A Bicriterion Maximal Covering Location Formulation Which Considers the Satisfaction of Uncovered Demand

Abstract

T h m ha= been many applications of the maximal Covering location problem (MCLP). An underlying assumption of the MCLP is that demand not covered (i.e.. not within a prespecified maximal distana of a facility) is not served. This may be an unrealistic assumption in many location planning scenarios, a p e c i d l y in the public sector. For example. in cascs such as fire protection or ambulance service. calls not technically covcrcd will still be serviced. The MCLP, however, docs not consider the distances or travel times necessary to service such demand.This paper presents a bicriterion locational covering modd which explicitly considers the travel distance or time necessary to service demand not within the maximal covering distance of a facility.The model may be used to generate noninferior (Pareto optimal) siting configurations which demonstrate the inherent trade-offs betwan a siting scheme designed to maximize total coverage and one designed to minimize total t n v d time for uncovmd demand to reach its nearest facility. In addition, it is shown that for MY particular weighting scheme on the two objectives. the problem can be solved as a p-median problem; a problem for which several efficient solution methods exist. Subject A m : Locrrrlon Mod& and Mathematical h#ramrnIn#.

A Survey of Operations Research Models and Applications in Homeland Security

“…Batta and Mannur (1990) extended the set covering models to include some demand points requiring responses from multiple units (for example, fire trucks or ambulances). Church et al (1991) formulated a bicritera maximal covering location model that maximizes the demand covered within the maximal distance and also minimizes the distance traveled from the uncovered demand to the nearest facility. Schilling et al (1979) developed the tandem equipment allocation model (TEAM) and the facility location, equipment, and emplacement technique (FLEET) model to allocate equipment with varying capabilities and demands.…”

Determining Optimal Police Patrol Areas with Maximal Covering and Backup Covering Location Models

“…Additionally, the MCLP can be seen as a variant formulation of other prominent location models including the p-Median model and the Location Set Covering model (Church and ReVelle 1976), and research has been conducted on the effects of data aggregation errors on solutions (Current and Schilling 1990). Variations of the MCLP have been formulated to include workload capacities (Pirkul and Schilling 1991), or to maximize coverage and minimize distances to demands outside the maximum covering distance (Church et al 1991). Several models that include conditional coverage , backup coverage (Hogan and ReVelle 1986), or both (Pirkul and Schilling 1988) have appeared, and a more thorough treatment of this literature appears in Section 3.2 below.…”

“…A bicriterion maximal covering formulation that attempts to maximize coverage while simultaneously minimizing the total weighted distance to uncovered incidents (Church et al 1991) may ameliorate this situation.…”

Solução simultânea de problemas logísticos de localização de depósitos e centralização de estoques

“…Os exemplos de aplicação são geralmente relacionados aos problemas de localização de facilidades cuja proximidade é indesejável. Church & Garfunkel (1978) aplicaram o modelo em problemas de localização de depó-sitos de lixo e Berman et al (1996), em problemas de localização de prisões e instalações militares.…”

“…Ele se distingue do problema de roteirização pelo fato de o ponto fi nal ser distinto do inicial e de a solução depender da decisão do ponto inicial do trajeto. Church & Eaton (1987) utilizaram um modelo de k-servos para determinar a localização de clínicas e hospitais.…”