Base polytopes of series-parallel posets: Linear description and optimization

We define the base polytope B(P, g) of a partially ordered set P and a supermodular function g on the ideals ofP as the convex hull of the incidence vectors of all linear extensions of P. This new class of polytopes contains, among others, the base polytopes of supermodular systems and permutahedra as special cases. After introducing the notion of compatibility for g, we givea complete linear description of B(P, g) for series-parallel posers and compatible functions g. In addition, we describe a greedy-type procedure which exhibits Sidney's job sequencing algorithm to minimize the total weighted completion time as a natural extension of the matroidal greedy algorithm from sets to posers. © 1998 The Mathematical Programing Society, Inc. Published by Elsevier Science B.V. Keywords." Polyhedral combinatorics; Series parallel posets; Base polytopes; Supermodular functions; Greedy algorithm; Integer programming

• Type: Journal
• Year: 1998
• Where: MP
• Authors: Rainer Schrader, Andreas S. Schulz, Georg Wambach
• Keywords: Base Polytopes, Greedy Algorithm, MP 1998, Supermodular Functions