Question

Pegasus Motors Corp. has its engine assembly plant in Milwaukee and its motorcycle assembly plant in Pittsburgh. Engines are transported using trucks from Roadway Inc, which costs $4,000 per trip. The motorcycle plant opens 50 weeks a year and 5 days a week. Each business day the plant produces 800 motorcycles. The holding cost for each engine is $100 per year. (4 points) a. How often should Pegasus transport engines and in what quantity? b. Supercheap Inc. offered to transport engines for Pegasus with the following pricing policy: for each trip a fixed $1,000 is charged; if the amount of engines transported is more than 2,500 then each additional engine is charged an extra S3. Wll Pegasus save money by using Supercheap Inc.? If yes, how much can Pegasus save?

Answer 1

(a) Production Quantity D = 800*50*5 = 200000/year

Transport Cost = C_o = $4000

Holding Cost = C_c = $100/year

Economic Transport Quantity Q* = √(2DC_o/C_c) = √(2*200000*4000/100) = 4000

Number of Transports in an year = 200000/4000 = 50

Days between transports = (50*5) / 50 = 5

Hence the transports are done every 5 days and the transportation quantity is 4000

(b) If Q* = 4000,

Total Annual Cost = Annual Inventory Holding Cost + Annual Transport Cost = (Q*/2)*C_c + (D/Q*) C_o = (4000/2)*100 + (200000/4000)*4000 = $400000

If C_o = $1000, Economic Transport Quantity Q* = √(2DC_o/C_c) = √(2*200000*1000/100) = 2000

=> Total Annual Cost = Annual Inventory Holding Cost + Annual Transport Cost = (Q*/2)*C_c + (D/Q*) C_o = (2000/2)*100 + (200000/2000)*1000 = $200000

Hence, amount saved = 400000 - 200000 = $200000