AQ$4.$ MRP $(19$ marks$)$

A firm uses subassemblies A and C and components B$,$ D and E to assemble the final product F; see a bill of materials in Figure $1.$

Figure $1$: Bill of materials used for Question AQ$4.$

$1.[4$ marks$]$ You are required to fill Table $1$ to prepare a master schedule for F$.$ Each time when the firm assembles F $,$ the firm always uses the "fixed period of $2"$ rule to make F $.$ The firm's assembly time for F is one week. The beginning inventory for F is $85$ ; the forecast and promised customer orders for this end item are provided in this table.

Table $1$: MPS table for the end item F in Question AQ$4.$

$2.[8$ marks$]$ Use the master production schedule for F in Table $2$ to develop material requirements plans $($MRPs$)$ for subassembly A and component B $.$ Note that you are required to finish the MRP table$-$i$.$e$.,$ Table $2-$ in which you can find the present on$-$hand quantity $($i$.$e$.,$ the beginning inventory$),$ lead time, ordering rule and scheduled receipts for each of the subassembly A and component B$.$ For subassembly C$,$ the on$-$hand inventory is zero, there is no scheduled receipt, lot$-$sizing policy is lot$-$for$-$lot, and lead time is $1$ week.

Table $2$: MRP table for Question AQ$4.$

$3.[\backslash (\backslash$mathbf$\{2\}\backslash )$ marks$]$ You are required to calculate the total inventory cost for the component B during the eight weeks, using the results in Question $2.$ Note that, for each week, the inventory cost may include a fixed cost and a holding cost. We assume that the per order fixed cost is $\backslash (\backslash$$ $1,000\backslash )/$order$,$ and the unit holding cost is $\backslash (\backslash$$ $1\backslash )$ per item per week. The fixed cost is incurred each time when the firm places an order. More precisely, if the firm places an order at the beginning of a week, then the firm incurs the fixed cost for this week; otherwise, the fixed cost for the week is zero. The holding cost is calculated according to the number of remaining items at the end of each week. For example, if $10$ units of the component B are remaining at the end of a week, then the holding cost for this week is $\backslash (\backslash$$ $1\backslash$times $10=\backslash$$ $10\backslash ).4.[5$ marks$]$ Assume that the lot$-$sizing policy for component B is changed from "lot$-$for$-$lot" to "lot size of $500$ units". You are required to consider the following two questions:

$($a$)$ Fill in the following table to re$-$do the MRP scheduling for the component B;

$($b$)$ Calculate the total inventory cost for the policy of lot size of $500$ units.