Related papers: Online Stochastic Bin Packing
The following online bin packing problem is considered: Items with integer sizes are given and variable sized bins arrive online. A bin must be used if there is still an item remaining which fits in it when the bin arrives. The goal is to…
In the online sorting problem, $n$ items are revealed one by one and have to be placed (immediately and irrevocably) into empty cells of a size-$n$ array. The goal is to minimize the sum of absolute differences between items in consecutive…
The knapsack problem is one of the classical problems in combinatorial optimization: Given a set of items, each specified by its size and profit, the goal is to find a maximum profit packing into a knapsack of bounded capacity. In the…
We study a variant of online bin packing, called colorful bin packing. In this problem, items that are presented one by one are to be packed into bins of size 1. Each item i has a size s_i \in [0,1] and a color c_i \in C, where C is a set…
Problems involving the efficient arrangement of simple objects, as captured by bin packing and makespan scheduling, are fundamental tasks in combinatorial optimization. These are well understood in the traditional online and offline cases,…
Many combinatorial optimization problems such as the bin packing and multiple knapsack problems involve assigning a set of discrete objects to multiple containers. These problems can be used to model task and resource allocation problems in…
In the recent paper \cite{BDT10} we introduced a new problem that we call Bin Packing/Covering with Delivery, or BP/CD for short. Mainly we mean under this expression that we look for not only a good, but a "good and fast" packing or…
Best-Fit is one of the most prominent and practically used algorithms for the bin packing problem, where a set of items with associated sizes needs to be packed in the minimum number of unit-capacity bins. Kenyon [SODA '96] studied online…
In this paper we present a theoretical analysis of the deterministic on-line {\em Sum of Squares} algorithm ($SS$) for bin packing introduced and studied experimentally in \cite{CJK99}, along with several new variants. $SS$ is applicable to…
We study the fault-tolerant variant of the online bin packing problem. Similar to the classic bin packing problem, an online sequence of items of various sizes should be packed into a minimum number of bins of uniform capacity. For…
The article proposes a heuristic approximation approach to the bin packing problem under multiple objectives. In addition to the traditional objective of minimizing the number of bins, the heterogeneousness of the elements in each bin is…
In the Colored Bin Packing problem a sequence of items of sizes up to $1$ arrives to be packed into bins of unit capacity. Each item has one of $c\geq 2$ colors and an additional constraint is that we cannot pack two items of the same color…
We consider a stochastic lost-sales inventory control system with a lead time $L$ over a planning horizon $T$. Supply is uncertain, and is a function of the order quantity (due to random yield/capacity, etc). We aim to minimize the…
We consider the online vector bin packing problem where $n$ items specified by $d$-dimensional vectors must be packed in the fewest number of identical $d$-dimensional bins. Azar et al. (STOC'13) showed that for any online algorithm $A$,…
The Bin Packing Problem is one of the most important optimization problems. In recent years, due to its NP-hard nature, several approximation algorithms have been presented. It is proved that the best algorithm for the Bin Packing Problem…
This paper presents theoretical and practical results for the bin packing problem with scenarios, a generalization of the classical bin packing problem which considers the presence of uncertain scenarios, of which only one is realized. For…
We study the Min-Weighted Sum Bin Packing problem, a variant of the classical Bin Packing problem in which items have a weight, and each item induces a cost equal to its weight multiplied by the index of the bin in which it is packed. This…
In modern computing systems, jobs' resource requirements often vary over time. Accounting for this temporal variability during job scheduling is essential for meeting performance goals. However, theoretical understanding on how to schedule…
We consider a variant of bin packing called multiple-choice vector bin packing. In this problem we are given a set of items, where each item can be selected in one of several $D$-dimensional incarnations. We are also given $T$ bin types,…
We study an edge-weighted online stochastic \emph{Generalized Assignment Problem} with \emph{unknown} Poisson arrivals. In this model, we consider a bipartite graph that contains offline bins and online items, where each offline bin is…