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Thread: Permutations and Combinations problem

  1. #1
    Aug 2019

    Permutations and Combinations problem

    I just joined and have a problem that is beyond my maths capability - in fact I don't even know if I am in the right forum so guidance would be appreciated.

    I work in civilian aviation and I am trying to understand the number of combinations or permutations I am grappling with in a tender we are preparing for.

    I have an environment where I need to establish a number of aircraft bases on which I can place anywhere from 1 to 5 aircraft on the base

    I then have another set of factors to apply on top of this such as the base can be open 24/7 or could be open 16 hours per day - has a significant impact on crewing numbers if anyone is interested why

    So in summary the variables are as follows:

    Aircraft Types - 7 Types; must use more than 1 type
    Aircraft supply options : Re-use existing AC which are two of the above types
    : Buy new AC
    : Use a blend of new and re-use
    Total Aircraft Number - Max of 20 aircraft
    Currently 2 aircraft on each of 10 bases but could reduce to a minimum of 6 bases
    Could be 3 aircraft between 2 bases (which means you can have one aircraft on a base but only when next to a base with 2)
    Could have 3 or 4 aircraft on one base but never more than 5
    2 types of Opening times - Ext day or 24/7

    So my question is

    How many combinations or permutation options do I have - I can work through the performance of each solution but I know there will be 000's of solutions

    My guess is an impossible number and I think I need to have a computer model applied to the problem

    I have calculated the 7 types of aircraft deliver 42 permutations and 21 combinations but then how do I layer this into the combinations of bases and then numbers of aircraft across bases and then extended opening or 24/7 opening....if feels like a big nested combination problem and I have no idea how to approach this or how to create the appropriate sets of data.

    Any help gratefully received
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  2. #2
    MHF Contributor
    Nov 2013

    Re: Permutations and Combinations problem

    some questions

    1) does each base accept all types of aircraft, if not, what types does each accept, are there a maximum # of type a base can handle?

    2) how many of each type of aircraft make up the 20 in the fleet

    3) are there types that must have 24/7 service?

    4) can planes of a given type be considered identical
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