Question

A rodent infestation has left a landlord with a major cleanup job; in fact, the cleanup will consist of ripping out all the walls and ceilings of an 1860 square foot house to replace them. A trip to the local home improvement store reveals that 4'x8' sheets of drywall have three price points as indicated in the table. Another consideration for the landlord is that he is equipped with only a humble half-ton pickup truck, that can hold at most 20 sheets. His truck sips fuel, so he considers only wear and tear on his vehicle at $5 to haul all the sheets he will use for the job. The holding percentage is 20%. The landlord believes the entire job — all walls and ceiling — will require 10,080 square feet of drywall.

Purchase Quantity	Price Per Sheet
1-20	$9.40
21-100	$9.30
101 or more	$9.20

Consider the $9.40 per sheet figure as the base price and use the information in Scenario 11.4 to answer the following question. What percentage discount from the base price results in an optimal order quantity of 101 sheets?

Answer 1

DEMAND = 10080

HOLDING COST = 20%

ORDERING COST = 5

EOQ = SQRT(2DS/H)

Optimal order quantity = Quantity with lowest total annual cost of inventory

TCI = annual holding cost + annual ordering cost + annual material cost

Annual holding = adjusted quantity / 2 * holding cost

Annual ordering = demand / adjusted quantity * ordering cost

Annual material cost = demand * cost per unit

ADJUSTED Q = EOQ IF EOQ > LOWER LIMIT, < UPPER LIMIT

LOWER LIMIT IF EOQ < LOWER LIMIT

UPPER LIMIT IF EOQ > UPPER LIMIT

NO.	LOWER BRACKET	UPPER BRACKET	PER UNIT	HC	EOQ	Q*	TOTAL COST	FORMULA
1	1	20	9.4	1.88	232	20	97290.8	(10080 * 9.4) + ((20 / 2) * 1.88) + ((10080 / 20) * 5) = 97291
2	21	100	9.3	1.86	233	100	94341	(10080 * 9.3) + ((100 / 2) * 1.86) + ((10080 / 100) * 5) = 94341
3	101	MORE	9.2	1.84	234	101	93327.93	(10080 * 9.2) + ((101 / 2) * 1.84) + ((10080 / 101) * 5) = 93328

OPTIMAL ORDER QUANTITY = 101
TOTAL COST OF INVENTORY = 93328