Parallel Machine Scheduling with Uncertain Communication Delays

Abstract

Abstract. This paper is concerned with scheduling when the data are not fully known before the execution. In that case computing a complete schedule off-line with estimated data may lead to poor performances. Some flexibility must be added to the scheduling process. We propose to start from a partial schedule and to postpone the complete scheduling until execution, thus introducing what we call a stabilization scheme. This is applied to the m machine problem with communication delays: in our model an estimation of the delay is known at compile time; but disturbances due to network contention, link failures, ... may occur at execution time. Hence the processor assignment and a partial sequencing on each processor are determined off-line. Some theoretical results for tree-like precedence constraints and an experimental study show the interest of this approach compared with fully on-line scheduling.

A robust approach for the single machine scheduling problem

“…On the other side, some proactive-reactive approaches tend to prioritize the quality robustness: a set of schedule solutions is computed so that the performance can be ensured whatever the selected solution is. In this second class, a temporal flexibility (Chiang and Fox 1990;Gao et al 1995;Davenport et al 2000;Leon et al 1994;Mehta and Uzsoy 1998;Herroelen and Leus 2004b;Tavares et al 1998) or a sequential flexibility (Wu et al 1999;Moukrim et al 2003;Billaut and Roubellat 1996;Esswein et al 2004;Aloulou et al 2002) is inserted into an initial deterministic solution in order to protect it against unforeseen events. Indeed, a solution which is sequentially or temporally flexible characterizes a set of solutions that can be used in the on-line phase.…”