
I'm a programmer, not a mathmatician. I heard about R, and I'm wondering if
anyone can tell me if there is an existing R function that can help with a
problem we're currently trying to find an algorithm for. If R is not the
answer, but you can recommend a known algorithm, that would help a lot!


I'm on a project in a retail corporation, working on a program to assist
retail buyers in creating their orders. The program will be used internally,
and not sold to other companies.


In retail terms, the problem is to determine the best assortment of case
packs to order for a given store, and given a set of desired quantities for
each size of a product. A case pack is a set of sizes that the supplier
assembles. The retailer must order in whole case packs.


For example,

For a given shoe style, in the color brown, a supplier has the following
case packs available.


Sizes - >   XS   S   M   L  XL  XXL XXXL
CasePack profiles:
cp1          1   3   5   4   2   1   0
cp2          0   2   2   2   0   0   0
cp3          0   2   3   3   1   0   0
cp4          2   4   5   5   4   1   0


And, for a given store, the retailer has determined the following set the
desired quantites of sizes to purchase. (This determination is based on
sales history, and is not at all based on what the case packs for this item
look like.)


Sizes - >   XS   S   M   L  XL  XXL  XXXL
             4  10  14  12   7   3    0


The question to be answered is, What set of quantities of the above case
packs will give me the closest distribution to the desired set of sizes?


The output would be a single recommendation for case-pack order quantities,
in a form like the following.


Case pack    Quantity
cp1             0
cp2             3
cp3             2
cp4             1


There will be some other factors that may operate outside of the above core
problem: 


There may be limits on the quantity available on some of the case packs. For
instance, the supplier only has ten available of cp2. It seems this factor
will need to be considered in the core algorithm.
We realize we'll need to apply tolerance levels to the calculation. For
example, for this shoe style, we will accept the solution if it comes to
within 10% (plus or minus) of our desired quantities on each size.
We may also apply a minimum. For example, the solution must have at least 1
of each size having a nonzero quantity.


Thanks for any help!


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