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 1,100 valves; order cost is $13 per order; and annual inventory holding costs are $7.55 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 (enter your response as a whole number).

Answer 1

VENDOR A IS THE BEST CHOICE WITH OPTIMAL ORDER QUANTITY = 100 UNITS AND TCI OF 34786

VALUES

DEMAND = 1100

ORDERING COST = 13

HOLDING COST = 7.55

THEORY

EOQ = SQRT(2 * DEMAND * ORDERING COST / HOLDING COST)

Q* = ADJUSTED QUANTITY BETWEEN THE UPPER AND LOWER LIMIT AND THE EOQ

AHC = ANNUAL HOLDING COST = (Q* / 2) * HOLDING COST PER UNIT

AOC = ANNUAL ORDERING COST = (DEMAND / Q*) * ORDERING COST

APC = ANNUAL PURCHASING COST = DEMAND * Q*

TCI = TOTAL COST OF INVENTORY = AHC + AOC + APC

VENDOR A

NO.	LOWER LIMIT	UPPER LIMIT	PER UNIT	HOLDING COST	EOQ	Q*	AHC	AOC	APC	TCI
1	1	14	35	7.55	62	14	(14 / 2) * 7.55 = 52.85	(1100 / 14) * 13 = 1021.43	1100 * 35 = 38500	52.85 + 1021.43 + 38500 = 39574.28
2	15	24	34.75	7.55	62	24	(24 / 2) * 7.55 = 90.6	(1100 / 24) * 13 = 595.83	1100 * 34.75 = 38225	90.6 + 595.83 + 38225 = 38911.43
3	25	99	33.55	7.55	62	62	(62 / 2) * 7.55 = 234.05	(1100 / 62) * 13 = 230.65	1100 * 33.55 = 36905	234.05 + 230.65 + 36905 = 37369.7
4	100	99	32.35	7.55	62	100	(100 / 2) * 7.55 = 377.5	(1100 / 100) * 13 = 143	1100 * 32.35 = 35585	377.5 + 143 + 35585 = 36105.5
5	100	399	31.15	7.55	62	100	(100 / 2) * 7.55 = 377.5	(1100 / 100) * 13 = 143	1100 * 31.15 = 34265	377.5 + 143 + 34265 = 34785.5
6	400	& MORE	30.75	7.55	62	400	(400 / 2) * 7.55 = 1510	(1100 / 400) * 13 = 35.75	1100 * 30.75 = 33825	1510 + 35.75 + 33825 = 35370.75

OPTIMAL ORDER QUANTITY = 100

TOTAL COST OF INVENTORY = 34786

VENDOR B

NO.	LOWER LIMIT	UPPER LIMIT	PER UNIT	HOLDING COST	EOQ	Q*	AHC	AOC	APC	TCI
1	1	24	34.75	7.55	62	24	(24 / 2) * 7.55 = 90.6	(1100 / 24) * 13 = 595.83	1100 * 34.75 = 38225	90.6 + 595.83 + 38225 = 38911.43
2	25	99	34	7.55	62	62	(62 / 2) * 7.55 = 234.05	(1100 / 62) * 13 = 230.65	1100 * 34 = 37400	234.05 + 230.65 + 37400 = 37864.7
3	100	199	32.8	7.55	62	100	(100 / 2) * 7.55 = 377.5	(1100 / 100) * 13 = 143	1100 * 32.8 = 36080	377.5 + 143 + 36080 = 36600.5
4	200	399	31.6	7.55	62	200	(200 / 2) * 7.55 = 755	(1100 / 200) * 13 = 71.5	1100 * 31.6 = 34760	755 + 71.5 + 34760 = 35586.5
5	400	& MORE	30.5	7.55	62	400	(400 / 2) * 7.55 = 1510	(1100 / 400) * 13 = 35.75	1100 * 30.5 = 33550	1510 + 35.75 + 33550 = 35095.75

OPTIMAL ORDER QUANTITY = 400

TOTAL COST OF INVENTORY = 35096

VENDOR C

NO.	LOWER LIMIT	UPPER LIMIT	PER UNIT	HOLDING COST	EOQ	Q*	AHC	AOC	APC	TCI
1	1	49	34.5	7.55	62	49	(49 / 2) * 7.55 = 184.98	(1100 / 49) * 13 = 291.84	1100 * 34.5 = 37950	184.98 + 291.84 + 37950 = 38426.81
2	50	149	33.75	7.55	62	62	(62 / 2) * 7.55 = 234.05	(1100 / 62) * 13 = 230.65	1100 * 33.75 = 37125	234.05 + 230.65 + 37125 = 37589.7
3	150	299	32.5	7.55	62	150	(150 / 2) * 7.55 = 566.25	(1100 / 150) * 13 = 95.33	1100 * 32.5 = 35750	566.25 + 95.33 + 35750 = 36411.58
4	300	& MORE	31.1	7.55	62	300	(300 / 2) * 7.55 = 1132.5	(1100 / 300) * 13 = 47.67	1100 * 31.1 = 34210	1132.5 + 47.67 + 34210 = 35390.17

OPTIMAL ORDER QUANTITY = 300

TOTAL COST OF INVENTORY = 35390

VENDOR D

NO.	LOWER LIMIT	UPPER LIMIT	PER UNIT	HOLDING COST	EOQ	Q*	AHC	AOC	APC	TCI
1	1	149	34.5	7.55	62	62	(62 / 2) * 7.55 = 234.05	(1100 / 62) * 13 = 230.65	1100 * 34.5 = 37950	234.05 + 230.65 + 37950 = 38414.7
2	150	299	33.75	7.55	62	150	(150 / 2) * 7.55 = 566.25	(1100 / 150) * 13 = 95.33	1100 * 33.75 = 37125	566.25 + 95.33 + 37125 = 37786.58
3	300	& MORE	32.5	7.55	62	300	(300 / 2) * 7.55 = 1132.5	(1100 / 300) * 13 = 47.67	1100 * 32.5 = 35750	1132.5 + 47.67 + 35750 = 36930.17

OPTIMAL ORDER QUANTITY = 300

TOTAL COST OF INVENTORY = 36930