Question

Chris Sandvig Irrigation, Inc., has summarized the price list from four potential suppliers of an underground control valve. See the table below. Annual usage is 800 valves; order cost is $12 per order; and annual inventory holding costs are $5.25 per unit. Vendor A Quantity Price 1-14 $35.00 15-24 34.75 25-99 33.55 100-199 32.35 200-399 31.15 400+ 30.75 Vendor B Quantity Price 1-24 $34.75 25-99 34.00 100-199 32.80 200-399 31.60 400+ 30.50 Vendor C Quantity Price 1-49 $34.50 50-149 33.75 150-299 32.50 300+ 31.10 Vendor D Quantity Price 1-149 $34.25 150-299 33.00 300+ 31.00 Which vendor should be selected and what order quantity is best if Sandvig Irrigation wants to minimize total cost? Chris Sandvig Irrigation should order units at a time from v (enter your response as a whole number).

Answer 1

CHRIS SHOULD ORDER 400 UNITS FROM VENDOR B

EXPLANATION

DEMAND = 800

ORDERING COST = 12

HOLDING COST = 5.25

EOQ = SQRT(2 * DEMAND * ORDERING COST / HOLDING COST) = SQRT(2 * 800 * 12 / 5.25) = 60

ANNUAL HOLDING COST = ADJUSTED EOQ / 2 * HOLDING COST PER UNIT

ANNUAL ORDERING COST = (ANNUAL DEMAND / ADJUSTED EOQ) * ORDERING COST

ANNUAL MATERIAL COST = ANNUAL DEMAND * OFFERED PRICE PER UNIT

TOTAL COST OF INVENTORY = ANNUAL(HOLDING + ORDERING + MATERIAL)

VENDOR A

OPTIMAL ORDER QUANTITY = 200

ASSOCIATED COST = 25493

NO.	LOWER LIMIT	UPPER LIMIT	PER UNIT PRICE	HOLDING COST	EOQ	ADJUSTED QUANTITY	ANNUAL HOLDING COST	ANNUAL ORDER COST	ANNUAL MATERIAL COST	TOTAL COST OF INVENTORY
1	0	14	35	5.25	60	14	(14 / 2) * 5.25 = 36.75	800 / 14 * 12 = 685.71	800 * 35 = 28000	36.75 + 685.71 + 28000 = 28722
2	15	24	34.75	5.25	60	24	(24 / 2) * 5.25 = 63	800 / 24 * 12 = 400	800 * 34.75 = 27800	63 + 400 + 27800 = 28263
3	25	99	33.55	5.25	60	60	(60 / 2) * 5.25 = 157.5	800 / 60 * 12 = 160	800 * 33.55 = 26840.	157.5 + 160 + 26840 = 27158
4	100	199	32.35	5.25	60	100	(100 / 2) * 5.25 = 262.5	800 / 100 * 12 = 96	800 * 32.35 = 25880	262.5 + 96 + 25880 = 26239
5	200	399	31.15	5.25	60	200	(200 / 2) * 5.25 = 525	800 / 200 * 12 = 48	800 * 31.15 = 24920	525 + 48 + 24920 = 25493
6	400	& MORE	30.75	5.25	60	400	(400 / 2) * 5.25 = 1050	800 / 400 * 12 = 24	800 * 30.75 = 24600	1050 + 24 + 24600 = 25674

VENDOR B

OPTIMAL ORDER QUANTITY = 400

ASSOCIATED COST = 25474

NO.	LOWER LIMIT	UPPER LIMIT	PER UNIT PRICE	HOLDING COST	EOQ	ADJUSTED QUANTITY	ANNUAL HOLDING COST	ANNUAL ORDER COST	ANNUAL MATERIAL COST	TOTAL COST OF INVENTORY
1	0	24	34.75	5.25	60	24	(24 / 2) * 5.25 = 63	800 / 24 * 12 = 400	800 * 34.75 = 27800	63 + 400 + 27800 = 28263
2	25	99	34	5.25	60	60	(60 / 2) * 5.25 = 157.5	800 / 60 * 12 = 160	800 * 34 = 27200	157.5 + 160 + 27200 = 27518
3	100	199	32.8	5.25	60	100	(100 / 2) * 5.25 = 262.5	800 / 100 * 12 = 96	800 * 32.8 = 26240.	262.5 + 96 + 26240 = 26599
4	200	399	31.6	5.25	60	200	(200 / 2) * 5.25 = 525	800 / 200 * 12 = 48	800 * 31.6 = 25280	525 + 48 + 25280 = 25853
5	400	& MORE	30.5	5.25	60	400	(400 / 2) * 5.25 = 1050	800 / 400 * 12 = 24	800 * 30.5 = 24400	1050 + 24 + 24400 = 25474

VENDOR C

OPTIMAL ORDER QUANTITY = 300

ASSOCIATED COST = 25700

NO.	LOWER LIMIT	UPPER LIMIT	PER UNIT PRICE	HOLDING COST	EOQ	ADJUSTED QUANTITY	ANNUAL HOLDING COST	ANNUAL ORDER COST	ANNUAL MATERIAL COST	TOTAL COST OF INVENTORY
1	0	49	34.5	5.25	60	49	(49 / 2) * 5.25 = 128.63	800 / 49 * 12 = 195.92	800 * 34.5 = 27600	128.63 + 195.92 + 27600 = 27925
2	50	149	33.75	5.25	60	60	(60 / 2) * 5.25 = 157.5	800 / 60 * 12 = 160	800 * 33.75 = 27000	157.5 + 160 + 27000 = 27318
3	150	299	32.5	5.25	60	150	(150 / 2) * 5.25 = 393.75	800 / 150 * 12 = 64	800 * 32.5 = 26000	393.75 + 64 + 26000 = 26458
4	300	& MORE	31.1	5.25	60	300	(300 / 2) * 5.25 = 787.5	800 / 300 * 12 = 32	800 * 31.1 = 24880	787.5 + 32 + 24880 = 25700

VENDOR D

OPTIMAL ORDER QUANTITY = 300

ASSOCIATED COST = 25620

NO.	LOWER LIMIT	UPPER LIMIT	PER UNIT PRICE	HOLDING COST	EOQ	ADJUSTED QUANTITY	ANNUAL HOLDING COST	ANNUAL ORDER COST	ANNUAL MATERIAL COST	TOTAL COST OF INVENTORY
1	0	149	34.25	5.25	60	60	(60 / 2) * 5.25 = 157.5	800 / 60 * 12 = 160	800 * 34.25 = 27400	157.5 + 160 + 27400 = 27718
2	150	299	33	5.25	60	150	(150 / 2) * 5.25 = 393.75	800 / 150 * 12 = 64	800 * 33 = 26400	393.75 + 64 + 26400 = 26858
3	300	& MORE	31	5.25	60	300	(300 / 2) * 5.25 = 787.5	800 / 300 * 12 = 32	800 * 31 = 24800	787.5 + 32 + 24800 = 25620

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