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Math Help - Regarding Maximization problems with multiple constraints.

  1. #1
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    Regarding Maximization problems with multiple constraints.

    Hi All,

    I would like to get insights into methods that could be employed for tackling Maximization Problems that involve multiple constraints. One example would be the optimal usage of elevators in a building. Say, if the Power consumed by the elevator and Customer Dissatisfaction were two factors, and the Efficiency Index would be something like -

    Code:
    E.I = 1/(P.C + C.D)
    
    E.I = Efficiency Index
    P.C = Power Consumed
    C.D = Customer Dissatisfaction
    Assuming that there are a said number of floors and elevators, and with each of these elevators at a particular floor, and people waiting at different floors having different destinations; and we have the factors like Energy Consumption depending on factors like opening/closing of Elevator door or its movement across floors; and the customer dissatisfaction depending on factors like a customer getting serviced, wait time for boarding, halt at a non-destination, what would be the best way to break down these kind of problems??? The motive is to maximize the Efficiency Index.

    Do these kind of problems fall into a particular category? Would appreciate any reference related to mathematical modeling of various real-world problems.

    Thanks
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  2. #2
    Grand Panjandrum
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    Re: Regarding Maximization problems with multiple constraints.

    Quote Originally Posted by mathemagic123 View Post
    Hi All,

    I would like to get insights into methods that could be employed for tackling Maximization Problems that involve multiple constraints. One example would be the optimal usage of elevators in a building. Say, if the Power consumed by the elevator and Customer Dissatisfaction were two factors, and the Efficiency Index would be something like -

    Code:
    E.I = 1/(P.C + C.D)
    
    E.I = Efficiency Index
    P.C = Power Consumed
    C.D = Customer Dissatisfaction
    Assuming that there are a said number of floors and elevators, and with each of these elevators at a particular floor, and people waiting at different floors having different destinations; and we have the factors like Energy Consumption depending on factors like opening/closing of Elevator door or its movement across floors; and the customer dissatisfaction depending on factors like a customer getting serviced, wait time for boarding, halt at a non-destination, what would be the best way to break down these kind of problems??? The motive is to maximize the Efficiency Index.

    Do these kind of problems fall into a particular category? Would appreciate any reference related to mathematical modeling of various real-world problems.

    Thanks
    How are you going to determine the relative importance of PC and CD? If you have an arbitary weighting why employ heavy weight mathematical machinery to optimise an objective which is just a matter of convienience.

    Before you even start with this you need a cost/utility model that allows you to combine the power consumption and customer dis/satisfaction.

    CB
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