John Martinovic We consider a recently proposed one-dimensional packing problem, called the overflowing bin packing problem (OBPP). In this scenario, we are given a set of items (of known sizes) and a set of bins (of known capacities). Roughly speaking, the task is to assign the items to the bins in such a way that the total … Read more
Given a set of jobs (or items), each of which being characterized by its resource demand and its lifespan, and a sufficiently large number of identical servers (or bins), the busy time minimization problem (BTMP) requires to find a feasible schedule (i.e., a jobs-to-servers assignment) having minimum overall power-on time. Although being linked to the … Read more
We consider two neighboring generalizations of the classical bin packing problem: the temporal bin packing problem (TBPP) and the temporal bin packing problem with fire-ups (TBPP-FU). In both cases, the task is to arrange a set of given jobs, characterized by a resource consumption and an activity window, on homogeneous servers of limited capacity. To … Read more
We consider the temporal bin packing problem with fire-ups (TBPP-FU), a branch of operations research recently introduced in multi-objective cloud computing. In this scenario, any item is equipped with a resource demand and a lifespan meaning that it requires the bin capacity only during that time interval. We then aim at finding a schedule minimizing … Read more
The temporal bin packing problem with fire-ups (TBPP-FU) is a two-dimensional packing problem where one geometric dimension is replaced by a time horizon. The given items (jobs) are characterized by a resource consumption, that occurs exclusively during an activity interval, and they have to be placed on servers so that the capacity constraint is respected … Read more
The aim of this letter is to design and computationally test several improvements for the compact integer linear programming (ILP) formulations of the temporal bin packing problem with fire-ups (TBPP-FU). This problem is a challenging generalization of the classical bin packing problem in which the items, interpreted as jobs of given weight, are active only … Read more
In this article we examine a specific version of the temporal bin packing problem (TBPP) that occurs in job-to-server scheduling. The TBPP represents a generalization of the well-known bin packing problem (BPP) with respect to an additional time dimension, and it requires to find the minimum number of bins (servers) to accommodate a given list … Read more
We consider the (single-stage) stochastic bin packing problem (SBPP) which is based on a given list of items the sizes of which are represented by stochastically independent random variables. The SBPP requires to determine the minimum number of unit capacity bins needed to pack all the items, such that for each bin the probability of … Read more
In this paper, we consider the (additive integrality) gap of the cutting stock problem (CSP) and the skiving stock problem (SSP). Formally, the gap is defined as the difference between the optimal values of the ILP and its LP relaxation. For both, the CSP and the SSP, this gap is known to be bounded by … Read more
The minimum connectivity inference (MCI) problem represents an NP-hard generalization of the well-known minimum spanning tree problem. Given a set of vertices and a finite collection of subsets (of this vertex set), the MCI problem requires to find an edge set of minimal cardinality so that the vertices of each subset are connected. Although the … Read more