I'm about to conduct an integer program where I am to transport some products from different cities to docks and refinement stations. I am however required to work with simulated data where I only have total demand to "match" the supplies to. There are however different product types which demands are specified as a percentage of the total demand. It is not specified how the supplies of these product types are spread, and it is my task to find these.
Thus, is there a mathematical approach to find a specified amount of terms, n (corresponding to the supply locations) that sums to a specified value (the percantage of the total demand for that specific product type)? It is not sufficient to assume a evenly distributed supply throughout every origin.
I hope anyone has any idea of some theorem, or method of finding these combinations of terms.
EDIT: If one has any tips regarding if there are any good tags to add, please let me know. I'm not quite sure into what mathematical field this question is suitable for.
Also, tips regarding algorithms are also welcome.
EDIT: I've found out that integer partitioning may be associated with these kinds of problems. I'm trying to read as much as I can in the subject to find a suitable algorithm. Any tips or hints regarding algorithms, or if some special type of integer partitioning may be applicable is very helpful. Or if it can be solved with other techqnicues.
Thanks in advance Cenderze