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Job Completion Problems Math Review #1 --
Calculating One Person's Productivity, and Some Words on Units
by Crystal Sloan 

Home  --- Resources --- Job Completion Problems Math Review.
See also: Job Completion Math Review #2, #3

Job Completion Problem Math Review #1


Given total amount of work done by one worker, and the time spent to do it, determine that worker's productivity: 

Productivity = amount of work done per unit time 
Productivity = total work done / total time worked

  1. Productivity is work performed per unit time.  Every 3 hours, Worker Joe builds another 6 units of Product A.  What is the worker's productivity, that is, how many units of Product A can the worker build in one hour on the average?  Answer: To find productivity (always measured in units of work per unit of time), divide the total units produced (the amount of work performed) by the time it took to do it.  Here, divide 6 units by 3 hours to get a productivity of 6/3 units of A/hour = 2 units of A/hour.  This figure means that the worker can make an average of 2 units of Product A in one hour.
  2. The above calculation will work even if the amount of work done is less than the number of hours worked.  For example, if the worker makes 5 units of Product B every 8 hours, the worker's productivity is 5 units of B/8 hours = 5/8 units of B/hour or alternatively 0.625 units of B/hour. Here the worker makes only a little more than half of one unit of Product B in an hour.  It is OK for the productivity value to be less than 1.  This just means that it takes more than one unit of time to perform that much work.
  3. Be aware at all times of the units you are using in your calculations.  The units of work being compared need to match, or you will be comparing apples and oranges. For example, if Worker Joe makes 6 units of Product A in 3 hours, and Worker Bob makes 7 units of Product B in 3 hours, what does that tell us about which worker is faster?  The answer is: not much, unless we know figures on how much work is involved in making Product A versus making Product B.

    Time units must match in your calculations, too.  If one productivity value is "work per hour" and another is "work per 8-hour day" or "work per month" or "work per minute," you will need to convert the units to match in order to compare  the two values.  For example, if Worker Joe makes 6 units of Product A in 3 hours--a productivity of 2 units of A/hour--and Worker Bob makes 24 units of Product A in each (8-hour) work day--a productivity of 24 units of A/day, which worker has a higher productivity?  To answer the question, convert one productivity value to the units of the other.  It does not matter which you convert, as long as your end result is two values using identical units.  Let us arbitrarily decide to convert Worker Bob's 24 units of A/day to units of A/hour: 24 units of A/day = 24/8 units of A/hour = 3 units of A/hour.  Worker Bob is doing 3 units of A/hour to Worker Joe's 2 units of A/hour, leaving Joe in the dust. 
  4. Never forget to keep track of the units you are using in your calculations.  As a project manager you may be presented with productivity figures and estimates using many different time units: seconds, minutes, hours, days, weeks, months, even years.  You will need to be able to convert freely from one time unit to another.  More will be mentioned about this in future sessions.  

    Tip: One key to success in all job completion problems is to always "know your units."  As you work each problem, don't just write down the numeric values, always write down the units for each value, in every step.  If you keep the units making sense, accurate  values will tend to follow.

Want more? See also: Job Completion Math Review #2

(This was written to graduate students in a Systems Development and Project Control class at the University of Maryland, University College, near the start of the term, but the information applies to anyone going into project management.)

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