Abstract
We consider scheduling realtime jobs in the classic flow shop model. The input is a set of n jobs, each consisting of m segments to be processed on m machines in the specified order, such that segment I_i of a job can start processing on machine M_i only after segment I_{i1} of the same job completed processing on machine M_{i1}, for 2 ≤ i ≤ m. Each job also has a release time, a due date, and a weight. The objective is to maximize the throughput (or, profit) of the n jobs, i.e., to find a subset of the jobs that have the maximum total weight and can complete processing on the m machines within their time windows. This problem has numerous reallife applications ranging from manufacturing to cloud and embedded computing platforms, already in the special case where m = 2. Previous work in the flow shop model has focused on makespan, flow time, or tardiness objectives. However, little is known for the flow shop model in the realtime setting. In this work, we give the first nontrivial results for this problem and present a pseudopolynomial time (2m+1)approximation algorithm for the problem on m ≥ 2 machines, where m is a constant. This ratio is essentially tight due to a hardness result of Ω(m/(log m)) for the approximation ratio. We further give a polynomialtime algorithm for the twomachine case, with an approximation ratio of (9+ε) where ε = O(1/n). We obtain better bounds for some restricted subclasses of inputs with two machines. To the best of our knowledge, this fundamental problem of throughput maximization in the flow shop scheduling model is studied here for the first time.
BibTeX  Entry
@InProceedings{benyamin_et_al:LIPIcs:2020:12651,
author = {Lior Ben Yamin and Jing Li and Kanthi Sarpatwar and Baruch Schieber and Hadas Shachnai},
title = {{Maximizing Throughput in Flow Shop RealTime Scheduling}},
booktitle = {Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020)},
pages = {48:148:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {9783959771641},
ISSN = {18688969},
year = {2020},
volume = {176},
editor = {Jaros{\l}aw Byrka and Raghu Meka},
publisher = {Schloss DagstuhlLeibnizZentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2020/12651},
URN = {urn:nbn:de:0030drops126510},
doi = {10.4230/LIPIcs.APPROX/RANDOM.2020.48},
annote = {Keywords: Flow shop, realtime scheduling, throughput maximization, approximation algorithms}
}
Keywords: 

Flow shop, realtime scheduling, throughput maximization, approximation algorithms 
Collection: 

Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020) 
Issue Date: 

2020 
Date of publication: 

11.08.2020 