In this paper, we discuss scheduling problems with m identical machines and n jobs where each job has to be assigned to some machine. The objective is to minimize the weighted makespan of jobs, i.e., the maximum weigh...
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In this paper, we discuss scheduling problems with m identical machines and n jobs where each job has to be assigned to some machine. The objective is to minimize the weighted makespan of jobs, i.e., the maximum weighted completion time of jobs. This scheduling problem is a generalization of minimizing the makespan on parallel machine scheduling problem. We present a (2-1m\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2-\fracefficient polynomial time approximation scheme{m}$$\end{document})-approximation algorithm and a randomized efficient polynomial time approximation scheme (EPTAS) for the problem. We also design a randomized fully polynomialtimeapproximationscheme (FPTAS) for the special case when the number of machines is fixed.
The Capacitated Vehicle Routing Problem with time Windows (CVRPTW) is the well-known combinatorial optimization problem having numerous valuable applications in operations research. Unlike the classic CVRP (without ti...
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ISBN:
(数字)9783030386290
ISBN:
(纸本)9783030386290;9783030386283
The Capacitated Vehicle Routing Problem with time Windows (CVRPTW) is the well-known combinatorial optimization problem having numerous valuable applications in operations research. Unlike the classic CVRP (without time windows constraints), approximability of the CVRPTW (even in the Euclidean plane) in the class of algorithms with theoretical guarantees is much less studied. To the best of our knowledge, the family of such algorithms is exhausted by the Quasi-polynomialtimeapproximationscheme (QPTAS) proposed by L. Song et al. for the general setting of the planar CVRPTW and two our recent approximation algorithms, which are efficient polynomial time approximation schemes (EPTAS) for any fixed capacity q and number p of time windows and remain PTAS for slow-growing dependencies q = q(n) and p = p(n). In this paper, combining the well-known instance decomposition framework by A. Adamaszek et al. and QPTAS by L. Song et al. we propose a novel approximationscheme for the planar CVRPTW, whose running time remains polynomial for the significantly wider range of q and p.
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