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Competitive Algorithms for Multistage Online Scheduling

  • We study an online flow shop scheduling problem where each job consists of several tasks that have to be completed in t different stages and the goal is to maximize the total weight of accepted jobs. The set of tasks of a job contains one task for each stage and each stage has a dedicated set of identical parallel machines corresponding to it that can only process tasks of this stage. In order to gain the weight (profit) associated with a job j, each of its tasks has to be executed between a task-specific release date and deadline subject to the constraint that all tasks of job j from stages 1, …, i-1 have to be completed before the task of the ith stage can be started. In the online version, jobs arrive over time and all information about the tasks of a job becomes available at the release date of its first task. This model can be used to describe production processes in supply chains when customer orders arrive online. We show that even the basic version of the offline problem with a single machine in each stage, unit weights, unit processing times, and fixed execution times for all tasks (i.e., deadline minus release date equals processing time) is APX-hard. Moreover, we show that the approximation ratio of any polynomial-time approximation algorithm for this basic version of the problem must depend on the number t of stages. For the online version of the basic problem, we provide a (2t-1)-competitive deterministic online algorithm and a matching lower bound. Moreover, we provide several (sometimes tight) upper and lower bounds on the competitive ratio of online algorithms for several generalizations of the basic problem involving different weights, arbitrary release dates and deadlines, different processing times of tasks, and several identical machines per stage.
Metadaten
Author:Michael Hopf, Clemens Thielen, Oliver Wendt
URN (permanent link):urn:nbn:de:hbz:386-kluedo-41195
Parent Title (English):European Journal of Operational Research
Document Type:Preprint
Language of publication:English
Publication Date:2015/07/09
Year of Publication:2015
Publishing Institute:Technische Universität Kaiserslautern
Date of the Publication (Server):2015/07/09
Tag:online optimization
GND-Keyword:On-line algorithm; competitive analysis; scheduling
Number of page:29
Faculties / Organisational entities:Fachbereich Mathematik
CCS-Classification (computer science):G. Mathematics of Computing / G.2 DISCRETE MATHEMATICS / G.2.3 Applications (NEW)
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
MSC-Classification (mathematics):05-XX COMBINATORICS (For finite fields, see 11Txx) / 05Cxx Graph theory (For applications of graphs, see 68R10, 81Q30, 81T15, 82B20, 82C20, 90C35, 92E10, 94C15) / 05C90 Applications [See also 68R10, 81Q30, 81T15, 82B20, 82C20, 90C35, 92E10, 94C15]
Licence (German):Standard gemäß KLUEDO-Leitlinien vom 13.02.2015