A manufacturer is sourcing a component for a new product. Expected monthly deman

Question

A manufacturer is sourcing a component for a new product. Expected monthly demand is 705 units. The component can be purchased from either supplier A or supplier B, with the following price breaks:

SUPPLIER A SUPPLIER B
Quantity    Unit Price             Quantity      Unit Price
1–199        $14.00 1–149         $14.10
200–499 13.80 150–349        13.90
500 + 13.60 350 + 13.50

Ordering cost is $39 and annual holding cost is 25 percent of unit price per unit.

a. Which supplier should be used?
b. What order quantity is optimal if the objective is to minimize total annual costs?
c. What is the minimum total annual cost?

Explanation / Answer

EOQ MORE THAN 500 EOQ MORE THAN 350 ANNUAL DEMAND 705 12 8460 ANNUAL DEMAND 705 12 8460 ORDERING COST PER ORDER 39 ORDERING COST PER ORDER 39 CARRYING COST 13.6 25% 3.4 CARRYING COST 13.5 25% 3.375 EOQ SQUARE ROOT OF (2*ANNUAL DEMAND*ORDERING COST)/CARRYING COST PER UNIT PER YEAR 194082.35 440.5478 EOQ SQUARE ROOT OF (2*ANNUAL DEMAND*ORDERING COST)/CARRYING COST PER UNIT PER YEAR 195520 442.1764 ORDERING COST ORDERING COST NO OF ORDERS 19.20337 748.9312 NO OF ORDERS 19.13263422 746.1727 CARRYING COST 748.9312 CARRYING COST 746.1727 VALUE OF INVENTORY 8460 13.6 115056 VALUE OF INVENTORY 8460 13.5 114210 TOTAL ANNUAL COST OF ORDER OF 500+ 116553.9 TOTAL ANNUAL COST OF ORDER OF 500+ 115702.3 EOQ AT ORDER BETWEEN 200- 499 EOQ 150 - 349 EOQ ANNUAL DEMAND 705 12 8460 ANNUAL DEMAND 705 12 8460 ORDERING COST PER ORDER 39 ORDERING COST PER ORDER 39 CARRYING COST 13.9 25% 3.475 CARRYING COST 13.8 25% 3.45 EOQ SQUARE ROOT OF (2*ANNUAL DEMAND*ORDERING COST)/CARRYING COST PER UNIT PER YEAR 189893.5 435.7677 EOQ SQUARE ROOT OF (2*ANNUAL DEMAND*ORDERING COST)/CARRYING COST PER UNIT PER YEAR 191269.57 437.3438 ORDERING COST ORDERING COST NO OF ORDERS 19.41401159 757.1465 NO OF ORDERS 19.34405 754.418 CARRYING COST 757.1465 CARRYING COST 754.418 VALUE OF INVENTORY 8460 13.9 117594 VALUE OF INVENTORY 8460 13.8 116748 TOTAL ANNUAL COST OF ORDER OF 500+ 119108.3 TOTAL ANNUAL COST OF ORDER OF 500+ 118256.8 EOQ AT ORDER BETWEEN 1- 199 EOQ AT 1 - 149 EOQ ANNUAL DEMAND 705 12 8460 ANNUAL DEMAND 705 12 8460 ORDERING COST PER ORDER 39 ORDERING COST PER ORDER 39 CARRYING COST 14.1 25% 3.525 CARRYING COST 14 25% 3.5 EOQ SQUARE ROOT OF (2*ANNUAL DEMAND*ORDERING COST)/CARRYING COST PER UNIT PER YEAR 187200 432.6662 EOQ SQUARE ROOT OF (2*ANNUAL DEMAND*ORDERING COST)/CARRYING COST PER UNIT PER YEAR 188537.14 434.2086 ORDERING COST ORDERING COST NO OF ORDERS 19.55318192 762.5741 NO OF ORDERS 19.48372 759.8651 CARRYING COST 762.5741 CARRYING COST 759.8651 VALUE OF INVENTORY 8460 14.1 119286 VALUE OF INVENTORY 8460 14 118440 TOTAL ANNUAL COST OF ORDER OF 500+ 120811.1 TOTAL ANNUAL COST OF ORDER OF 500+ 119959.7 COST IS MINIMUM AT 350+ UNITS OF SUPPLIER B BECAUSE WHERE TOTAL INVENTORY COST IS MINIMUM OF 115702 WHICH IS LEAST AMONG ALL THE ORDERS SUPPLIER B SHOULD BE CHOOSEN ORDER QUANTITY OF 350+ IS OPTIMAL MINIMUM TOTAL ANNUAL COST IS 115702

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