Lower bound on size of branch-and-bound trees for solving lot-sizing problem

TL;DR

This paper proves that for certain lot-sizing problem instances, any branch-and-bound algorithm, even with general split disjunctions, must explore an exponential number of nodes, indicating inherent computational complexity.

Contribution

It establishes a lower bound on the size of branch-and-bound trees for specific lot-sizing problem instances, highlighting fundamental complexity limitations.

Findings

Exponential lower bound on branch-and-bound tree size for some instances

Branching on general split disjunctions does not reduce complexity

Inherent difficulty in solving certain lot-sizing problems efficiently

Abstract

We show that there exists a family of instances of the lot-sizing problem, such that any branch-and-bound tree that solves them requires an exponential number of nodes, even in the case when the branchings are performed on general split disjunctions.