Rylon Corporation is an assembler of electrical components. The company estimate
ID: 469053 • Letter: R
Question
Rylon Corporation is an assembler of electrical components. The company estimates that for the next year, the demand will be 800 units. The company is performing on an 80 percent learning curve. The company is considering purchasing some assembly machinery to acceler- ate the assembly time. Most assembly activities are 85–90 percent labor intensive. However, with the new machinery, the assembly activities will be only 25–45 percent labor intensive. If the company purchases and installs the new equipment, it will occur after the 200th unit is pro- duced. Therefore, the remaining 600 units will be produced with the new equipment. The 200th unit will require 620 hours of assembly. However, the 201st unit will require only 400 hours of assembly but on a 90 percent learning curve. 1) Will the new machine shorten product assembly time for all 800 units and, if so, by how many hours? Explain how you arrived at your answer. 2) If the company is burdened by $70 per hour, and the new equipment is depreciated over five years, what is the most money that the company should pay for the new equipment? What assumptions have you made? Explain how you arrived at your answer.
Explanation / Answer
Up to 200 units, assembly activities are 85 to 90 percent labor intensive, or 87.5% [=(85 + 90)/2] labour intensive. which means, labor time for 200th unit = 620*0.875 = 542.5 hours, Machine time = 620 - 542.5 = 77.5 hours.
Only labor time is changed as per learning curve, machine time remains fixed.
Labor time required to assemble 200th unit = 620*0.875 = 542.5 hours
Learning Curve = 80%
Therefore labor time required to produce first unit = 542.5 / 0.8^(LN(200)/LN(2)) = 2986.5 hours
As per existing process, total labor time required to produce the first 200 units as per existing process = 156987 hours
As per existing process, total labor time required to produce the first all the 800 units as per existing process = 406703 hours.
Therefore, labor time required to produce last 600 units = 406703 - 156987 = 249716 hours
Total time (labor + machine) required to produce last 600 units = 249716 + 77.5*600 = 296216 hours
New process
201st unit takes 400 hours, and assembly activity is only 25 to 45% labor intensive or on an average 35% [=(25+45)/2] labor intensive.
Labor time for 201st unit = 400*35% = 140 hours , machine time = 400 - 140 = 260 hours
On a 90% learning curve, cumulative labor time required to produce 600 units = 37334 hours , calculaed as below
total machine time required to produce 600 units = 260*600 = 156000 hours
Total time required (including machine time and labor time) to produce 600 units = 37344 + 156000 = 193344 hours
New machine will shorten the assembly time by = 296216 - 193344 = 102872 hours
Time required to produce 1st unit = 2987 Learning rate = 0.8000 Total Number of units to be produced (X) = 800 Using Crawford's formula Yc = XY = aXKb K = [L(1+b)/(N21+b - N11+b)]-1/b = 244.7128 where: K = the algebraic midpoint of the lot. a = time (or cost) required to produce the first unit. 2987 X = Total Number of Units 800 L = the number of units in the lot. 800 b = log of learning rate / log of 2 -0.3219 N1 = the first unit in the lot minus 1/2. 0.5 N2 = the last unit in the lot plus 1/2. 799.5 Total Time required to produce 800 units = 406702.47Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.