Scheduling Seminar: Scheduling machines subject to unrecoverable failures and other related stochastic sequencing problems


Datum / čas
Date(s) - 09.11.
15:00 - 17:00

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Alessandro Agnetis (University of Siena)

Scheduling machines subject to unrecoverable failures and other related stochastic sequencing problems


November 9, 2022 at 15 CET

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The abstract:
Typical scheduling problems deal with a set of activities (jobs) requiring various resources (machines) to be performed. In most scheduling scenarios, it is assumed that machines are continuously avalable (possibly except in some scheduled maintenance intervals), and this gives rise to problems in which the typical scheduling objectives (makespan, total weighted completion time etc) are pursued. A significantly different scenario arises if machines may actually fail, i.e., (i) while performing a job i, a machine becomes unavailable (e.g. breaks down) with probability \pi_i, and (ii) such failures are unrecoverable, in the sense that from then onwards the machine is lost and so are the jobs already allocated and not yet processed on that machine. If a job i is successfully completed, a reward r_i is attained. In this context, the basic problem is how to assign the jobs to the machines and how to sequence them so that the expected reward is maximized. In this talk we review the main results, discuss relationships with other sequencing problems and point out some open problems. We address the following scenarios. 1) m parallel (identical) machines. While the single-machine case is easy, for two or more machines the problem is hard and various approaches have been proposed to address it. For general m, list scheduling yields a 0.8531-approximate solution. The argument of the proof is similar to the one used by Schwiegelshohn to prove Kawaguchi and Kyan’s bound for the minimization of total weighted completion time. 2) In order to hedge against machine failures, one can use job replication. In this case, copies of the same job can be scheduled on different machines, and the reward r_i is attained if at least one copy is successfully completed. Although also this problem is hard for m>=2, relatively simple algorithms provide solutions which are provably close to optimality. 3) This class of sequencing problems is also related to testing problems, as follows. A system consists of n components, each of which can be either functioning or not. Only if all components are functioning, the system is „up“. Component i is functioning with probability \pi_i, and testing it costs c_i. As soon as a component that is not functioning is detected, the testing stops (concluding that the system is „down“). The problem is to decide in which order should the components be tested, in order to minimize the expected costs. While the single-tester problem is solved by a simple priority rule, various problem variants can be considered. In particular, if several testers operate in parallel, under time constraints, the problem gets more complicated. While it is NP-hard for three or more testers, its complexity with two testers is still open.

Alessandro Agnetis graduated in Electrical Engineering from the Università degli Studi di Roma „La Sapienza“ in 1987. He got a PhD in Systems Engineering from the same University in 1992, where he became Assistant Professor of Industrial Automation in 1994. In November 1998 he joined the Università di Siena as Associate Professor of Operations Research. He is Full Professor since 2001.


The seminar is organized by Zdeněk Hanzálek (CIIRC CTU in Prague), Michael Pinedo (New York University) and Guohua Wan (Shanghai Jiao Tong).

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