par Arbib, Claudio;Servilio, Mara;Labbé, Martine
Référence Networks, 58, 2, page (103-113)
Publication Publié, 2011-09
Article révisé par les pairs
Résumé : We investigate polyhedral properties of the following scheduling problem: given two sets of unit, indivisible jobs and revenue functions of the jobs completion times, find a one-machine schedule maximizing the total revenue under the constraint that the schedule of each job set respects a prescribed chain-like precedence relation. A solution to this problem is an order preserving assignment of the jobs to a set of time-slots. We study the convex hull of the feasible assignments and provide families of facet-defining inequalities in two cases: (i) each job must be assigned to a time-slot and (ii) a job does not need to be assigned to any time-slot. © 2011 Wiley Periodicals, Inc.