P$1.$ Beer Distribution

A beer distributor sells $100$ cases of regular $12-$oz$.$ Budweiser per week for $50$ weeks each year from its warehouse in North Austin. The distributor currently orders a one$-$week supply of $100$ cases at the beginning of each week from a supplier at a cost of $$8$ per case. They also pay a fixed cost of $$10$ for each delivery. The beer distributor estimates its annual per$-$unit inventory holding cost $($cost of capital, insurance, etc.$)$ at $25$ percent. The goal of the problem is to figure out the optimal level of cycle inventory.

$($a$)$ What is the annual inventory holding cost for the distributor given its current ordering schedule?

What is the annual amount of cost that they incur for deliveries? Does the distributor hold the right

amount, too much, or too little cycle inventory? Why?

$($b$)$ What order size would you recommend the beer distributor adopts? Under the ordering policy yourecommend, on average, how long would a case of beer sit on the shelf before being sold?

$($c$)$ What is the percentage reduction in the total cost per unit $($including the costs of purchasing,

holding, and receiving deliveries$)$ that would be achieved from implementing the order quantity you

recommended in part $($c$)?$

$($d$)$ If the distributor sells each case of regular $12-$oz$.$ Budweiser for $$8\mathrm{.}80,$ what would be the

percentage increase in profit per unit from implementing your recommendation in part $($c$)?$

The distributor also operates a warehouse in South Austin. The South Austin warehouse is identical to the North Austin warehouse, except that the South Austin warehouse$$s weekly demand is only $80$ cases per week, and that they currently order $200$ cases every $2\mathrm{.}5$ weeks. The distributor is considering replacing the two warehouses with a single warehouse in Central Austin, which would serve all demand currently served by the existing warehouses.

$($e$)$ Assume that the North Austin warehouse now follows the ordering policy that you recommended in part $($b$).$ What is the total average amount of cycle stock that the distributor holds across the two warehouses, and what is the distributor$$s total annual inventory holding cost? What is the total amount that they pay per year for deliveries at the two warehouses combined? What is the total cost per unit $($case$)$ across the two warehouses?

$($f$)$ What order size would you recommend the beer distributor adopts if it replaces the existing two

warehouses with a single centralized warehouse?

$($g$)$ If the distributor replaced its two existing warehouses with a single centralized warehouse and

followed your recommendation in part $($f$)$: What would be the average cycle stock at the new

centralized warehouse, and what would be the total annual inventory holding cost? What is the

total amount that the distributor would pay per year for deliveries at the new warehouse?

$($h$)$ By how much would their total cost per case for the $12-$oz$.$ Budweiser increase or decrease if the

distributor replaced its current warehouses in North and South Austin with the one in Central Austin?

$($i$)$ What other costs$/$issues would you like to have information about before recommending that the

distributor moves forward with the Central Austin warehouse?