More on ordered open end bin packing

TL;DR

This paper studies the Ordered Open End Bin Packing problem, providing improved bounds for online algorithms and an approximation scheme for the offline case, advancing understanding of this complex bin packing variant.

Contribution

It introduces the first online algorithm with an asymptotic competitive ratio below 2 and develops an approximation scheme for the offline problem.

Findings

First online algorithm with ratio below 2

Improved bounds on asymptotic competitive ratio

Polynomial time approximation scheme for offline case

Abstract

We consider the Ordered Open End Bin Packing problem. Items of sizes in $(0,1]$ are presented one by one, to be assigned to bins in this order. An item can be assigned to any bin for which the current total size strictly below $1$. This means also that the bin can be overloaded by its last packed item. We improve lower and upper bounds on the asymptotic competitive ratio in the online case. Specifically, we design the first algorithm whose asymptotic competitive ratio is strictly below $2$ and it is close to the lower bound. This is in contrast to the best possible absolute approximation ratio, which is equal to $2$. We also study the offline problem where the sequence of items is known in advance, while items are still assigned to bins based on their order in the sequence. For this scenario we design an asymptotic polynomial time approximation scheme.