Scheduling tasks with comb precedence constraints on dedicated machines

A set of n nonpreemptive tasks are to be scheduled on m dedicated machines in order to minimize the overall makespan. Precedence constraints among the tasks, deterministic processing times and processing machine of each task are given. We present lower bounds of the minimum makespan and heuristic algorithms for two relevant cases in manufacturing applications, namely when the precedence constraints form a comb or a caterpillar. Promising preliminary computational tests are also reported proving the efficiency and effectiveness of the proposed solution algorithm.