Question

Harley Davidson purchases components from three suppliers. Components purchased from Supplier A are priced at $ 5 each and used at the rate of 206700 units per year. Components purchased from Supplier B are priced at $ 4 each and are used at the rate of 25,000 units per year. Components purchased from Supplier C are priced at  $ 5 each and used at the rate of 10,000 units per year. Currently Harley purchases a separate truckload from each supplier. As part of its JIT drive, Harley has decided to aggregate purchases from the three suppliers. The trucking company charges a fixed cost of $ 400 for the truck with an additional charge of $100 for each stop. Thus, if Harley asks for a pickup from only one supplier, the trucking company charges $ 500; from two suppliers it charges $ 600; and from three suppliers it charges $ 700. Harley incurs a holding cost of 20% (of the price) for each component. What is the minimal annual inventory cost of the new aggregate replenishment strategy ?  What is the minimal annual inventory cost of the Harley’s current strategy of ordering separately from each supplier ? How much is the saving resulted ? PLEASE SHOW WORK

Answer 1

Supplier A	Supplier B	Supplier C
DA = 206,700	DB = 25,000	DC = 10,000
S = 500	S = 500	S = 500
CA = 5	CB = 4	CC = 5
H = .2	H= .2	H = .2

Minimal annual inventory cost of new aggregate replenishment strategy:

S* = S + SA + SB + SC = 400 + 100 + 100 + 100 = 700

Optimal joint order frequency:

N* = SQRT((206700*0.2*5 + 25000*0.2*4 + 10000*0.2*5)/(2*700)) = 13

Order quantities corresponding to N*:

QA = DA/N* = 206700/13 = 15,900

QB = DB/N* = 25,000/13 = 1923.08

QC = DC/N* = 10,000/13 = 769.23

Holding and order cost:

A = (QA/2)hC = (15,900/2)*0.2*5 = 7950

B = (QB/2)hC = (1923.08/2)*0.2*4 = 769.23

C = (QC/2)hC = (769.23/2)*0.2*5 = 384.62

Total holding cost = 7950 + 769.23 + 384.62 = 9103.85

Total order cost = N*S* = 13*700 = 9,100

Total cost = total holding cost + total order cost = 9103.85+9100 = $18,203.85

Minimal annual inventory cost of current strategy:

	Supplier A	Supplier B	Supplier C
Demand per year	206700	25,000	10,000
Fixed cost/order	500	500	500
Optimal order size	14,377 SQRT=((2*206700*500)/(0.2*5))	5590 SQRT=((2*25000*500)/(0.2*4))	3,162 SQRT=((2*10000*500)/(0.2*5)
Order frequency	14.38/year (206,700/14,377)	4.47/year (25,000/5590)	3.16/year (10,000/3,162)
Annual cost	14,377 (206,700/14377)500 + (14,377/2)(.2)(5)	4,472 (25000/5590)500 + (5590/2)(.2)(4)	3,162 (10000/3162)500 + (3162/2)(.2)(5)

Total cost = 14,377 +4,472+ 3,162 = $22,011

Harley would save $22,011 - $18,203.85 = $3,807.15

Note : I took approximations in between, but the whole procedure is correct. Please go through everything.