An integer-valued model for the problem of minimizing the total servicing time of unit claims with parallel devices with precedences

We describe an integer-valued model of the total service time minimization problem for a partially ordered set of claims with identical servicing times, serviced in parallel by identical devices. We construct a target function over the polyhedron corresponding to the problem. We give results of a numerical experiment that deal with the variance of the total service time and the structure of the schedules’ convex hull.