Question

H purchases components from three suppliers. Components purchased from A are priced at $4.5 each and used at the rate of 20,000 units per year. Components purchased from B are priced at $5 each and are used at the rate of 3,500 units per year. Components purchased from C are priced at $4.7 each and used at the rate of 1,000 units per year. Currently, H purchases a separate truckload from each supplier. As part of its JIT drive, H has decided to aggregate purchases from the three suppliers. The trucking company charges a fixed cost of $550 for the truck with an additional charge of $80 for each stop. Thus, if H asks for a pickup from only one supplier, the trucking company charges $630; from two suppliers, it charges $710; and from three suppliers, it charges $790. Suggest a replenishment strategy (lots ordered independently or jointly?) for Harley that minimizes annual cost. Assume a holding cost of 25% per year.

Answer 1

A replenishment strategy where lots are ordered jointly minimizes annual cost.

Component A		Component B		ComponentC
Demand, Da	20000	Demand, Db	3500	Demand, Dc	1000
Shipping pickup, S = Fixed cost (550) + one stop (80)	$             630.00	Shipping pickup, S	$         630.00	Shipping pickup, S	$       630.00
Price	$                  4.50	Price	$             5.00	Price	$            4.70
Holding cost, Ha	$                1.125	Holding cost, Hb	$             1.00	Holding cost, Hc	$            0.94
(25% of the price)		(25% of the price)		(25% of the price)
EOQ = Sqrt(2DS/H)	4732.86	EOQ	2100.00	EOQ	1157.77
Current Strategy - Ordered individually
Cycle inventory = D/EOQ	4.23		1.67		0.86
Inventory cost = (EOQ*H)/2	$          2,662.24	Inventory cost = (EOQ*H)/2	$     1,050.00	Inventory cost = (EOQ*H)/2	$       544.15
Order cost = (D/EOQ) * 500	$          2,662.24	Order cost = (D/EOQ) * 500	$     1,050.00	Order cost = (D/EOQ) * 500	$       544.15
Total inventory cost current strategy= 2662.24+1050+544.15	$       4,256.390
Total order cost current strategy	$       4,256.390
Total cost Current strategy	$          8,512.78	(4256.39+4256.39)
New Shipping cost, Sn = 790	$             790.00
Optimal joint order frequency, N
n* = SQRT((DAHa + DBHb + DcHC)/(2S*))
DAHa + DBHb + DcHC =	26940
2S	1,580.00
n*= sqrt (26940/1580)	4.13
Order Quantity for A, Qa = Da/n*	4843.50	Order Quantity for B, Qb = Db/n*	847.61	Order Quantity for C, Qc = Dc/n*	242.18
Inventory cost = (Q*H)/2	$          2,724.47	Inventory cost = (Q*H)/2	$         423.81	Inventory cost = (Q*H)/2	$       113.82
Total inventory cost new strategy	$          3,262.10
Total order cost new strategy= 790*4.13	$          3,262.10
		Saving in Inventory cost	$         994.29
		Saving in ordering cost	$         994.29
		Total Savings	$     1,988.58