F$2024$ MGTS $352($CC$91)$ Case Assignment $-$ Inventory Management $(10\backslash \%,$ Total $10$ points$)$

The 'Try to Have Just One' $($THJO$)$ sunflower seed company roasts and seasons sunflower seeds $($in shell$).$ For their production, they require a specific type of oil that they source from a local supplier; the lead time on orders is $3$ days. The oil comes in a box that is lined with plastic, with each box of oil costing THJO $\backslash (\backslash$$ $72\backslash )($this is the product cost$).$ Demand averages $100$ boxes per day, with a standard deviation of $26($assume that they run production $365$ days$/$year$).$

Ordering is done by a Procurement Specialist working at THJO and requires checking with the Production Department to see if there are any plans that might cause a sudden change in demand, creating a purchase order $($PO$),$ transmitting the purchase order by email and following up with the supplier, and then processing the product receipt and invoice when the product arrives $-$ a recent study by the Procurement department estimates a total administrative cost of $\backslash (\backslash$$ $30\backslash )$ per PO $($independent of order quantity$).$

The Accounting and Finance Department has requested that a rate of $\backslash (19\backslash \%\backslash )$ be used when determining holding costs of inventory $($this includes cost of capital, insurance, variable storage, and other costs that vary with the amount of inventory on hand$).($For the sake of this analysis, ignore seasonality in demand, and any quantity discounts or transportation costs.$)$ Currently, they order $\backslash ($ Q$=500\backslash )$ boxes when inventory reaches $\backslash ($ R$=350\backslash )$ boxes. $1.(3$ points$)$ Diagram their current ordering policy in a "sawtooth" diagram that clearly labels the order quantity, reorder point, cycle stock, average cycle stock, safety stock and lead time. Start time zero with $450$ units on hand $($so your first order will be placed at day $1).*$Hint $-$ Cycle Stock is a changing variable while Average Cycle Stock is a constant. They are two different concepts.

$*$ NOTE $-$ Equations and calculations are tangible ways to implement a concept, but the concept is important as well $-$ be sure to understand what you are doing and why, and not just how to make the calculation when completing this assignment.

Inventory

Time $($Days$)2.(3\mathrm{.}5$ points$)$ Find the annual ordering and holding costs associated with the current ordering policy $(\backslash ($ Q$=\backslash$mathbf$\{500\}\backslash )$ boxes$).$ Then determine the optimal order quantity to minimize total annual ordering plus holding costs. $($Note $-$ it will be necessary to use annual demand to do this.$)$

$3.(3\mathrm{.}5$ points$)$ Finally, what is the cycle service level $($CSL$)$ if the reorder point is $300$ boxes? What is the reorder point required to ensure a $\backslash (96\backslash \%\backslash )$ cycle service level?

Cycle service level $($CSL$)($when R$=300$ boxes$)$: