Job shop scheduling with unit length tasks
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 46 (2012) no. 3, pp. 329-342.

In this paper, we consider a class of scheduling problems that are among the fundamental optimization problems in operations research. More specifically, we deal with a particular version called job shop scheduling with unit length tasks. Using the results of Hromkovič, Mömke, Steinhöfel, and Widmayer presented in their work Job Shop Scheduling with Unit Length Tasks: Bounds and Algorithms, we analyze the problem setting for 2 jobs with an unequal number of tasks. We contribute a deterministic algorithm which achieves a vanishing delay in certain cases and a randomized algorithm with a competitive ratio tending to 1. Furthermore, we investigate the problem with 3 jobs and we construct a randomized online algorithm which also has a competitive ratio tending to 1.

DOI : 10.1051/ita/2011132
Classification : 68Q25
Mots-clés : online algorithms, competitive analysis, job shop scheduling 
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     title = {Job shop scheduling with unit length tasks},
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     publisher = {EDP-Sciences},
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Akveld, Meike; Bernhard, Raphael. Job shop scheduling with unit length tasks. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 46 (2012) no. 3, pp. 329-342. doi : 10.1051/ita/2011132. http://www.numdam.org/articles/10.1051/ita/2011132/

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