Scheduling with periodic due date to minimize the maximum tardiness in lean production of medical equipment

Abstract

In the paper, we study the scheduling problem in single-machine and parallel-machine environment in lean production of medical equipment. We no longer follow the exploration idea of scheduling problems under the traditional duration rules, and no longer set the duration of a job as its own attribute, that is, we no longer specifically set the duration of a job one by one, but specify it by the sequencing position of the jobs in the specific scheduling scheme. And the interval length between two consecutive construction due dates is equal. This rule is called periodic due dates. The goal we are considering is to minimize the maximum tardiness. For single-machine environment, we give an optimal schedule in polynomial time; for two parallel-machine environment, we demonstrated the problem is binary NP-hard; for parallel-machine environment, we prove the problem is strong NP-hard.