Bi-objective scheduling on a restricted batching machine

In this work, we consider a batching machine that can process several jobs at the same time. Batches have a restricted batch size, and the processing time of a batch is equal to the largest processing time among all jobs within the batch. We solve the bi-objective problem of minimizing the maximum lateness and number of batches. This function is relevant as we are interested in meeting due dates and minimizing the cost of handling each batch. Our aim is to find the Pareto-optimal solutions by using an epsilon-constraint method on a new mathematical model that is enhanced with a family of valid inequalities and constraints that avoid symmetric solutions. Additionally, we present a biased random-key genetic algorithm to approximate the optimal Pareto points of larger instances in reasonable time. Experimental results show the efficiency of our methodologies.