Lead time is $1$ week, setup cost is $$200,$ and holding cost is $$10$ per week. Stockouts are not allowed due to company policy $($i$.$e$.$ If there is an expected stock$-$out, two batches of order size must be placed$).$ Develop an ordering plan and calculate the costs for:

Lot$-$for$-$lot ordering policy.

EOQ $($Economic order quantity$)$ ordering policy.

POQ $($Periodic order quantity$)$ ordering policy.

Which ordering policy is better? Why one of the ordering policies results in a substantially higher cost?