Abstract
In this work, two network design concepts which have been proven to be relevant with respect to telecommunication applications, are joined within a unified approach. First, the cable trench problem searches for cost-minimizing network structures that take into account two types of edge costs appearing in the installation of wire-based networks, namely trenching costs and cable costs. Second, the facility location problem considers the placement of shared telecommunication equipment, like switches or concentrators, together with an assignment of entities to demand nodes. Following practical needs, we join these concepts within the new capacitated cable trench problem with facility costs and service capacity in terms of number of customers that can be served by facilities. Within this setting, facility location decisions in wire-based networks can be taken under a more realistic cost scenario. A mixed-integer linear program and valid inequalities are proposed. Experiments indicate a positive impact of the valid inequalities on computational time and integrality gap.
Highlights
Facility location models study the optimal placement of service entities and are of particular interest in telecommunication network design, e.g., in the placement of concentrators (Yaman 2005; Gourdin et al 2002)
The observed integrality gap is given as Adding valid inequalities (13) and (14) to cCTP-FL increases the optimal value of the LP-relaxation to gL P(13,14) = 2860, leading to a new intregrality gap of g∗/gL P(13,14) = 6060/2860 = 2.12
To verify the improvements obtained by the valid inequalities, two paired t-tests have been carried out to investigate whether the differences in computational time and whether the differences in the gap are significant
Summary
Facility location models study the optimal placement of service entities and are of particular interest in telecommunication network design, e.g., in the placement of concentrators (Yaman 2005; Gourdin et al 2002) In such models, expenses for connecting demand to source nodes are typically defined through a single cost type. A further extension of the p-CTP is the p-cable trench problem with covering ( p-CTPC), (Gutiérrez-Jarpa et al 2015; Marianov et al 2015) In this approach, demand nodes are connected through a hierarchical two-level system where only the primary and secondary servers are forming a wire-based network. The inclusion of facility setup expenses is a common component in facility location problems; see, e.g., Klose and Drexl (2005) and Yaman (2005) for telecommunication applications in particular To integrate this aspect within the cCTP-FL, node-dependent facility opening costs fi are introduced for each node i.
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