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Stronger Multi-Commodity Flow Formulations of the (Capacitated) Sequential Ordering Problem

Adam N. Letchford(a.n.letchford***at***lancaster.ac.uk)
Juan José Salazar González(jjsalaza***at***ull.es)

Abstract: The "sequential ordering problem" (SOP) is the generalisation of the asymmetric travelling salesman problem in which there are precedence relations between pairs of nodes. Hernández & Salazar introduced a "multi-commodity flow" (MCF) formulation for a generalisation of the SOP in which the vehicle has a limited capacity. We strengthen this MCF formulation by fixing variables and adding valid equations. We then use polyhedral projection, together with some known results on flows, cuts and metrics, to derive new families of strong valid inequalities for both problems. Finally, we give computational results, which show that our findings yield good lower bounds in practice.

Keywords: sequential ordering, travelling salesman problem with precedence constraints, multi-commodity flows, metrics, polyhedral combinatorics

Category 1: Combinatorial Optimization (Branch and Cut Algorithms )

Category 2: Network Optimization

Category 3: Integer Programming ((Mixed) Integer Linear Programming )

Citation: Lancaster University, May 2015.

Download: [PDF]

Entry Submitted: 05/26/2015
Entry Accepted: 05/26/2015
Entry Last Modified: 05/26/2015

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