The Flow Set with Partial Order

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 sequencedependent characterization of the lifting coefficients. We prove, however, if the partial order is defined by an arbore...

• Type: Journal
• Year: 2008
• Where: MOR
• Authors: Alper Atamtürk, Muhong Zhang
• Keywords: Coefficients, Lifting Sequences, MOR 2008, Partial Order