Arnaud Malapert

Margaux Nattaf, Arnaud Malapert

This paper studies the scheduling of jobs of different families on parallel machines with qualification constraints. Originating from semiconductor manufacturing, this constraint imposes a time threshold between the execution of two jobs of the same family. Otherwise, the machine becomes disqualified for this family. The goal is to minimize both the flow time and the number of disqualifications. Recently, an efficient constraint programming model has been proposed. However, when priority is given to the flow time objective, the efficiency of the model can be improved. This paper uses a polynomial-time algorithm which minimize the flow time for a single machine relaxation where disqualifications are not considered. Using this algorithm one can derived filtering rules on different variables of the model. Experimental results are presented showing the effectiveness of these rules. They improve the competitiveness with the mixed integer linear program of the literature.

Arnaud Malapert, Margaux Nattaf

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