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BCOL RESEARCH REPORT 05.03 Industrial Engineering & Operations Research
 

Summary: BCOL RESEARCH REPORT 05.03
Industrial Engineering & Operations Research
University of California, Berkeley, CA
Forthcoming in Mathematics of Operations Research
THE FLOW SET WITH PARTIAL ORDER
ALPER ATAMTšURK AND MUHONG ZHANG
Abstract. The flow set with partial order is a mixed-integer set described by
a budget on total flow and a partial order on the arcs that may carry positive
flow. This set is a common substructure of resource allocation and scheduling
problems with precedence constraints and robust network flow problems under
demand/capacity uncertainty.
We give a polyhedral analysis of the convex hull of the flow set with partial
order. Unlike for the flow set without partial order, cover-type inequalities
based on partial order structure are a function of a lifting sequence. We study
the lifting sequences and describe structural results on the lifting coefficients
for general and simpler special cases. We show that all lifting coefficients can
be computed in polynomial time by solving maximum weight closure problems
in general. For the special case of induced-minimal covers, we give a sequence-
dependent characterization of the lifting coefficients. We prove, however, if the
partial order is defined by an arborescence, then lifting is sequence-independent

  

Source: Atamtürk, Alper - Department of Industrial Engineering and Operations Research, University of California at Berkeley

 

Collections: Engineering