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Optimization problem with POISSON formula

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    Optimization problem with POISSON formula

    Hello, i have an optimization problem, it is about an airplane with a total number of 180 seats. Seat one is business class, and seat 2 is economy. The demand of seat two is 180, so always enough. The demand for seat 1 is with a poission distrubution with average of 32. Price of seat 1 is 510 price of seat 2 is 140.
    I already got this in my excel, and I know i should use the solver to optimize the total profit. But I don't know how to make a variable with poisson that can be changed by the solver.
    Thanks in advance!
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    Re: Optimization problem with POISSON formula

    @Konesmeijer

    Welcome on the forum.

    You get better help if you add an excel file, without confidential information.

    Please also add the desired result.
    Notice my main language is not English.

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    Re: Optimization problem with POISSON formula

    airline seats.xlsx
    This is the file, I would like to have the maximum profit, and to know what amount of seat 1 has te be sold.

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    Re: Optimization problem with POISSON formula

    The demand for seat 1 is with a poission distrubution with average of 32.

    Explain this in other words, since I don't understand it.

    In your file, I don't see manualy added the desired (expected) result.

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    Re: Optimization problem with POISSON formula

    The demand for seat 1 is poison distributed with an average of 32 seats. The question is, how much seats of seat 1 should be reservated for the profit to be maximum. Since the demand for seat 1 is via the poison distribution, there is a certain chance of filling x seats. It's my job to find out how many seats should be reservated.
    I hope you understand it better now.
    Thanks for your help!

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    Re: Optimization problem with POISSON formula

    I get no good translation on the word poison.

    But the profit is maximum is you can sell all chairs of seat (since the profit on that chair 1 is higher than chair 2).

    And also you don't answer the question, what you expect to be the maximum profit.

    If you know the rules how this is calculated, members of the forum can help you finding the right formula.

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    Re: Optimization problem with POISSON formula

    with poisson I mean the mathematical poisson distribution, maybe this is more of a mathematical question than a directly excel related one.

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    Re: Optimization problem with POISSON formula

    If this is more of a math question, I might start with something like http://en.wikipedia.org/wiki/Poisson_distribution to understand the properties of the Poisson distribution.

    In Excel, there is the =POISSON.DIST() function https://support.office.com/en-us/art...3-7772695d9636 Once you understand how to use the Poisson distribution for this kind of problem, then the worksheet function should make implementation relatively easy.

    I'm not sure if I can be of much more help. I'm not enough of a statistician to know what should go into "x" and what should go into "mean".
    Quote Originally Posted by shg
    Mathematics is the native language of the natural world. Just trying to become literate.

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    Re: Optimization problem with POISSON formula

    Seems to me like there's something missing, like the tradeofff between the total number of seats and the number of business seats, which occupy more space.

    If the airline chose to, it could alwys fill all open business seats with coach passengers, no?
    Last edited by shg; 01-08-2015 at 05:25 PM.
    Entia non sunt multiplicanda sine necessitate

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