Infinite Horizon $[6]$

Frozen Yoghurt shop is open $24/7$ and uses liquid nitrogen in most products, but its consumption varies based on customer footfall. Analysing past demand over a year shows a normal distribution with an average of $178$L and a standard deviation of $18$L$.$

They monitor the storage tank regularly and have a reliable supplier ready to dispatch an order anytime. However, transportation is expensive $($it costs $$1750$ per order$)$ and time$-$ consuming $($it takes precisely three days from order to receipt$),$ so they can$$t wait until the tank is empty. An accounting firm estimated their daily inventory holding cost at $$0\mathrm{.}10$ per L$.$ In the current agreement, the supplier owns inventory in transit, so payment is due only on receipt of goods.

Being a famous shop serving a premium product, management has decided that the service level should be at least $99\%.$

$4\mathrm{.}1.$ What is the nitrogen level in the tank that should trigger an order? Round up your

answer to the nearest litre. $[1]$

$4\mathrm{.}2.$ What is the annual inventory management cost $($consider the ordering cost and

holding costs of cycle and safety stock$)?$ Assume $52$ weeks in a year. Round your

answer to the nearest dollar. $[1]$

$4\mathrm{.}3.$ The supplier offers a $20\%$ discount on the transportation cost, but payment is due on

order $($so the shop owns inventory in transit$).$ Would you recommend taking this

deal? Please justify your answer. You don$$t need to show calculations. $[1]$

Management thinks monitoring the tank levels is a massive distraction for the staff. They want to switch to ordering every Monday morning.

$4\mathrm{.}4.$ What should be the order$-$up$-$to level with this new policy? Round up your answer to

the nearest litre. $[1]$

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$4\mathrm{.}5.$ Owing to the increased congestion on highways due to a massive expansion project likely to last a few years, the transportation duration has increased to four days. The staff plans to increase the review period by an extra day $($from seven to eight days$)$ to accommodate this. What$$s your advice in this scenario? You don$$t need to show calculations. $[1]$

$4\mathrm{.}6.$ After analysing the receipts against orders, you note that the congestion has also made the transportation duration unreliable. It now fluctuates with an average of four days and a standard deviation of one day. What should be the impact of this issue on the ordering policy? You don$$t need to show calculations. $[1]$