Due to different rates for different ordering quantities, we need to compare inv

Question

Due to different rates for different ordering quantities, we need to compare inventory cost for quantities at various levels.

First lets calculate EOQ for quantity between 2001 and 5000:

EOQ = (2 * Annual Demand * Cost per order)/ (Cost per unit * Holding cost)

EOQ = (2 * 46,200 * 205)/ (1.60 * 0.55) = 4639.5 4640 units

Now, lets compare:

Hence, we see that according to this calculations, the EOQ is 5001 units.

Lets compare this with order of 10001 units:

No. of Orders (O=46,200/q) = 4.62

OC = Ordering Cost (O*205) = 947.1

HC = Holding Cost (0.55*RespectivePrice*q/2) = 3437.8

CP = Cost of Purchase (RespectivePrice*46200) = 57750

TOTAL INVENTORY COST (OC+HC+CP) = $62135

Hence, after comparison we see that the EOQ is 10001 units.

This is also logically sound as this is the least amount we need to order to qualify for most discount and any additional quantity in an order would only increase holding costs and total inventory cost.

Answers:

A) 10001 units

B) $3437.8

C) $947.1

D) $57750

E) $62135

(as calculated above)

Order Quantity (q) 2000   4640 5001 No. of Orders (O=46,200/q) 23.1 9.95 9.23 OC = Ordering Cost (O*205) 4735.5 2039.75 1892.15 HC = Holding Cost (0.55*RespectivePrice*q/2) 990 2041.6 1925.385 CP = Cost of Purchase (RespectivePrice*46200) 83160 73920 64680 TOTAL INVENTORY COST (OC+HC+CP) 88885.5 78001.35 68497.5

Explanation / Answer

The catering manager of LaVista Hotel, Lisa Ferguson, is disturbed by the amount of silverware she is losing every week. Last Friday night, when her crew tried to set up for a banquet for 500 people, they did not have enough knives. She decides she needs to order some more silverware, but wants to take advantage of any quantity discounts her vendor will offer.

For a small order (2,000 pieces or less) her vendor quotes a price of $1.80/ piece

If she orders 2,001 to 5,000 pieces the price drops to $1.60/piece 5,001 to 10,000 pieces brings the price to $1.40/piece

10,001 and above reduces the price to 1.25/piece

Lisa's order costs are $205205 per order, her annual holding costs are 55%, and the annual demand is 46 comma 20046,200 pieces. For the best option (the best option is the price level that results in an EOQ within the acceptable range):

ANSWER THE FOLLOWING

A) What is the optimum ordering quantity?

B) What is the annual holding cost?

C) What is the annual ordering cost?

D) What are the annual cost of the silverware with an optimal order quantity?

E) What is the total annual cost, including ordering, holding, and purchasing the silverware?

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