A polynomially solvable case of the pooling problem

TL;DR

This paper identifies a specific case of the pooling problem that can be solved efficiently in polynomial time, expanding understanding of its computational complexity.

Contribution

It demonstrates that the pooling problem with one pool and limited inputs is polynomially solvable by linear programming methods.

Findings

Polynomial-time solution for pooling problem with one pool and bounded inputs

Overview of complexity results and open problems in pooling problem

Clarification of the boundary between NP-hard and polynomial cases

Abstract

Answering a question of Haugland, we show that the pooling problem with one pool and a bounded number of inputs can be solved in polynomial time by solving a polynomial number of linear programs of polynomial size. We also give an overview of known complexity results and remaining open problems to further characterize the border between (strongly) NP-hard and polynomially solvable cases of the pooling problem.