Question
Dear Randy,
My question is that is there a mathematical system that can be used to assign a finite number of resources to a certain number of users with statistical distribution without getting any fractions.
let's say we have 15 resources that need to be distributed to 6 users and we have the proportion that each person should get let's say 17%,20%,10%,23%,18% and 12% is there mathematical calculation or analysis that distribute all the 15 resources without getting any fraction in the distribution (i can't assign 1.5 resource it should be either 1 or 2)

Hi Elias,

The simplest answer to your question is that one could just round the distributions either up or down depending on the fraction, as you suggest. In other words, no specific mathematical system.

On the other hand, the example proportions (percentages) you list look like they could be the solutions to a so-called linear programming problem. Linear programming is a well-known, though somewhat complicated method of optimizing the distribution of raw materials in the manufacture products based on costs and profits (or analogous multi-component processes). Algorithms based on this method have been developed that assume the materials and products to be whole numbers (integers). So you could look into 'integer linear programming' if this sounds like it is relevant to your case.

Randy

Volunteer

#### randy patton

##### Expertise

college mathematics, applied math, advanced calculus, complex analysis, linear and abstract algebra, probability theory, signal processing, undergraduate physics, physical oceanography

##### Experience

26 years as a professional scientist conducting academic quality research on mostly classified projects involving math/physics modeling and simulation, data analysis and signal processing, instrument development; often ocean related

Publications
J. Physical Oceanography, 1984 "A Numerical Model for Low-Frequency Equatorial Dynamics", with M. Cane

Education/Credentials
M.S. MIT Physical Oceanography, B.S. UC Berkeley Applied Math

Past/Present Clients
Also an Expert in Oceanography