Supply Chain Management: Study Notes
SYST 4050 Supply Chain Management – Homework 5
1. Harley Davidson has its engine plant in Milwaukee and its motorcycle assembly plant in Pennsylvania. Engines are transported between the two plants using trucks, with each trip costing $1,000. The motorcycle plant assembles and sells 3000 motorcycles a year. Each engine costs $500, and Harley incurs uses holding cost of 20 percent.
a) How many engines should Harley load onto each truck (i.e. what is the optimal order quantity)?
D = 3,000
S = 1,000
C = 500 h = 0.2
Q* = SQRT((2DS)/(hC)) = SQRT((2*3000*1000)/(0.2*500)) = SQRT(6000000/100) = 244.979
b) What is the corresponding optimal order frequency?
n* = D/Q* = 3000/244.979 = 12.247
c) What is the cycle inventory of engines at Harley?
Cycle inventory = Q*/2 = 244.979/2 = 122.474
d) What is the corresponding total cost (holding and ordering cost only – do not include material cost)?
Total Cost (TC) = Ordering Cost (OC) + Holding Cost (HC)
= (D/Q*)S + (Q/2)hC = (3000/244.979)*1000 + (244.979/2)*0.2*500
= 12,474.45 + 12,474.45 = 24,494.90
e) If order quantities must be in units of 150, how many engines should Harley ship at a time to minimize total cost (compare the two quantities in units of 150 that are closest to the optimal order quantity)?
Q* = 244.979, hence try Q = 150 and Q = 300.
TC(Q=150) = (D/Q*)S + (Q/2)hC = (3000/150)*1000 + (150/2)*0.2*500 = 20,000 + 7,500 = 27,500
TC(Q=300) = (D/Q*)S + (Q/2)hC = (3000/300)*1000 + (300/2)*0.2*500 = 10,000 + 15,000 = 25,000
Taking Q= 300 minimizes cost.
f) What should the order cost be if a load of 300 engines is to be optimal for Harley?
Given that Q = SQRT((2DS)/(hC)). In order to find S, we bring it to the left hand side
S = (hC(Q*2))/(2D) = ((0.2*500*(3002))/2*3000) = $1,500.00
g) If demand, and thus production, for Harley motorcycle grows, but all other input data remain unchanged. Would you expect cycle inventory of engines at Harley to increase or
1. Harley Davidson has its engine plant in Milwaukee and its motorcycle assembly plant in Pennsylvania. Engines are transported between the two plants using trucks, with each trip costing $1,000. The motorcycle plant assembles and sells 3000 motorcycles a year. Each engine costs $500, and Harley incurs uses holding cost of 20 percent.
a) How many engines should Harley load onto each truck (i.e. what is the optimal order quantity)?
D = 3,000
S = 1,000
C = 500 h = 0.2
Q* = SQRT((2DS)/(hC)) = SQRT((2*3000*1000)/(0.2*500)) = SQRT(6000000/100) = 244.979
b) What is the corresponding optimal order frequency?
n* = D/Q* = 3000/244.979 = 12.247
c) What is the cycle inventory of engines at Harley?
Cycle inventory = Q*/2 = 244.979/2 = 122.474
d) What is the corresponding total cost (holding and ordering cost only – do not include material cost)?
Total Cost (TC) = Ordering Cost (OC) + Holding Cost (HC)
= (D/Q*)S + (Q/2)hC = (3000/244.979)*1000 + (244.979/2)*0.2*500
= 12,474.45 + 12,474.45 = 24,494.90
e) If order quantities must be in units of 150, how many engines should Harley ship at a time to minimize total cost (compare the two quantities in units of 150 that are closest to the optimal order quantity)?
Q* = 244.979, hence try Q = 150 and Q = 300.
TC(Q=150) = (D/Q*)S + (Q/2)hC = (3000/150)*1000 + (150/2)*0.2*500 = 20,000 + 7,500 = 27,500
TC(Q=300) = (D/Q*)S + (Q/2)hC = (3000/300)*1000 + (300/2)*0.2*500 = 10,000 + 15,000 = 25,000
Taking Q= 300 minimizes cost.
f) What should the order cost be if a load of 300 engines is to be optimal for Harley?
Given that Q = SQRT((2DS)/(hC)). In order to find S, we bring it to the left hand side
S = (hC(Q*2))/(2D) = ((0.2*500*(3002))/2*3000) = $1,500.00
g) If demand, and thus production, for Harley motorcycle grows, but all other input data remain unchanged. Would you expect cycle inventory of engines at Harley to increase or