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Fixed-charge transportation problems on trees

Gustavo Angulo(gustavo.angulo***at***uclouvain.be)
Mathieu Van Vyve(mathieu.vanvyve***at***uclouvain.be)

Abstract: We consider a class of fixed-charge transportation problems over graphs. We show that this problem is strongly NP-hard, but solvable in pseudo-polynomial time over trees using dynamic programming. We also show that the LP formulation associated to the dynamic program can be obtained from extended formulations of single-node flow polytopes. Given these results, we present a unary expansion-based formulation for general graphs that is computationally advantageous when compared to a standard formulation, even if its LP relaxation is not stronger.

Keywords: fixed-charge transportation problem; single-node flow polytope; dynamic programming; pseudo-polynomial extended formulation

Category 1: Integer Programming ((Mixed) Integer Linear Programming )

Category 2: Network Optimization


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Entry Submitted: 11/25/2015
Entry Accepted: 11/25/2015
Entry Last Modified: 11/25/2015

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