Novel Approach for Solving a Variant of Equal Flow Problem

TL;DR

This paper introduces a novel local minima approach for a subclass of the NP-hard Integer Equal Flow problem, transforming it into a solvable linear integer programming problem using convex space projections.

Contribution

It presents a new local minima solution method that converts a complex subclass of the Equal Flow problem into a linear integer programming problem.

Findings

The approach effectively resolves the equal flows in inventory management systems.

It transforms the problem into a known linear integer programming form.

Standard optimization strategies can be applied successfully.

Abstract

In this article we consider a certain sub class of Integer Equal Flow problem, which are known NP hard [8]. Currently there exist no direct solutions for the same. It is a common problem in various inventory management systems. Here we discuss a local minima solution which uses projection of the convex spaces to resolve the equal flows and turn the problem into a known linear integer programming or constraint satisfaction problem which have reasonable known solutions and can be effectively solved using simplex or other standard optimization strategies.