Question $1$: 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\mathrm{.}70$ per bag. The following information is available about these bags.

Demand $=90$ bags$/$week

Order cost $=$ $$54/$order

Annual holding cost $=27$ percent of cost

Desired cycle$-$service level $=80$ percent

Lead time $=3$ weeks $(18$ working days$)$

Standard deviation of weekly demand $=15$ bags

Current on$-$hand inventory is $320$ bags, with no open orders or backorders. $[30$ points, $6$ for each part$]$

Part $1$: What is the EOQ? What would be the average time between orders $($in weeks$)?[$Note: You don$$t need to round off the average time.$]$

Answer:

EOQ $=$

Average time between orders $=$

Work:

Part $2$: What should reorder point R be$?$

Answer:

R $=$

Work:

Part $3$: The store currently uses a lot size of $500$ bags $($i$.$e$.,$ Q$=500).$ What is the annual holding cost of this policy? Annual ordering cost?

Answer:

Annual Holding Cost $=$

Annual Order Cost $=$

Work:

Part $4$: In Part $3,$ Without calculating the EOQ, how can you conclude from these two calculations that the current lot size is too large?

Explanation:

Part $5$: What would be the annual cost saving by shifting the order size from $500-$bag lot to the EOQ?

Answer:

Work: