Scheduling job families on non-identical parallel machines with time constraints

This paper studies the scheduling of lots (jobs) of different product types (job families) on parallel machines, where not all machines are able (i.e. are qualified) to process all job families (non-identical machines). This is known in the literature as scheduling with machine eligibility restrictions. A special time constraint, associated with each job family, should be satisfied for a machine to remain qualified for processing a job family. This constraint imposes that there must be at most a given time interval (threshold) between processing two jobs of the same job family, on a qualified machine. A machine is considered to be qualified to process a certain job if and only if, at a given time instant t, the time threshold corresponding to the job family of the job is not violated. This problem comes from semiconductor manufacturing, when Advanced Process Control constraints are considered in scheduling problems, as for example in the photolithography area. To solve this problem, a Time Indexed Mixed Integer Linear Programming (MILP) model was proposed and solved in a previous paper. A new adapted model will be provided in this paper. A bicriteria objective function, that includes scheduling and qualification criteria, is considered. Dedicated heuristics are proposed. Numerical experiments are conducted to compare heuristic and exact solutions.