Minimum size generating partitions and their application to demand fulfillment optimization problems

TL;DR

This paper introduces the concept of generating partitions of an integer and finds the minimum size partition capable of generating all size-k partitions, with applications to demand fulfillment optimization.

Contribution

It defines generating partitions, solves for the minimum size partition that generates all size-k partitions, and applies this to combinatorial optimization problems.

Findings

Identified minimum size generating partitions for given parameters

Provided a method to generate all size-k partitions from a single partition

Applied the concept to optimize demand fulfillment problems

Abstract

For $n$ and $k$ integers we introduce the notion of some partition of $n$ being able to generate another partition of $n$. We solve the problem of finding the minimum size partition for which the set of partitions this partition can generate contains all size-$k$ partitions of $n$. We describe how this result can be applied to solving a class of combinatorial optimization problems.