Minimising total flow-time on two parallel machines with planned downtimes and resumable jobs

This study considers the flow-time minimisation problem on two identical parallel machines, where the machines are subject to planned downtimes. Jobs that are interrupted due to machine downtimes may resume processing once the machine becomes available without incurring additional costs or setup times. We identify optimality properties, develop upper and lower bounding procedures, and present a branch and bound methodology based on the proposed properties and bounds. The computational efficiency is tested on problem instances with up to 35 jobs