Problem No. 1. A company has a large number of machines that break down accordin
ID: 347278 • Letter: P
Question
Problem No. 1. A company has a large number of machines that break down according to the Poisson distribution at the rate of three per hour during an eight hour work day. The company wants to decide between hiring either John or Sally. John can repair machines with an exponential repair time distribution at an average rate of four machines per hour and charges $200 for an eight hour day. Sally can also repair machines with an exponential repair time distribution but with an average rate of six machines per hour She is demanding an outrageous sum of $800 per eight hour work day. If the cost of an idle machine is S50 per hour, which person should be hired ? (Assume that the repair person will be paid regardless of whether s/he is busy or idle .)Explanation / Answer
Arrival rate (breakdown rate), = 3 per hour
John
John's service rate, = 4 per hour
John's cost, Cs = 200/8 = 25 per hour
Machine idle cost, Cw = 50 per hour
Number of machines waiting to be repaired and being repaired, L = /(-) = 3/(4-3) = 3
Total cost per hour = Cs + L*Cw = 25 + 3*50 = $ 175 per hour
Sally
Sally's service rate, = 6 per hour
Sally's cost, Cs = 800/8 = 100 per hour
Machine idle cost, Cw = 50 per hour
Number of machines waiting to be repaired and being repaired, L = /(-) = 3/(6-3) = 1
Total cost per hour = Cs + L*Cw = 100 + 1*50 = $ 150 per hour
Total hourly cost of Sally is lower than John's
Therefore, Sally should be hired
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.