory withdrawal of 10 bags was just made. Is it time to reorder?
4. The store currently uses a lot size of 500 bags (i.e., $\text{Q}=\text{5}00$). What is the animal holding cost of this policy? Annual ordering cost? Without calculating the EOQ, how can von conclude from these two calculations that the current lot size is too large?
5. What would be the annual cost saved by shifting from time 500-bag lot size to time EOQ?