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Math Help - Optimization problems

  1. #1
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    Optimization problems

    Please help!

    I am struggling with this problem.

    I work in a call centre and I'm looking how I can optimise our quota management techniques.

    I would like to minimize the number of dials made, required to achieve our targets, by effective quota management.

    My constraints are as follows:

    (gender)
    Male >= 441
    Female >=459

    (age)
    18-29 >=147
    30-44 >=297
    45-59 >=243
    60-74 >=171

    (social economic class)
    A/B >=207
    C1/C2 >=396
    DE >=231

    total >=1000

    I know how many dials are made and know how the interlocked (male 18-29 AB) quotas fall out.

    I made my objective function to be the number of dials made divided by the number of interviews completed per quota (quotas listed below)

    Men 18-29 ABMen 30-44 ABMen 45-59 ABMen 60-74 ABMen 18-29 C1C2Men 30-44 C1C2Men 45-59 C1C2Men 60-74 C1C2Men 18-29 DEMen 30-44 DEMen 45-59 DEMen 60-74 DEFem 18-29 ABFem 30-44 ABFem 45-59 ABFem 60-74 ABFem 18-29 C1C2Fem 30-44 C1C2Fem 45-59 C1C2Fem 60-74 C1C2Fem 18-29 DEFem 30-44 DEFem 45-59 DEFem 60-74 DE

    I realise that the coefficients to the variables in the objective function will fluctuate. There are 24 variables, I have 368 completes.

    When I use Solver in excel to minimise the objective function, it comes up with a solution and the expected minimising of dials is expected to be 10 times greater than what we currently do.

    I can't see how the small variable chanage would impact so greatly on the optimal solution.

    Can anyone help as to how I can go about tweaking it to make it more efficient?
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  2. #2
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by aftab.baig View Post
    I work in a call centre and I'm looking how I can optimise our quota management techniques.I would like to minimize the number of dials made, required to achieve our targets, by effective quota management.
    Could you define "target"?
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  3. #3
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    I was speaking to a friend and they explained that the problem is my objective function.

    That now leaves me with a whole new problem - what is my objective function.

    I'm going to give the full brief, in order to make it easier to understand.

    Work in a call centre, carrying out surveys with the general public.
    We have quotas to achieve - in this case the quotas are as follows:

    Male >=441
    Female >=459

    18-29 >=147
    30-44 >=297
    45-59 >=243
    60-74 >=171

    AB >=207
    C1C2 >=396
    DE >=231

    Total >=1000

    The quotas interlock, i.e. you can have a Male 45-59 DE or equally Female 19-29 C1C2.

    As it transpires, my objective is to minimise the productive time.

    Productive time = find time + interviewing time

    The interviewing time currently stands at 7.65 minutes per person that we would speak with.

    It is currently taking about 12.92 minutes to find someone to take part. The proportions in which they agree are as below.

    Male 18-29 AB = 1.78%
    Male 30-44 AB = 2.03%
    Male 45-59 AB = 4.82%
    Male 60-74 AB = 4.57%
    Male 18-29 C1C2 = 8.63%
    Male 30-44 C1C2 = 3.55%
    Male 45-59 C1C2 = 6.85%
    Male 60-74 C1C2 = 5.58%
    Male 18-29 DE = 4.06%
    Male 30-44 DE = 1.27%
    Male 45-59 DE = 2.03%
    Male 60-74 DE = 3.05%
    Female 18-29 AB = 2.03%
    Female 30-44 AB = 3.05%
    Female 45-59 AB = 4.57%
    Female 60-74 AB = 2.03%
    Female 18-29 C1C2 = 7.11%
    Female 30-44 C1C2 = 5.08%
    Female 45-59 C1C2 = 8.88%
    Female 60-74 C1C2 = 7.61%
    Female 18-29 DE = 1.78%
    Female 30-44 DE = 1.52%
    Female 45-59 DE = 4.06%
    Female 60-74 DE = 4.06%

    The targets that I set for these interlocked quotas (Male 18-29 AB etc) must result in satisfying the constraints given above (Male >=441 etc).

    Once I hit the target for a given quota, I do not interview them, thus the interviewing time = 0 on that instance (would have been 7.65 minutes), however, the find time still naturally increases.

    So, the question is, what should I set the targets to in order to minimise the productive hours.

    Thanks,
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