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    I can never tell which row/column to delete in the two person zero-sum matrices! Any advice in how to tell which one dominates which?


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    Has anyone noticed how question 7 in the June 2010 paper isn't on the mark scheme?


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    (Original post by kashagupta)
    I can never tell which row/column to delete in the two person zero-sum matrices! Any advice in how to tell which one dominates which?


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    It depends whether you are looking from player A's perspective or player B's perspective. Let's take this matrix I found on google as an example.

    Attachment 219591

    Consider player A:

    Look at the outcomes for A plays 1 and A plays 3. You should notice that A1 always has a better outcome than A3.

    If B plays 1: +3 > -4.
    If B plays 2: -2 > -3.
    If B plays 3: +2 > +1.

    So if they ask you to reduce a matrix by domination, you just have to do it by observation really and look at pairs of rows where one value is always bigger than the other. All 3 have to be bigger for the domination argument to work. If one of them was smaller then the row does not dominate, because clearly there is one option that B could play where the other row would result in a better outcome.

    Consider player B:

    This is a similar idea, but you just have to remember that the matrix is represent from A's perspective, so we are looking at B's losses here. Therefore, we want the payoffs to be as small as possible.

    Look at B plays 2, and B plays 3. Again you should hopefully notice, B2 is always less than B3, so B2 dominates because the losses are minimised.

    If A plays 1: -2 < +2
    If A plays 2: 0 < +4
    If A plays 3: -3 < +1

    B2 dominates because the losses are always less in B2 than in B3. So its a similar sort of idea to player A's perspective but we are looking at losses instead, so these are to be minimised.

    I hope this helps!
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    (Original post by kashagupta)
    Has anyone noticed how question 7 in the June 2010 paper isn't on the mark scheme?


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    You must have downloaded an incomplete copy, here's a full one
    Attached Images
  1. File Type: pdf 10 June D2 mark scheme.pdf (271.8 KB, 46 views)
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    (Original post by Arsey)
    it is because if player X? is playing safe then his best option is to pick the highest point of the lowest lines, which in this case is where Y2 and Y3 meet. Therefore, Y should not play Y1.

    Where is this question from?
    On the game theory linear programming formulating questions, could they tell us a specific method we have to use, or do we only need to know one of the methods?
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    Anyone got any tips of what might come up on this paper?

    I'm thinking there might be some annoying definitions in there, since we haven't had those for a while.

    Hoping for a dynamic programming question on a graph, instead of a table. We might also get linear programming on game theory?

    By the way, is it common practice for Edexcel to help us out a bit on the dynamic programming questions? By usually starting off the table or something or telling us what state/stage/action actually is in the table headings, like on the last paper? That would make my life a bit easier :s
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    I think it is common that they start the table off, however last years paper was a bit hideous if you hadn't practiced enough. Was a paragraph, no table no graph and they didn't start us off. So I think this year the dynamic programming will be easier. Im hoping there isn't going to be a huge constraint or game theory question.
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    (Original post by Caramelapps)
    I think it is common that they start the table off, however last years paper was a bit hideous if you hadn't practiced enough. Was a paragraph, no table no graph and they didn't start us off. So I think this year the dynamic programming will be easier. Im hoping there isn't going to be a huge constraint or game theory question.
    Okay good. Thing is last year, even then at least they included table headings so you knew how to go about starting it off. A nightmare scenario for me would be like the examples in the textbook, where its just a wall of text and you have to do everything yourself. :s

    By the way guys, can I just ask a quick question please? In the hungarian algorithm, I'm really worried that I'll cover the zeros by drawing more than the required number of lines, and I'll miss a situation where I can cover more than one zero with a line or something. Does anyone know how this would affect the algorithm? Anyone with any tips on avoiding this?

    If it was the last iteration, I presume that I could tell I went wrong? Because surely there would be no unique allocation for each worker or something. God I hate that algorithm :s
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    (Original post by Hamburglar)
    Anyone got any tips of what might come up on this paper?

    I'm thinking there might be some annoying definitions in there, since we haven't had those for a while.

    Hoping for a dynamic programming question on a graph, instead of a table. We might also get linear programming on game theory?

    By the way, is it common practice for Edexcel to help us out a bit on the dynamic programming questions? By usually starting off the table or something or telling us what state/stage/action actually is in the table headings, like on the last paper? That would make my life a bit easier :s
    D2 is pretty easy to predict, there is always one question from each topic and then an LP on Allocation, Transportation or Game Theory. Game theory seems most likely.

    My money would be on a minimax / maximin DP question, they will not start you off on this.

    Salesman could well have a short cuts question as this hasn't been asked for a few papers.
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    (Original post by brittanna)
    On the game theory linear programming formulating questions, could they tell us a specific method we have to use, or do we only need to know one of the methods?
    They are never going to ask you to solve graphically as in D1. It is very unlikely you will have to use Simplex. Which means other than context Game Theory is always the same.
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    (Original post by Arsey)
    They are never going to ask you to solve graphically as in D1. It is very unlikely you will have to use Simplex. Which means other than context Game Theory is always the same.
    Sorry, I meant as in you can either:

    Let
    p_1 = P(A plays 1)
    p_2 = P(A plays 2)
    p_3 = P(A plays 3)

    or

    Let  x_i=\frac{p_i}{v} and continue using this format.

    They have the two methods in this mark scheme on page 167: http://www.edexcel.com/migrationdocu...7_UA021531.pdf

    Because in D1 they could specify which method to use in linear programming (points testing or profit line), so could they do the same thing here by telling you which method you have to use to formulate it as a linear programming problem?
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    Could someone explain this question to me i mean the mark scheme why does it not include a zero.
    Name:  DP.PNG
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    Thanks,
    Smith
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    (Original post by smith50)
    Could someone explain this question to me i mean the mark scheme why does it not include a zero.
    Name:  DP.PNG
Views: 101
Size:  23.2 KB
    Thanks,
    Smith
    Could you please screenshot the mark scheme or something? I can't really identify what you mean by zero.

    If you're referring to the stages then, I don't think it matters what you call them really. You could arbitrarily call them 0-4 as you could 1-5 I believe. I also think they allow you to do the stages in whichever order (5-1 or 1-5).
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    (Original post by brittanna)
    Sorry, I meant as in you can either:

    Let
    p_1 = P(A plays 1)
    p_2 = P(A plays 2)
    p_3 = P(A plays 3)

    or

    Let  x_i=\frac{p_i}{v} and continue using this format.

    They have the two methods in this mark scheme on page 167: http://www.edexcel.com/migrationdocu...7_UA021531.pdf

    Because in D1 they could specify which method to use in linear programming (points testing or profit line), so could they do the same thing here by telling you which method you have to use to formulate it as a linear programming problem?
    Oh don't do the second method, you can but don't.


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    (Original post by Lilmzbest)
    Very good idea, might start doing that
    There are quite a few tricky ones on the Solomon papers.


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    (Original post by Arsey)
    Oh don't do the second method, you can but don't.


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    It's just because I was doing a paper, (I think it was a Solomon paper) and it said define your objective function in terms of your decision variables, and the only method listed in the mark scheme was the second one. But I never really understood it, but if they can't specify which, then i'm happy with that . Thank you.
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    Guys I just have a quick question if that is okay.

    When you're calculating shadow costs and stuff, does it matter if you still have your original route in the table? I've seen some papers where the mark schemes has the shadow costs surrounding the original route. I've seen other mark schemes where the shadow costs surround a table which actually has the improvement indices in it.

    Does it matter which way you show your shadow costs and improvement indices? Thanks.

    EDIT: These cases are what I am referring to.

    Name:  Screenshot on 2013-05-28 at 16.16.33.png
Views: 90
Size:  32.1 KB

    Name:  Screenshot on 2013-05-28 at 16.16.48.png
Views: 85
Size:  19.5 KB

    EDIT 2: Another question please if someone could answer it? In a hungarian algorithm question where there is data missing, does it matter what large value we assign to the missing data? Mark scheme was kind of specific about 60, and I had 55 or something.

    Thanks!
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    (Original post by Hamburglar)
    Guys I just have a quick question if that is okay.

    When you're calculating shadow costs and stuff, does it matter if you still have your original route in the table? I've seen some papers where the mark schemes has the shadow costs surrounding the original route. I've seen other mark schemes where the shadow costs surround a table which actually has the improvement indices in it.

    Does it matter which way you show your shadow costs and improvement indices? Thanks.

    EDIT: These cases are what I am referring to.

    Name:  Screenshot on 2013-05-28 at 16.16.33.png
Views: 90
Size:  32.1 KB

    Name:  Screenshot on 2013-05-28 at 16.16.48.png
Views: 85
Size:  19.5 KB

    EDIT 2: Another question please if someone could answer it? In a hungarian algorithm question where there is data missing, does it matter what large value we assign to the missing data? Mark scheme was kind of specific about 60, and I had 55 or something.

    Thanks!
    No it doesn't

    I always surround the table with SC and put II inside the table.


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    (Original post by brittanna)
    It's just because I was doing a paper, (I think it was a Solomon paper) and it said define your objective function in terms of your decision variables, and the only method listed in the mark scheme was the second one. But I never really understood it, but if they can't specify which, then i'm happy with that . Thank you.
    It used to be used on old spec where you solved using Simplex. That method makes it easier.


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    (Original post by Arsey)
    No it doesn't

    I always surround the table with SC and put II inside the table.


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    Ah okay, thanks.

    I always thought it was a bit weird with shadow costs on the outside, and the route inside because the route numbers have nothing to do with the shadow costs on the side, and it's quite distracting.
 
 
 
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