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Math Help - Real life case study

  1. #1
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    Real life case study

    Hi,

    I've noticed that there are a lot of references to teachers/pupils etc however I have a work related issue. Apologies if this is against the rules - I have looked but couldn't see anything saying this site was specifically for teaching. Here goes anyway...

    I work in purchasing and a large part of my role is coordinating the evaluation of bids from suppliers. Quite often price is not the only factor in evaluating bids and there are other qualitative factors that are important to my firm, e.g. delivery times, geographical coverage, track record etc. In these cases, bids are scored out of 100% with a certain proportion being attributable to the qualitative aspects (herein referred to as quality) and a certain proportion attributable to price, e.g. 70% quality/30% price or 50% quality/50% price etc.
    Quality scores are determined through evaluators subjectively awarding a % score (up to the maximum of the quality portion referred to previously) for the qualitative aspects of the suppliersí bids.
    Price scores are then determined through an Excel based formula which in essence determines the cheapest bid and then compares all other bids to this price. The % score is calculated on a proportional basis from the cheapest bid. For example, where the price proportion is 30% and Supplier 1 submits the cheapest price of £100 they get the maximum 30% allocation. Now if Supplier 2 submits a bid exactly twice the price of Supplier 1 (£200) they get 15% and so on.
    The quality and price scores are added together to give an overall % total and the supplier with the greatest % wins the business. This is all fine and I feel very comfortable operating this process. So why the post then? Well weíve had a new computer system installed to automatically run the evaluation process which doesnít work in the same way at all L
    The new piece of software has both qualitative and price elements however they now relate to each other very differently. Now, instead of the supplier getting the business if they get the most out of 100% they win the business if they provide the lowest price. However, to ensure quality can still be taken into account there is now the facility to weight the bid price by a factor to account for quality. To do this, the evaluator enters a quality score out of 100% for each supplier and the system then converts this % score into a factor based upon the highest quality score submitted. For example, Supplier 1 is awarded the highest score of 80% out of 100% and thus gets a factor of 1. Supplier 2 is awarded a score of 40% out of 100% and thus gets a factor of 0.5. The factors are then applied to the respective prices submitted and the supplier with the lowest factored price wins. Taking the previous example and assuming both suppliers submit a price of £100, Supplier 1ís factored price would be £100 (£100/1) and Supplier 2ís factored price would be £200 (£100/0.5). Supplier 1 is ranked 1st by factored price and thus wins the business. Itís probably worth pointing out that these calculations arenít visible to the suppliers and no matter what calculation is run on the bid price we always pay the bid price.
    It all sounds logical, so whatís my issue? Well, under the new system quality is always of the same proportional importance when compared to price. As quality is always scored out of 100% there is no way, as there is with the current manual system, to create evaluation models where quality can be weighted as more or less important. There is a glimmer of hope however. As it is possible to override the factor calculated by the system Iíve been trying unsuccessfully for the past couple of weeks to develop a formula that converts the combination of a fixed price/quality split (as with the old process) and a supplierís quality score (out of 100% as with the new system) into a factor to input into the new system. Unfortunately, Iíve failed miserably and am looking for some help.
    So... is anyone still reading this essay? Does this make any sense whatsoever? Is there anyone out there that might be able to help?
    Thanks in advance,

    Phil
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  2. #2
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    To understand the current evaluation system I feel we need more information.
    Eg what is the factor for the 3rd ranked supplier? (1st - 1, 2nd - 0.5, so third can be in geometric progression ie 0.25 or else). Likewise down to the n-th ranked supplier.

    to develop a formula that converts the combination of a fixed price/quality split (as with the old process) and a supplier’s quality score (out of 100% as with the new system) into a factor to input into the new system.
    furthermore, if you could give an example of 1-3 suppliers ranking under the current and desired system, it would be easier to see what mathematical equation/model this would fit it.
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  3. #3
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    Hi Volga and thanks for replying,

    The factor used for the third supplier would depend on the score out of 100% they received . In the example I gave Supplier 1 scored the highest at 80% and is therefore allocated the highest factor of 1.0. Supplier 2 scored 40% (half of Supplier 1's 80%) and was allocated a factor of 0.5 (half of Supplier 1's 1.0). If Supplier 3 was to score 20% they would indeed get a factor of 0.25 however suppliers can score anywhere between 0% and 100% so Supplier 4 might score 65% and be allocated a factor of 0.8125. It's also worth pointing out that the calculated factor is dependent on the score the highest % scoring supplier receives, e.g. if in the above example Supplier 1 only scored 60% then they would still get a factor of 1.0 but Supplier 2 would get a factor of 0.6666666etc (40%/60%).

    To answer the second part of your question I've created a quick spreadsheet to illustrate the issue I'm having...

    N.B. It's probably best not to view the systems as "current" and "desired" as I'm not able to use the old system because of the new system coming in. As such, I'd like to try and work with the factors of the new system to replicate the old system.

    Thanks for your help!

    Philip
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by gottogethelp View Post
    [FONT=Arial][FONT=Arial][SIZE=2]It all sounds logical, ...
    No in fact it sounds arbitrary. There is no rational behind your system, at least as you explain it.

    I hate to say this but I suggest you google "Analytic Hierarchy Process"

    CB
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