This paper is concerned with scheduling when the data are not fully knownbefore the execution. In that case computing a complete schedule off-linewith estimated data may lead to poor performances. Some flexibility must beadded 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 stabilizationscheme. This is applied to the m machine problem with communicationdelays: 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 theoreticalresults for tree-like precedence constraints and an experimental study show the interest of this approach compared with fully on-line scheduling.

A recently introduced dualization technique for binary linear programs with equality constraints, essentially due to Poljak et al. [13], and further developed in Lemaréchal and Oustry [9], leads to simple alternative derivations of well-known, important relaxations to two well-known problems of discrete optimization: the maximum stable set problem and the maximum vertex cover problem. The resulting relaxation is easily transformed to the well-known Lovász θ number.

The classical colouring models are well known thanks in large part to their applications to scheduling type problems; we describe the basic concepts of colourings together with a number of variations and generalisations arising from scheduling problems such as the creation of school schedules. Some exact and heuristic algorithms will be presented, and we will sketch solution methods based on tabu search to find approximate solutions to large problems. Finally we will also mention the use of colourings for creating schedules in sports leagues and for computer file transfer problems. This paper is an extended version of [37].