A first approximation algorithm for the Bin Packing Problem with Setups

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 α-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 α-approximation algorithm for the BPPS.