In: Operations Management
Part A Harley Davidson has its engine assembly plant in Milwaukee and its motorcycle assembly plant in Pennsylvania. Both plants run 365 days a year. Engines are transported from the Milwaukee plant to the Pennsylvania plant using trucks. Each truck trip costs $1,500. The motorcycle plant assembles and sells 300 motorcycles each day. Each engine costs $450 and Harley incurs a holding cost of 20 percent per year. How many engines should Harley load onto each truck? What is the cycle inventory of engines at Harley? What is the annual total inventory cost?
Part B Harley has decided to implement just-in-time (JIT) at the motorcycle assembly plant. As part of this initiative it has reduced the number of engines loaded on each truck to 100. If each truck trip still costs $1,500, how does this decision impact on the annual total inventory cost? What should the cost of each truck trip be if a load of 100 engines is to be optimal for Harley?
Part A
Annual demand, D = 300*365 = 109500
Trip cost, K = 1,500 per trip
Unit cost, C = $450
Unit carrying cost, h = 20% of C = $90 per annum
So, optimal shipping quatity per truck, Q = (2.D.K / h)1/2 = SQRT(2*109500*1500/90) = 1,911 engines
Average cycle stock inventory = Q/2 = 955 engines
Total cost of inventory = (D/Q)*K + (Q/2)*h = (109500/1911)*1500 + 955*90 = $171,900
Part B
Q = 100
Total cost of inventory = (D/Q)*K + (Q/2)*h = (109500/100)*1500 + (100/2)*90 = $1,647,000
So, there will be an ncrease in inventory cost from 171,900 to 1,647,000 i.e. $1,475,100
100 = (2*109500*K / 90)1/2
or, 10000 = 2*109500*K / 90
or, K = 10000*90 / (2*109500)
or, K = 4.11
So, Q=100 to become optimal, the trip cost should be as less as $4.11 per trip.