Closest assignment constraints in discrete location problems

Capacitated p -center problem with failure foresight

“…Constraints (9)-(12) resemble the classical constraints in discrete location problems. In our formulation they ensure allocation of a site to two different centers and fix the number of centers at p. Due to the capacity constraints we need to add closest assignment constraints (CAC) to the formulation (a recent and complete study of CAC can be consulted in Espejo, Marín, and Rodríguez-Chía, 2012). Constraints (13) improve on those proposed in Wagner and Falkson (1975), and force a variable x ij to take value one if j is the closest center with respect to site i.…”

When centers can fail: A close second opportunity

“…In this formulation this is done by means of Closest Assignment Constraints (CAC) (4). Recent studies of CAC for standard discrete location formulations can be consulted in [16,22]. Actually, constraints (4) can be replaced by the stronger constraints…”

“…In the case of formulation (F2), we have compared the plain formulation with the formulation reinforced with valid inequalities (16) and (17) (from now on, (F2) 0 ). Regarding the formulations presented in Section 5 (the formulation using covering variables) we have always used in our computational experiments its improved form (F4b) and considered two settings: the plain formulation (F4b) with upper bound, and the reinforcement of (F4b) which incorporates constraints (25), that we will denote by (F4b) 0 .…”

“…To see how (16) works, assume that there exists a site k such that d ik 4 d ij with x ik ¼ 1. This means site i is allocated to a center further from i than j, and then all p centers (apart from i itself) must be also further from i than j.…”

Capacity management in public service facility networks: a model, computational tests and a case study

“…Indeed, this mechanism will drive the reallocation of users previously assigned to closed (or downsized) facilities to the ones that are still active; it will also play a pivotal role in the assessment of the damage imposed on the users themselves. It has to be highlighted that most of the surveyed papers (regardless of their classification) assume that users choose the closest available facility (Espejo et al, 2012); this assumption implicitly considers all facilities being equally attractive. In real-world applications, it can be reasonably supposed that the distance is not the only factor to be considered in the choice, as facilities are characterized by different attractiveness profiles.…”