Optimal parallel machines scheduling with machine availability and eligibility constraints

In reality, the machine might become unavailable due to machine breakdowns or various inevitable reasons, and machine might have different capability to processing job. Motivated by this, we consider the problem of scheduling n non-preemptive and independent jobs on m identical machines incorporating machine availability and eligibility constraints while minimizing the maximum lateness. Each machine is capable of processing at specific availability intervals. We develop a branch and bound algorithm applying several immediate selection rules for solving this scheduling problem.