A branch-and-price algorithm for the temporal bin packing problem

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.

An introduction to stochastic bin packing-based server consolidation with conflicts

“…By way of example, we refer the reader to some (by far not exhaustive) surveys (Delorme et al 2016;Valério de Carvalho 2002) and standard references about approximation algorithms (Coffman et al 2013(Coffman et al , 1984, branch-and-bound based techniques (Belov and Scheithauer 2006;Valério de Carvalho 1999;Vance 1998;Vance et al 1994), classical pseudo-polynomial integer linear programming (ILP) formulations (Dyckhoff 1981;Martinovic et al 2018;Valério de Carvalho 2002), or modern and advanced approaches (Brandão and Pedroso 2016;Clautiaux et al 2017;Delorme and Iori 2020;Wei et al 2020). Moreover, in the last couple of years, (deterministic) generalizations with respect to a temporal dimension have been proposed in various articles (Aydin et al 2020;de Cauwer et al 2016;Dell'Amico et al 2020).…”

“…By this common interval, all feasibility conditions for the consolidation will be contained in the optimization problem-even if single jobs start a little earlier or stop a bit later. A more detailed investigation with distinct job-specific start and end times would result in a stochastic version of the Temporal Bin Packing Problem (TBPP), see(Aydin et al 2020;de Cauwer et al 2016;Dell'Amico et al 2020;Martinovic et al 2021). For this purpose, however, the basics of the ordinary stochastic BPP must first be derived, and this is precisely the aim of the present article.…”

On the Use of Equivalence Classes for Optimal and Suboptimal Bin Packing and Bin Covering

“…Pseudo-polynomial formulations, [5], [6], [7], allow a more compact formulation and avoid the complexity introduced in the implementation of branch-and-price based algorithms. Of interest in some practical applications is also temporal extensions, [8], where the capacity of a bin must be consumed within a given time window.…”

Variable and constraint reduction techniques for the temporal bin packing problem with fire-ups

“…Each job is characterized by a size (or resource demand) and a lifespan (time window in which the job is active), a jobs-to-servers assignment is feasible if and only if the capacity of the servers is respected at any instant of time. The TBPP is a challenging problem with a high practical and theoretical interest which has been recently introduced in the literature, see [9,10]. It belongs to the rich family of cutting and packing problems, object of intense research in the last decades.…”

“…The TBPP is introduced in an application-oriented article, see [9], dealing with efficient workload server management in data centers-one of the key challenges in light of the ever-growing energy demand of the IT industry [1,12,14]. As far as the TBPP solution methods are concerned, we refer the reader to [10], an article which presents several heuristic and exact approaches. The state-of-the-art exact algorithm for the TBPP is a branch-and-price algorithm, which exploits in preprocessing a plethora of heuristic algorithms (see [10] for further details).…”