$3.$ Fixed Horizon

Murphy Metals wants to plan a production schedule based on confirmed customer orders for its silver discs in $2025.$ The table below shows the details at a monthly level.

Mon Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Orders $306075809570453565408540$

Murphy Metals can rent a foundry on the first day of every month to produce as many discs as it wants. They must pay $$2700$ if and only if they use the foundry. Please note that the foundry cannot be used at any other time during the month.

The discs produced are shipped to the customers throughout the month. The foundry offers space to store the discs for free during the month. However, it applies a storage fee of $$10$ per item for any discs left in the store on the last day of the month $($when they physically count the inventory$).$

Any inventory left at the end of the month can be added to any items produced at the beginning of the next month and used to fulfil orders during the next month.

Due to watertight contracts, Murphy Metals must have enough stock during the month to meet the confirmed orders.

The company has approached you for advice on optimising production$/$storage costs.

$3\mathrm{.}1.$ You decide to produce every month to cater to that month$$s orders. What$$s the total cost of this policy? $[1]$

$3\mathrm{.}2.$ You decide to produce for the entire year in one go$.$ What$$s the total cost of this policy? $[1]$

$3\mathrm{.}3.$ You want to try the POQ $($Periodic Order Quantity$)$ policy. If you produce every two months, what$$s the total cost of this policy? $[1]$

$3\mathrm{.}4.$ You wonder if trying EOQ $($Economic Order Quantity$)$ for this scenario makes sense. What$$s the total cost if you apply this policy? $[1]$

$3\mathrm{.}5.$ What are some reasons why EOQ may not be a practical option for Murphy Metals over the next few years? $[1]$

$3\mathrm{.}6.$ You want to use the production frequency recommended by EOQ to see if your POQ strategy can be improved. If you produce using this frequency, what$$s the total cost of this policy? $[1]$