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Regular version of the site

Book chapter

Approximate Method for Solving Scheduling Problems With Minimax Criteria

P. 56-57.

We are given a set $N=\{1,\dots,n\}$ of $n$ jobs that must beprocessed on $m$ machines $M=\{1,\dots,m\}$. Preemption of thejobs is not allowed. Each machine can handle only one job at atime. For each job $j$ we have: $r_j$ -- release date $0\lep_{ji}\le +\infty$ -- processing time job $j$ on the machine $i$(if $p_{ji}=+\infty,$ then job $j$ can not process on the machine$i$) $d_j$ -- due date. Between jobs ratios of a precedence inthe form of an acyclic oriented graph $G \subset N \times N $ areset. Through $\pi_i$ we will definete the schedule of the jobsprocesseded on the machine $i, i=1,\dots,m$. Naturally, admissibleschedules without artificial idle times of the machines,satisfying the graph are considered only.