Productivity

Question

I need the formula for the following: I have 39 technicians working 8 hours a day. The technicians should be loaded with 4.5 jobs per day, but are currently loaded with 2.4 jobs per day. What is the formula to find available hours?

Answer 1

I'm assuming the 4.5 and 2.4 jobs/day refers to all 39 technicians.

Total work hours: 39*8=312 hours/day

Should be doing 4.5 jobs/day, so they need 312/4.5 = 69.3 hours/job

They are doing 2.4 jobs/day, so they work 69.3*2.4 = 166 hours/day

Available hours: 312-166=146 hours (3.7 hours per technician)

Answer 2

Case 1: 39 technicians, 8 hours per day, 4.5 jobs per day.

 

Total hours = (39)*(8) = 312 man hours

Total jobs = (39)*(4.5) = 175.5 jobs per day

 

Therefore, each job takes 0.5625 hours. [i.e., 0.5625 hours per job)

 

Case 2: 39 technicians, X hours per day, 2.4 jobs per day.

 

We may safely assume that the number of hours to complete one job will remain constant in both cases, so that

 

[(39)*(2.4)]/[(39)*X] = 0.5625

 

[(2.4)/(X)] = 0.5625

 

(0.5625)X = 2.4

 

X = (2.4)/(0.5625) = 4.266 hours per day