[R] ?currency challenge ?knapsack challenge ?probabilities

[Jim Lemon]

Hi Calum,
Does this include an error tolerance for the match between the ordered and
delivered quantities? That is, is it okay to have a maximum of one unit
difference or do deliveries have to exactly match orders?

Jim


On Sun, Dec 27, 2015 at 10:08 PM, Polwart Calum (COUNTY DURHAM AND
DARLINGTON NHS FOUNDATION TRUST) <calum.polwart at nhs.net> wrote:

> I am currently working on a project that is producing Gigabyte sized
> vectors that kill R.  It can take 24 hours to run. So frustrating to get
> that far and have to scale back my inputs and rerun...
>
>
> The problem i'm trying to solve as i see it is very similar to optimal
> currency denominations problems combined with a knapsack problem. Let me
> TRY to explain.
>
>
> We have a product that we want to manufacture in as few sizes as
> possible.  like currency if you want 30cents but a 30cent coin doesnt exist
> you can join multiple products together. (3x10 cent, 25cent +5 cent, etc)
>
>
> Unlike currency we dont need every value to be possible, we have a list of
> known values which are effectively related to each other by the next size
> up being 25% bigger. So for instance 64, 80 100.
>
>
> We have some rules that say you can't use more than X products combined to
> make the final size.  A bit like saying never give more than 10 coins as
> change, so you cant issue 20x5cents for a dollar of change.
>
>
> All of that fits a standard currency denomination challenge.
>
>
> We dont need the combinations to be calculated using greedy method. [We
> will calculate and store as a table]
>
>
> BUT - we do have a manufacturing limitation that means can manufacture to
> any whole number size, we cant do smaller than size5. (We dont go as low as
> that anyway... size 11 is as low as needed).  So different from any
> currency problem I've seen where the lowest coin size is always a 1
> allowing any size to be produced.
>
>
> So i have three questions I'm trying to answer:
>
>
> - what is the smallest product range we can make that achieves our rules
> for max combinations of sizes?
>
>
> - Is there a more optimal range. Say the smallest range was 4 sizes, for
> example 5,6,23,40.  Its possible adding a 22 and a 46 to that may actually
> be cheaper than supplying 2x5 and 2x6 or 2x23...
>
> Currently I'm identifying every possible combination into a matrix.  We
> have a manufacturing constraint of max size 49 as well.  So i take every
> end user size possible (from 11 thru to 125).  For each size i then take
> every combination of possible sizes from 5 to 49 (45 sizes) that we COULD
> make and work out how i can achieve all the possible end user sizes,
> discarding any combinations that break our rules for max combinations.
>
> Thats a giant set of for loops.  Once i establish the options we  can
> apply the manufacturing costs and usage data to find the answer.
>
> For now 45 sizes,combined in any of up to 5 different combinations to do
> 10 end user sizes is creating vectors too big for R to handle...
>
> Long explanation of the problem, to basically say... has anyone come
> across a function in R that might simplify this?
>
>
>
> Sent from TypeMail<http://www.typeapp.com/r>
>
>
> On 27 Dec 2015, at 08:00, "Polwart Calum (COUNTY DURHAM AND DARLINGTON NHS
> FOUNDATION TRUST)" <calum.polwart at nhs.net<mailto:calum.polwart at nhs.net>>
> wrote:
>
>
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