Multi‐Type, Multi‐Zone Facility Location

Abstract

The placement of facilities according to spatial and/or geographic requirements is a popular problem within the domain of location science. Objectives that are typically considered in this class of problems include dispersion, median, center, and covering objectives—and are generally defined in terms of distance or service‐related criteria. With few exceptions, the existing models in the literature for these problems only accommodate one type of facility. Furthermore, the literature on these problems does not allow for the possibility of multiple placement zones within which facilities may be placed. Due to the unique placement requirements of different facility types—such as suitable terrain that may be considered for placement and specific placement objectives for each facility type—it is expected that different suitable placement zones for each facility type, or groups of facility types, may differ. In this article, we introduce a novel mathematical treatment for multi‐type, multi‐zone facility location problems. We derive multi‐type, multi‐zone extensions to the classical integer‐linear programming formulations involving dispersion, centering and maximal covering. The complexity of these formulations leads us to follow a heuristic solution approach, for which a novel multi‐type, multi‐zone variation of the non‐dominated sorting genetic algorithm‐II algorithm is proposed and employed to solve practical examples of multi‐type, multi‐zone facility location problems.

Optimisation of tower site locations for camera-based wildfire detection systems

“…It has been shown how a Multi-Objective Evolution Algorithm may find more non-dominated solutions than are found by a weighted-sum approach, and as a result, may achieve a superior Pareto-front approximation to a weighted-sum approach (Kim et al, 2008). Examples of the application of Multi-Objective Evolutionary Algorithms to placement problems include the placement of transmitters (Meunier et al, 2000;Raisanen and Whitaker, 2005), wind turbines (Kwong et al, 2014;Yamani Douzi Sorkhabi et al, 2016), and observation equipment (Kim et al, 2004;Tong et al, 2009;Bao et al, 2015;Heyns and Van Vuuren, 2015;Heyns and van Vuuren, 2018).…”

Reduced Target-Resolution Strategy for Rapid Multi-Observer Site Location Optimisation

“…The raster points provide an initial set of candidate sites for facility placement and are typically reduced to those which satisfy certain placement requirements, such as lying within allowable geographical and administrative/municipal boundaries, or exhibiting terrain characteristics that are suitable for placement [19]- [22]. The final set of candidate sites is called the Placement Zone (PZ) [1]. Similarly, the raster points also provide an initial set from which the final set of demand points are identified -e.g.…”

“…Covering location problems form a fundamental branch in the field of facility location science [1]- [3]. In these problems, the aim is to locate systems of facilities or equipment in such a manner that they service multiple demand points optimally [3].…”

“…visible or detectable) from a specific assignment of facility locations, an estimation of coverage of these regions achieved by the system may be calculated. Examples of typical facilities which are considered in this context include cellular transmitters [5]- [7], weather radar [8]- [10], military equipment such as radars and weapons [1], [11], and surveillance sensors [12]- [15]. The work presented in this paper is focussed towards application with such equipment using a uniformly-spaced demand representation, and the possibility of service depends on factors such as terrain obstruction of visibility between an observer location and a demand point, and facility visibility/detection ranges.…”

“…The strategy developed here is easily replicable and does not require any elaborate site/demand abstraction processes investigated in the literature, or heuristics, and may be beneficial to various modern site-selection problems, e.g. the siting of wildfire detection towers [12], cellular transmitters [5]- [7], weather radar [8]- [10], and military equipment such as signal jammers [37], and radars and weapons [1], [11].…”