Question $3.$ In$-$transit Inventory $(10$ pts$)$

A manager of an appliance manufacturing company $($located in the West Coast, USA$)$ promoting a

line of household appliances in a market in the East Coast. The demand of the items will be served

through a warehouse located near the market.

a$)$ The forecasted annual demand of the product is $1500.$ The order processing cost is $$250/$ order.

Item cost is $$20/$item$/$year$.$ How many appliance unit should it order in one shipment? Assume,

a capital gain charge or interest, $($

I$)$ is $20\%(2$ pts$.)$

D $=1500$ units$/$year

S$=$ $$250/$order

C$=$ $$20/$item$/$year

I $=20\%$ or $0\mathrm{.}2($Interest$)$

H $=($I x C$)=0\mathrm{.}2$ x $$20=4/$item$/$year

Find EOQ $=$ Q $=$ Square Root of $[(2$ x D x S$)/$ H$]$

b$)$ The company choses the reorder point system and safety stock.

In order to accommodate uncertainties in delivery and the customer demand, the manager

wishes to hold inventory for $2$ weeks of demand as safety stock $($SS$).$ What should be the

reorder point $($ROP$)$ considering the delivery lead time $($transport$),$ T is $1$ week? $(2$ pts$.)$

ROP $=$ D $\backslash$times T $+$ SS $($LT $=1/52$ weeks$/$year$)$

SS $=$ D $\backslash$times LH $=$ D $\backslash$times $2/52(52$ weeks$/$year$)$

Find ROP $=$ D $\backslash$times T $+$ SS $=($D $\backslash$times T$)+($D $\backslash$times LH$)=$ D $($T $+$ LH$)$

c$)$ Due to many other products in the promotion, the manager wants to set a periodic inventory

control system to review the inventory needs.

The inventory will be evaluated $($periodic LP$)$ after every $3-$week time period. Therefore, design

of the inventory policy should hold, LP is $3$ weeks of demand for review time period and

transport lead time, T is $2$ weeks period. Due to safety stock policy, additional $2$ weeks of

demand, LH is hold for the safety stock $($to manage demand uncertainly$).$

How many appliance units should be ordered? $(2$ pts$.)$

M $=$ D $($Lp $+$ T$)+$ SS

Given, Lp $=3/52,$ T $=2/52$ and SS $=$ D $\backslash$times LH $=$ D $+2/52$

d$)$ The company want to find the best transportation carrier. The in$-$transit $($inventory$)$ transport

selection has the following options:

$$ Options: two options are available for transportation: by truck and by rail.

$$ Lead time $($T$)$: Truck transportation takes $1$ week, while rail transportation takes $2$ weeks

of lead time.

$$ Cost: Truck transportation costs $$2$ per item, while by rail the transportation cost is $$1$ per

item. Transport cost is mainly due to transport vehicle and fuel.

$$ Policy: The company wants to hold enough inventory to cover demand for twice the

transport lead time. In$-$transit inventory cost is mainly due to investment capital holdup and

goods maintenance during the freight time.

The decision is impacted only by the safety stock, transportation cost and the transit inventory

costs. All other costs are remaining the same.

Find the following cost for both $($Truck & Rail$)$ options $(4$ pts$)$

Truck:

Safety stock $=$ SS $=1500(2/52)=$

Annual cost of holding safety stock $=$ SS $\backslash$times H $=$ SS x $$4/$item$/$year

Annual cost of transportation $=$ D $\backslash$times $$2$

Annual transit inventory cost $=$ D $\backslash$times H $\backslash$times T

Total $($of the above$)$ costs $=$

Rail:

Safety stock $=$ SS $=1500(4/52)=$

Annual cost of holding safety stock $=$ SS $\backslash$times H $=$ SS x $$4/$item$/$year

Annual cost of transportation $=$ D $\backslash$times $$1$

Annual transit inventory cost $=$ D $\backslash$times H $\backslash$times T

Total $($of the above$)$ costs $=$

Conclusion:

$$ Which transportation option cost less?

$$ What is the reorder point for each option?

Truck: The reorder point, ROP $=$

D $\backslash$times

T$($truck$)+$

SS$($truck$)$

Rail: The reorder point, ROP $=$

D $\backslash$times

T$($rail$)+$

SS$($rail$)$