A Branch-and-Price Algorithm for the Temporal Bin Packing Problem

TL;DR

This paper introduces a branch-and-price algorithm to solve the temporal bin packing problem, an extension of classical bin packing considering time-dependent item capacities, with extensive computational testing.

Contribution

It develops a novel branch-and-price algorithm for the exponential formulation of the temporal bin packing problem, enhancing solution methods for this complex extension.

Findings

The algorithm effectively solves instances of the problem.

The combined approach outperforms existing methods.

Extensive computational experiments validate the approach.

Abstract

We study an extension of the classical Bin Packing Problem, where each item consumes the bin capacity during a given time window that depends on the item itself. The problem asks for finding the minimum number of bins to pack all the items while respecting the bin capacity at any time instant. A polynomial-size formulation, an exponential-size formulation, and a number of lower and upper bounds are studied. A branch-and-price algorithm for solving the exponential-size formulation is introduced. An overall algorithm combining the different methods is then proposed and tested trough extensive computational experiments.