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. NETWORKS, 2011