Related papers: Vector Bin Packing with Multiple-Choice
In the online bin packing problem, a sequence of items is revealed one at a time, and each item must be packed into an available bin instantly upon its arrival. In this paper, we revisit the problem under a setting where the total number of…
We provide a Polynomial Time Approximation Scheme (PTAS) for the Bayesian optimal multi-item multi-bidder auction problem under two conditions. First, bidders are independent, have additive valuations and are from the same population.…
We formalize the problem of selecting the optimal set of options for planning as that of computing the smallest set of options so that planning converges in less than a given maximum of value-iteration passes. We first show that the problem…
Motivated by modern-day applications such as Attended Home Delivery and Preference-based Group Scheduling, where decision makers wish to steer a large number of customers toward choosing the exact same alternative, we introduce a novel…
We consider a natural generalization of classical scheduling problems in which using a time unit for processing a job causes some time-dependent cost which must be paid in addition to the standard scheduling cost. We study the scheduling…
Many combinatorial optimisation problems can be modelled as valued constraint satisfaction problems. In this paper, we present a polynomial-time algorithm solving the valued constraint satisfaction problem for a fixed number of variables…
This paper presents a trace-based simulation methodology for constructing representations of workload-allocator interaction. We use two-dimensional rectangular bin packing (2DBP) as our foundation. Classical 2DBP algorithms minimize their…
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…
In the incremental knapsack problem ($\IK$), we are given a knapsack whose capacity grows weakly as a function of time. There is a time horizon of $T$ periods and the capacity of the knapsack is $B_t$ in period $t$ for $t = 1, \ldots, T$.…
This paper addresses the Quadratic Multiple Constraints Variable-Sized Bin Packing Problem (QMC-VSBPP), a challenging combinatorial optimization problem that generalizes the classical bin packing problem by incorporating multiple capacity…
Modern parcel logistic networks are designed to ship demand between given origin, destination pairs of nodes in an underlying directed network. Efficiency dictates that volume needs to be consolidated at intermediate nodes in typical…
We consider a general class of binary packing problems with a convex quadratic knapsack constraint. We prove that these problems are APX-hard to approximate and present constant-factor approximation algorithms based upon three different…
In package-handling facilities, boxes of varying sizes are used to ship products. Improperly sized boxes with box dimensions much larger than the product dimensions create wastage and unduly increase the shipping costs. Since it is…
Imagine a large firm with multiple departments that plans a large recruitment. Candidates arrive one-by-one, and for each candidate the firm decides, based on her data (CV, skills, experience, etc), whether to summon her for an interview.…
We consider the problem of coordinating a fleet of robots in a warehouse so as to maximize the reward achieved within a time limit while respecting problem and robot specific constraints. We formulate the problem as a weighted set packing…
We consider the robust version of items selection problem, in which the goal is to choose representatives from a family of sets, preserving constraints on the allowed items' combinations. We prove NP-hardness of the deterministic version,…
Suppose there is a large collection of items, each with an associated cost and an inherent utility that is revealed only once we commit to selecting it. Given a budget on the cumulative cost of the selected items, how can we pick a subset…
At modern warehouses, mobile robots transport packages and drop them into collection bins/chutes based on shipping destinations grouped by, e.g., the ZIP code. System throughput, measured as the number of packages sorted per unit of time,…
We efficiently solve the optimal multi-dimensional mechanism design problem for independent bidders with arbitrary demand constraints when either the number of bidders is a constant or the number of items is a constant. In the first…
In the online simple knapsack problem items are presented in an iterative fashion and an algorithm has to decide for each item whether to reject or permanently include it into the knapsack without any knowledge about the rest of the…