Scheduling two chains of unit jobs on one machine: A polyhedral study

Abstract

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, (ii) a job does not need to be assigned to any time-slot.

A comparative study of formulations and solution methods for the discrete ordered p-median problem

“…Similar studies of (simpler) polytopes related to location problems have been carried out by e.g. Arbib et al [1], Guignard [8], Cornuéjols and Thizy [4], de Farias Jr. [5] and Vasilyev et al [19].…”

“…The objective function (10) is equivalent to (1). Assume that the k-th smallest allocation cost is equal to c (h k ) for some h k ; then by the definition of the variable…”

Editorial: Preface to the Special Issue

“…Polyhedral aspects of a one‐machine scheduling problem where two sets of unit indivisible jobs compete for a single resource over time are studied by Arbib et al [3]. For the case of a single chain, a complete description of the convex hull of feasible solutions is provided.…”