Please explain how/show the work Millennium Liquors is a wholesaler of sparkling
ID: 374876 • Letter: P
Question
Please explain how/show the work
Millennium Liquors is a wholesaler of sparkling wines. Its most popular product is the French Bete Noire, which is shipped directly from France. Weekly demand is 45 cases. Millennium purchases each case for $120, there is a $300 fixed cost for each order (independent of the quantity ordered), and its annual holding cost is 25 percent.
a.
What order quantity minimizes Millennium’s annual ordering and holding costs?
b.
If Millennium chooses to order 300 cases each time, what is the sum of its annual ordering and holding costs?
c.
If Millennium chooses to order 100 cases each time, what is the sum of the ordering and holding costs incurred by each case sold?
d.
If Millennium is restricted to ordering in multiples of 50 cases (e.g., 50, 100, 150, etc.), how many cases should it order to minimize its annual ordering and holding costs?
e.
Millennium is offered a 5 percent discount if it purchases at least 1000 cases. If it decides to take advantage of this discount, what is the sum of its annual ordering and holding costs?
a.
What order quantity minimizes Millennium’s annual ordering and holding costs?
b.
If Millennium chooses to order 300 cases each time, what is the sum of its annual ordering and holding costs?
c.
If Millennium chooses to order 100 cases each time, what is the sum of the ordering and holding costs incurred by each case sold?
d.
If Millennium is restricted to ordering in multiples of 50 cases (e.g., 50, 100, 150, etc.), how many cases should it order to minimize its annual ordering and holding costs?
e.
Millennium is offered a 5 percent discount if it purchases at least 1000 cases. If it decides to take advantage of this discount, what is the sum of its annual ordering and holding costs?
Explanation / Answer
Given Data:
(D) Demand ( Weekly) = 45 Cases => Demand (Annually) = 45*52 = 2340 Cases
Annual Holding Cost (H) = 25% of $300 = $75 ( Assuming this holding cost is per unit cost, as nothing is mentioned in the question)
Ordering Cost (S) = $300
Solution:
a) The ordering quantity that would minimize Millenium's Annual cost is called the Economic Order Quantity ( EOQ) and is calculated by the following formula:
EOQ = Sqrt(2*D*S/H) where, D,S & H are as given in the data above.
Please note that in the above formula, make sure that the time period for H as well as D should be same. That means if your are using H as holding cost per month, then D shold also be demand per month.
Now, Substituting the values in the above formula, we have
EOQ = Sqrt( 2*2340*300/75) = Sqrt (18720) = 136.82 ~ 137
Thus, if the order quantity would be maintained at 137 cases, then the Millenium's costs would be minimum.
b) Given Data: Ordering Lot Size(Q) = 300 Cases
So, Annual Holding cost = Average Inventory * Holding Cost = (Q/2)*75 = 150*75 = $11,250
Annual Ordering cost = Number of orders per year * Ordering Cost = (D/Q)*S = (2340/300)*300 = $2340
Therefore, Total Annual ordering & holding cost = 11250+2340 = $13,590.
c) Given Data: Ordering lot size ( Q) = 100 Cases
So, Annual Holding cost = Average Inventory * Holding Cost = (Q/2)*75 = 50*75 = $3750
Annual Ordering cost = Number of orders per year * Ordering Cost = (D/Q)*S = (2340/100)*300 = $7020
Total Annual ordering & holding cost = 3750+7020 = $10,770
Total Annual ordering & Holding cost per case sold = 10770/D = 10770/2340 = $4.60
d) By our calculation in part a, we find that the EOQ = 137 Cases, so in the given case, the Millenium company should order near about same value.
So, the options are to order either 100 Cases or 150 Cases. If millenium orders 100 Cases, chances of stockout are there. Thus, to be on the safe side, Millenium should order 150 Cases.