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Math Help - Resource Allocation Problem

  1. #1
    Newbie
    Joined
    Jun 2008
    Posts
    5

    Resource Allocation Problem

    Hi Folks,

    This is an interesting problem.
    I have been thinking about how to do it for a few days.

    I would like to calculate a probable time to arrive at work based on a resource list and the number of initial customer cases.

    Each morning we come into work, there is a list (from 0 to M) of employees/resources who will handle customer cases.
    R1=John
    R2=Steve
    R3=Frank
    R4=Joel
    etc

    There is an initial number of cases to be handled immediately i.e. Cinitial (from 0 to N), and then new cases come in at random intervals.

    Each case gets assigned to a resource based on the order of the resource list. When a resource has finished handling a case, they go back onto the bottom of the list.

    So if Cinitial = 2 cases, then John and Steve will be occupied handling the cases immediately at 9am. Frank and Joel will be waiting around for new cases to randomly arrive.

    I am able to get statistics for each day - the number of initial cases at 9am, the times the new cases come in (and therefore the times resources 0 to M) are needed, and the total number of new cases during the day.


    What would be interesting to calculate - based on Cinitial, what time is most likely for R(x) to be needed? (R(x) could sleep in a little and not need to get to work at 9am).

    Then we ask the question sometime during the day instead of in the morning - there was Cinitial cases at the start of the day, Cnew cases have come in, it is now Time t>9am , what is the probable time R(x) is needed?


    Your ideas are appreciated on how to work out this problem / what models are needed.
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  2. #2
    Newbie
    Joined
    Jun 2008
    Posts
    5

    Re: Resource Allocation Problem

    My guess..

    T(R_x) = time in mins past 9am resource R_x is needed at work.
    C_i = Cinitial initial cases at start of the day
    F = function F that returns probable assignment of case based on the number of resources not currently assigned

    If C_i \geq R_x \text then T(R_x)=0

    C_i < R_x then T(R_x)=F(R_x - C_i)

    How do I use the statistics I have to make function F?
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