Characterizing the set of feasible sequences for n jobs to be carried out on a single machine

This paper deals with the problem of the scheduling of jobs on a single machine presented in terms of decision-aid. This leads to determining the characteristics of the set of schedules which are compatible with the earliest starting times and the latest finishing times of the jobs. A theorem, which enables the determination of the necessary and sufficient conditions for the feasibility of jobs sequences, is proposed. From this basis, an iterative procedure is presented which permits to define the characteristics of the feasible schedules. A Boolean model is used to represent and handle the conditions of feasibility of the schedules.