Part $A-$ Periodic Review Inventory System

$(Answ5er$ requires one final numerical result only: Order Quantity $tobe$ placed$)$

A $logistics$ facility manages its replenishment $of$ a popular industrial component through $a$

Periodic Review Inventory System. This part $is$ critical $to$ the company's production

process and experiences steady weekly consumption. Orders are reviewed and placed

every $7$ days, with $an$ average lead time $of4$ days from the supplier. The facility

maintains $a95\%$ cycle service level, for which the $Z-$value $is1\mathrm{.}65.$

Demand for the component over the last $12$ weeks has been recorded $as$ follows:

The standard deviation $of$ weekly demand $is22\mathrm{.}4$ units, based $on$ historical analy$-$

sis. The inventory position $at$ the end $of$ the current review period $is210$ units $(this$

includes $on-$hand stock, outstanding orders, and subtracts backorders$).$

The management wants $to$ determine the optimal Order$-Up-To$ Level $(T)$ using the

Periodic Review Model, $to$ ensure that the stock covers the full protection period.

The protection period $is$ defined $as$ the review period plus lead time, totaling $11$

days. Since the demand $is$ tracked weekly, convert daily demand accordingly.

Use the following formulas:

Average weekly demand:

$mu=\frac{su{m}_i}{12}=1^{12}{D}_i$

Average daily demand:

$d=\frac{mu}{7}$

Mean demand during protection period $(in$ units$)$:

$m{u}_{pp}=dxx11$

Standard deviation during protection period:

${}_{pp}={}_{\text{w}\text{e}\text{e}\text{k}}\sqrt[\phantom{2}]{\frac{11}{7}}$

Order$-Up-To$ Level:

$T={}_{pp}+Z*{}_{pp}$

Order Quantity:

$Q=T-$ Inventory Position

Final Question:

Using the information provided above, calculate the Order Quantity that must $be$

placed now, $at$ the end $of$ the current review period, $to$ achieve the required service level.

Provide only the final answer $(in$ units$)$ after all calculations.

Part $B-$ EOQ with Quantity Discounts

$(Answer$ requires one final numerical result only: Optimal Order Quantity $in$ units$)$

A manufacturing facility regularly purchases a critical raw material used $in$ production.

The purchasing manager must decide the optimal order quantity considering quantity

discounts offered $by$ the supplier. The supplier's pricing schedule $is$:

Other relevant data:

Annual demand $D=5,000$ units

Ordering cost per order $S=800$

Holding cost rate $=18\%of$ the unit purchase price per year

The facility wants $to$ minimize Total Annual Cost $(TAC),$ which includes:

Purchase Cost $=D$ Unit Price

Ordering Cost $=\frac{D}{Q}S$

Holding Cost $=\frac{Q}{2}H,$ where holding cost per unit $H=0\mathrm{.}18$ Unit Price

Task:

Compute the Economic Order Quantity $(EOQ)at$ each price break, using:

EOQ$=\sqrt[\phantom{2}]{\frac{2DS}{H}}$ Part $C-$ Aggregate Production Planning Using Level

Strategy

$(Answer$ requires one final numerical result only: Total Cost for $6$ months$)$

A factory manufactures a single product and forecasts demand for the next six months

$as$ follows:

The factory's production and cost data:

Regular production capacity: $600$ unit$\frac{s}{m}$onth

Regular production cost: $120$ per unit

Overtime production capacity: $upto200$ unit$\frac{s}{m}$onth

Overtime $pr5$oduction cost: $160$ per unit