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November 26th, 2008, 05:37 PM   #1
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Permutation or Combination

Please help me solve this problem for work. I run a maintenance and operation department for a water district and I am trying to figure out how many different possibilities I have for organizing my work force each day.

Each day I have 6 tasks to complete. Each task requires: 1 foreman, 1 equipment operator, and 2 laborers. I have 6 foreman, 6 operators, and 12 laborers to choose from. How many different ways are there to set up the crews?

I use 6! for the foreman (720) and 6! for the operators (720). So for just the foreman and the operators there are 518,400 different ways to set them up to complete the six tasks. But I do not know how to handle the laborers and how that is factored into the total number of options.

Thank you in advance.
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November 27th, 2008, 06:00 PM   #2
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Re: Permutation or Combination

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Originally Posted by mainetriguy
Please help me solve this problem for work..
You'd convince me better if you'd name the specific tasks and the specific duties of each worker [I've worked in that environment, and no of no six tasks requiring the same number in the crew in the same proportions.] If I then believe that they demand this sort of analysis these days, I might be able to offer some help. But I do not do homework.

Dave.
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November 28th, 2008, 02:19 AM   #3
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Re: Permutation or Combination

I work for a 100 year old water district...we just celebrated our centennial. And they have some 100 year old habits. Send a four people to each job. Foreman with a crew truck and a compressor, an operator with a backhoe, and one laborer with a 7 yard dump and another with a wheeler. There are no assigned crews and work is scheduled day by day. In addition, every job was considered a one day job, whether they are replacing a curb stop and setting it back to street line, renewing a service, re-packing a valve, retiring a service, fixing a leak, or installing a fire hydrant. I plan to use the answer to this question to show the staff that the current structure (or lack of structure) creates thousands (or millions) of different combinations of crews every day. It is an over simplified question, but will be delivered to the crews exactly as I asked it here. I am trying to drive home the point that we need to begin restructuring our approach to the way we schedule, plan, assign and package our work in order to become more efficient.
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November 28th, 2008, 04:10 AM   #4
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Re: Permutation or Combination

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Originally Posted by mainetriguy
I work for a 100 year old water district...we just celebrated our centennial.
Good enough. Then the solution is not as complex as you have made it to be. It is simply 1x1x2x6x6x12 = 864.

I'm still curious as to why you would want the end result. Having obtained it, how would you then schedule? Do you intend to actually set up all of these work schedules? If so, a spreadsheet might come in handy.

I'd be cautious about giving such information to the work crews who would not understand the implications, not likely care. I just can't picture the average guy leaning on the end of a shovel contemplating the number of ways he can do any specific job.
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November 28th, 2008, 07:29 AM   #5
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Re: Permutation or Combination

I plan to introduce the winter crew structure on Monday. This is my first year with this district. Needless to say, I have put a lot of thought into this structure. I have a reason for how I place each individual based on many factors including attitude and ability. These guys are ruthless know it alls. It is the most "old school" culture I have ever encountered. No matter how I set up the crews, I have guys asking me: why do I have to go with him, why don't I get to go on leaks, why don't I get the jobs with overtime, why are you sending me with that crew, why does he always get to operate the big excavator, this is not fair, he's a jerk can't I go with someone else...etc. It is insane. I am trying to give them a sense of how many different options there are and you are not always going to get what you want. I am basically trying to find a professional way to say "this is how it is, deal with it." I want them to understand that it is not as easy as they think...there are not just 6 different ways to look at it...there are over 800. They can't argue with numbers...so I want to use some numbers to use.
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