We define the base polytope B(P,g) of a partially
ordered set P and a supermodular function g on
the ideals of P 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 give a
complete linear description of B(P,g) for
series-parallel posets 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 posets.
