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This paper considers the scheduling of job families on parallel machines withtime constraints on machine qualifications. In this problem, each job belongsto a family and a family can only be executed on a subset of qualifiedmachines. In addition, machines can lose their qualifications during theschedule. Indeed, if no job of a family is scheduled on a machine during agiven amount of time, the machine loses its qualification for this family. Thegoal is to minimize the sum of job completion times, i.e. the flow time, whilemaximizing the number of qualifications at the end of the schedule. The paperpresents a new Constraint Programming (CP) model taking more advantages of theCP feature to model machine disqualifications. This model is compared with twoexisting models: an Integer Linear Programming (ILP) model and a ConstraintProgramming model. The experiments show that the new CP model outperforms theother model when the priority is given to the number of disqualificationsobjective. Furthermore, it is competitive with the other model when the flowtime objective is prioritized.

A new CP-approach for a parallel machine scheduling problem with time constraints on machine qualifications