The Network Design Problem with Relays

University of Alberta School of Business Research Paper No. 2013-1080

European Journal of Operational Research Volume 180, Issue 2, 16 July 2007, Pages 834–844

Posted: 2 Jul 2013

Date Written: June 1, 2006

Abstract

The network design problem with relays (NDPR) is defined on an undirected graph G = (V, E, K), where V = {1, … , n} is a vertex set, E = {(i, j) : i, j ∈ V, i < j} is an edge set. The set K = {(o(k), d(k))} is a set of communication pairs (or commodities): o(k) ∈ V and d(k) ∈ V denote the origin and the destination of the kth commodity, respectively. With each edge (i, j) are associated a cost cij and a length dij. With vertex i is associated a fixed cost fi of locating a relay at i. The NDPR consists of selecting a subset of edges of E and of locating relays at a subset of vertices of V in such a way that: (1) the sum Q of edge costs and relay costs is minimized; (2) there exists a path linking the origin and the destination of each commodity in which the length between the origin and the first relay, the last relay and the destination, or any two consecutive relays does not exceed a preset upper bound λ. This article develops a lower bound procedure and four heuristics for the NPDR. These are compared on several randomly generated instances with |V| ⩽ 1002 and |E| ⩽ 1930.

Suggested Citation

Cabral, Edgar Alberto and Erkut, Erhan and Patterson, Raymond and Laportec, Gilbert, The Network Design Problem with Relays (June 1, 2006). University of Alberta School of Business Research Paper No. 2013-1080, European Journal of Operational Research Volume 180, Issue 2, 16 July 2007, Pages 834–844, Available at SSRN: https://ssrn.com/abstract=2282061

Erhan Erkut

Independent ( email )

Raymond Patterson

Independent

Gilbert Laportec

HEC Montréal ( email )

Montréal, H3T 2A7
Canada

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