As a result of many process improvements and IT implementations (like EDI), Big
ID: 370076 • Letter: A
Question
As a result of many process improvements and IT implementations (like EDI), Big Box-Mart has been able to reduce its order costs from $20 to $4.25 when purchasing cases of paper towels from its main paper-products supplier. Annual demand is expected to be 140,000 cases and annual holding costs are 3.50 per case. Based on this information, what will be the new optimal order quantity (using the reduced ordering cost)?
When using the reduced ordering cost, as compared to the original ordering cost, by how many cases will the average inventory go down? (Display your answer to twodecimal places.)
What will be the annual total combined savings to ordering costs and holding costs when using the reduced order cost, as compared to the original ordering cost? (Display your answer to two decimal places.)
Explanation / Answer
Optimal order Quantity ( EOQ) is determined as per Economic Order Quantity model.
EOQ is expressed as :
EOQ = Square root ( 2 x Co x D / Ch )
Co = Ordering cost
D = Annual demand = 140,000
Ch = Annual unit holding cost = $ 3.5
Therefore ,
EOQ = Square root ( 2 x 140,000 x Co/3.5)
= Square root ( 80000x Co)
Thus,
EOQ basis old ordering cost of $20 = Square root ( 80,000 x 20) = 1264.91 ( 1265 rounded to nearest whole number)
EOQ basis new ordering cost of $4.25 = Square root ( 80,000 x 4.25) = 583.09 ( 583 rounded to nearest whole number )
NEW OPTIMAL ORDER QUANTITY = 583 CASES
Average Inventory = EOQ /2
Therefore , the amount by which average inventory will go down
= 1264/ 2 – 583/2
= 632 – 291.5
= 340.5
AVERAGE INVENTORY WILL GO DOWN BY 340.5 CASES
Basis original ordering cost :
Annual ordering cost
= Co x Number of orders
= Co x Annual demand /EOQ
= 20 x 140,000/1264
= $2215.19
Annual inventory holding cost
= Ch x Average inventory
= 3.5 x 632
= $2212
Total cost
= Annual ordering cost + Annual Inventory holding cost
= $2215.19 + $2212
= $4427.19
Basis revised ordering cost :
Annual ordering cost
= Co x Number of orders
= 4.25 x Annual demand /EOQ
= 4.25 x 140,000/583
= $1020.58
Annual inventory holding cost
= Ch x Average inventory
= 3.5 x 583/2
= 1020.25
Total cost
= Annual ordering cost + Annual Inventory holding cost
= $1020.58 + $1020.25
= $2040.83
Thus annual total combined savings = $4427.19 - $2040.83 = $2386.36
ANNUAL TOTAL COMBINED SAVINGS = $2386.36
NEW OPTIMAL ORDER QUANTITY = 583 CASES
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