Minimizing Total Weighted Earliness and Tardiness for Parallel Batch-processing Machines with Incompatible Job Families

Abstract

This paper considers the parallel batch-processing machines with incompatible job families, that is, jobs with the same recipe can be processed together as a batch, and the sizes of these jobs in a batch should not exceed the capacity limit of a machine. Additionally, setups are required between batches with different families on a machine. Jobs come from the same customer have identical due dates, and according to contracts, penalty occurs when orders are delivered early or late. Thus, in this paper we attempt to formulate a constrained programming model to find a schedule for minimizing the weighted earliness and tardiness. By examining the model using two instances, the results showed that it requires a lot of computation time to find the optimal solution for the given examples due to its inherent complexity. It leads us to develop some heuristic algorithms to obtain optimal or near-optimal solutions efficiently in the future.