A branch-and-cut algorithm for the plant-cycle location problem

The fleet size and mix location-routing problem with time windows: Formulations and a heuristic algorithm

“…The second valid inequality, which was used by Labbé et al (2004) for plant-cycle location problem is as follows:…”

Location-routing: Issues, models and methods

“…Paper Section Stochastic LRP 5.2 Dynamic LRP Laporte and Dejax (1989) 5.3 Hamiltonian p-median Branco and Coelho (1990) 4.2 Road-train routing Semet (1995) 6.4 Vehicle routing-allocation (VRAP) Nascimento and Beasley (1996) 6.3 Many-to-many LRP Nagy and Salhi (1998) 6.2 Eulerian location Ghiani and Laporte (1999) 3 LRP with mixed fleet Wu et al (2002) 4.3 Location-routing-inventory Liu and Lee (2003) 5.2 Plant cycle location Labbé et al (2004) 3 Many-to-many LRP Wasner and Zäpfel (2004) 6.2 Multi-level location-routing-inventory Ambrosino and Scutellà (2005) 6.4 Deterministic LRP Albareda-Sambola et al (2005) 4.4 VRAP (median cycle problem) Labbé et al (2005) 6.3 LRP with non-linear costs Melechovský et al (2005) 4.4 Planar LRP (single-depot) Schwardt and Dethloff (2005) 4.2 Restricted VRAP Gunnarsson et al (2006) 6.3 Planar LRP (multi-depot) Salhi and Nagy (2007) 4.3 Table 1. ILP formulations for various LRP problems…”

Cost‐effective designs of fault‐tolerant access networks in communication systems

“…Inspired by the study on the SDHNDP mentioned above, Labbé et al [14] investigated a special LRP, called the plantcycle location problem (PCLP), in which the customers play the role of SSs and the plants play the role of SPs. The PCLP consists of choosing plants to be opened, assigning each customer to an open plant that serves the customer, and routing cycles each containing exactly one open plant and the customers it serves.…”

“…The capacities considered in previous studies [3,14] were fixed features of SPs, and were specified before searching for solutions of the problems. However, new technology allows for greater flexibility in network design and, therefore, offers opportunities for finding cheaper solutions.…”

“…Unlike previous work on heuristic or exact solution approaches, which might suffer from poor solution quality [3] or numerical instability or excessive time consumption [14], we examine the AND problems from the perspective of polynomial-time approximation in view of the NP-hardness (indeed, APX-hardness) of the problems. The known approximation approaches to the FLP do not apply to the AND problems in that in the former problem a direct link from the facility to any of its customers is required, whereas in the latter problems a facility is linked to all its customers through a single cycle.…”