Pareto optimization scheduling of family jobs on a p-batch machine to minimize makespan and maximum lateness

This paper studies the Pareto optimization scheduling problem of family jobs on an unbounded parallel-batching machine to minimize makespan and maximum lateness. In the problem, the jobs are partitioned into families and scheduled in batches, where each batch is a set of jobs belonging to a common family and the processing time of a batch is defined to be the longest processing time of the jobs in the batch. The objective is to find all Pareto optimal points for minimizing makespan and maximum lateness and, for each Pareto optimal point, provide a corresponding Pareto optimal schedule. We present an algorithm to solve this Pareto optimization problem. Our algorithm is of polynomial-time when the number of families is a constant.