Scheduling jobs with machine-dependent release dates on unrelated machines

This paper considers the job scheduling problem with varying release dates on unrelated parallel machines. Our model involves the machine-dependent release dates and the makespan criterion. The two developed and presented constructive deterministic algorithms use different decomposition strategies that result logically from exploiting the problem structure. The approximation factor of the greedy polynomial algorithm depends on the machines. An efficient adaptation of the well-known brute-force technique to solve
$Rm\vert r_{i,j}\vert C_{\max}$
is also considered in this paper. A series of numerical experiments are conducted to compare the quality of schedules.