A first approximation algorithm for the Bin Packing Problem with Setups

TL;DR

This paper introduces a new approximation algorithm for the Bin Packing Problem with Setups, combining classical heuristics with a merging phase to achieve a guaranteed approximation ratio.

Contribution

It presents a novel two-phase heuristic that guarantees a 2α-approximation for BPPS, improving upon the limitations of classical heuristics.

Findings

Classical BPP heuristics perform poorly on BPPS instances.

The proposed heuristic is a 2α-approximation algorithm for BPPS.

The method effectively merges bins after applying BPP approximations.

Abstract

We study constant-factor approximation algorithms for the Bin Packing Problem with Setups (BPPS). First, we show that adaptations of classical BPP heuristics can have arbitrarily poor worst-case performance on BPPS instances. Then, we propose a two-phase heuristic for the BPPS that applies an {\alpha}-approximation algorithm for the BPP to the items of each class and then performs a merging phase on the open bins. We prove that this heuristic is a 2 {\alpha}-approximation algorithm for the BPPS.