Optimal booking of machines in a virtual job-shop with stochastic processing times to minimize total machine rental and job tardiness costs

We treat a virtual job-shop problem of sequencing n jobs on m unique machines. Each machine is outsourced with known renting cost per time unit. The job-operation processing times have random durations, and each job has its tardiness penalty function. The objective is to determine in advance the machine booking schedule that maximizes an economic gain. We present a simulation based on a cyclic coordinate descent search- algorithm and greedy priority dispatching rule that delivers a rent timetable that minimizes the expected total cost.