On Lazy Bin Covering and Packing problems

AbstractIn this paper, we study two interesting variants of the classical bin packing problem, called Lazy Bin Covering (LBC) and Cardinality Constrained Maximum Resource Bin Packing (CCMRBP) problems. For the offline LBC problem, we first prove the approximation ratio of the First-Fit-Decreasing and First-Fit-Increasing algorithms, then present an APTAS. For the online LBC problem, we give a competitive analysis for the algorithms of Next-Fit, Worst-Fit, First-Fit, and a modified HARMONICM algorithm. The CCMRBP problem is a generalization of the Maximum Resource Bin Packing (MRBP) problem Boyar et al. (2006) [1]. For this problem, we prove that its offline version is no harder to approximate than the offline MRBP problem

Task Allocation Strategies in Multi-Robot Environment

Multirobot systems (MRS) hold the promise of improved performance and increased fault tolerance for large-scale problems. A robot team can accomplish a given task more quickly than a single agent by executing them concurrently. A team can also make effective use of specialists designed for a single purpose rather than requiring that a single robot be a generalist. Multirobot coordination, however, is a complex problem. An empirical study is described in the thesis that sought general guidelines for task allocation strategies. Different strategies are identified, and demonstrated in the multi-robot environment.Robot selection is one of the critical issues in the design of robotic workcells. Robot selection for an application is generally done based on experience, intuition and at most using the kinematic considerations like workspace, manipulability, etc. This problem has become more difficult in recent years due to increasing complexity, available features, and facilities offered by different robotic products. A systematic procedure is developed for selection of robot manipulators based on their different pertinent attributes. The robot selection procedure allows rapid convergence from a very large number of candidate robots to a manageable shortlist of potentially suitable robots. Subsequently, the selection procedure proceeds to rank the alternatives in the shortlist by employing different attributes based specification methods. This is an attempt to create exhaustive procedure by identifying maximum possible number of attributes for robot manipulators.Availability of large number of robot configurations has made the robot workcell designers think over the issue of selecting the most suitable one for a given set of operations. The process of selection of the appropriate kind of robot must consider the various attributes of the robot manipulator in conjunction with the requirement of the various operations for accomplishing the task. The present work is an attempt to develop a systematic procedure for selection of robot based on an integrated model encompassing the manipulator attributes and manipulator requirements

The Maximum Resource Bin Packing Problem

Usually, for bin packing problems, we try to minimize the number of bins used or in the case of the dual bin packing problem, maximize the number or total size of accepted items. This paper presents results for the opposite problems, where we would like to maximize the number of bins used or minimize the number or total size of accepted items. We consider off-line and on-line variants of the problems. For the off-line variant, we require that there be an ordering of the bins, so that no item in a later bin fits in an earlier bin. We find the approximation ratios of two natural approximation algorithms, First-Fit-Increasing and First-Fit-Decreasing for the maximum resource variant of classical bin packing. For the on-line variant, we define maximum resource variants of classical and dual bin packing. For dual bin packing, no on-line algorithm is competitive. For classical bin packing, we find the competitive ratio of various natural algorithms. We study the general versions of the problems as well as the parameterized versions where on the item sizes, for some integer k. there is an upper bound of 1/