CARÁCTER EXPERIMENTAL DE UN MANUAL. ÍNDICE GLOBAL

and Owen, 1999).

Maximal Covering Location Problems (MCLP) was developed by Church and ReVelle (1974) to increase the cost factor of the decision making process of the LSCP.

They observed that out of many solutions of a particular LSCP, it is possible that the minimum service distance that can provide total coverage for a fixed cost (number of facilities) is quite larger than the desired service distance, D. This may lead the decision maker to shift focus from total coverage with the larger service distance, to total coverage with the desired service distance, D. This will require more facilities and expenditure. With limited resources, the resort may be to cover as many demand as possible within D and the available resources. This led to the formulation of the MCLP by Church and ReVelle (1974) that seeks to locate p facilities to maximize the demand or population covered within a specified service distance or time. In this case, if the available resources cannot meet the desired total coverage level, the objective is relaxed to provide the coverage to as many demands as possible. In other words, the total coverage requirement within the exogenously specified distance is relaxed. The MCLP has been applied in many health service facility location problems. For example, Meskarian et al. (2017) used the MCLP for planning clinic locations for sexual health services in Hampshire, United Kingdom.

p-Centre Location Problems (PCLP) seeks to minimize the maximum travel tance or time between demand location and facility location. In this case, service dis-tance or time is not known. It is a location-allocation problem that simultaneously finds optimal locations of facilities and allocates demand to those facilities. In this circum-stance, all the demand locations must be covered within an endogenously determined maximum distance. Lu (2013) developed a p-centre model to locate relief distribution centres for emergency natural disaster on-set that was applied to earthquake case in Taiwan.

The facility location problem for this research falls in the category of covering problems because it seeks to provide service coverage to the population, with the ob-jective function of maximizing coverage within a service distance. It also seeks to mini-mize the maximum travel distance between the farthest demand and its closest facility.

2.5 Considerations for Locating Healthcare Facilities

Despite the considerable uncertainties and imbalance underlying real-life decision-making process of location selection for HCFs, most location models are focused on the intrinsic assumptions of proportionate basic input parameters, such as the popula-tion size, HCF capacity, the number and the locapopula-tion of HCFs, and the service distance.

These models take these parameters as static and constant inputs, and tend to ignore the reality varying population sizes and access to health services that affect the dis-tribution of scarce service providers, HCFs and resources. These location problems are solved as static (Ahmadi-Javid et al., 2017) or deterministic (Boonmee et al., 2017)

O. Olowofoyeku 2.5. CONSIDERATIONS FOR LOCATING HEALTHCARE FACILITIES

location problems. For example, Dekle et al. (2005) used the deterministic approach to locate disaster recovery centres in a Florida County. The objective was to minimize the total number of recovery centres that will cover the residence within fixed dis-tance radius. Also, Ye et al. (2015) developed emergency warehouse location problem (EWLP) as an extension of the P-centre problem and used Variable Neighbourhood Search (VNS) heuristic to locate fixed number of emergency warehouse within given coverage radius in China. These models assumed equal capacity for the facilities. How-ever, Wang and Ma (2018) in their deterministic model considered unfixed capacity in location-allocation for locating nursing homes for the elderly people in Kongjiang Road area, Shanghai. The objectives were to minimize the total construction costs and mini-mize the total weighted distances from the nursing home to the community. Kim and Kim (2013) also solved a public healthcare facility location problem using Lagrangian heuristic algorithm applied to North and South Chungcheong Provinces, Korea. The aim was to maximize patient coverage with fixed budget constraint. The model con-sidered allocating low-income patients to the public HCFs and high-income patients to both public and private HCFs.

In real-world situation however, healthcare facility locations are characterised with uncertainties and are therefore not often predictable (Afshari and Peng, 2014). Inter-est in recent facility location problems has shifted to such uncertainties which in turn have influence in the input parameters. The integration of the varying uncertainty fac-tors has been identified as a major challenge in real-world location problems (Daskin and Owen, 1999; Snyder, 2006). Different approaches have been applied to address this in HCF location decision (Snyder, 2006). Murawski and Church (2009) identi-fied the lack of all-weather roads in the under-developed countries where changes in weather conditions such as rains affect the states of the roads, and therefore has im-pact in accessibility. The authors developed the Maximal Covering Network Improve-ment Problem (MC-NIP) model to predict the accessibility to health services based on road improvement and applied it to a rural area in Ghana. Mestre et al. (2015) developed two stochastic location-allocation models for planning hospital networks re-organization under uncertainty associated with the demand and supply of hospi-tal services, when the decision maker considers improving geographical access, while minimizing costs. The models were applied to the Portuguese National Health Service.

Harper et al. (2005) also developed a discrete-event geographical location–allocation simulation model using stochastic approach for location of health service centers that considered variable patient flows, travelling times, and transport preferences, includ-ing different services. Also, in their work, Wang et al. (2018) addressed uncertainties in medical demands and costs with a bi-level multi-objective particle swarm optimiza-tion (BLMOPSO) using fuzzy and stochastic factors that was applied to a case study in China.

Another limitation in the traditional covering HCF location models is the mod-elling of the real-world as homogeneous system where the environment is assumed to have similar characteristics. Spatial heterogeneity of the real-world in terms of

varia-O. Olowofoyeku 2.5. CONSIDERATIONS FOR LOCATING HEALTHCARE FACILITIES

tions of environmental characteristics or conditions (roads, vegetation, wetlands, pop-ulation distribution) influences the HCF locational choice, resources, demand alloca-tion, travel time, service area, service distance, and number and location of HCFs. Spa-tial heterogeneity has been identified to influence imbalance in accessibility to health-care services (Yin et al., 2018) and ambulance service time (Leknes et al., 2017). The simplification of the complex real-world heterogeneous problem are location models with the same geographic characteristics. However, each HCF has a unique combina-tion of populacombina-tion and spatial features within its catchment that results in distinguish-able capacity, size of healthcare workers, and resource allocation. Therefore, HCFs characteristics are location-dependent based on the social, economic, demography and geographical environment (Zhang et al., 2016).

Although the number of facilities, for example, may be suggested based on a fa-cility density ratio as a function of the aggregate population size, it is evident that the spatial distribution of population is heterogeneous (Su et al., 2010). Such distribution has a direct impact on the population size within a setting. A group of people may dwell within certain regions based on ethnicity or religious belief, while a settlement may be influenced by economic activities and geographical features. For example, fish-ing activities may be a factor for dwellfish-ing close to rivers. Other settlement pattern may be due to commercial activities and proximity to roads, schools or workplaces. Few works have considered spatial heterogeneity and combined GIS with other locational techniques (Malczewski, 1999). In this regard GIS plays a valuable means of informing the decision. For example, Zhang et al. (2016) considered the heterogeneous spatial distribution of population and economic development in Hong Kong, that is charac-terised with mountainous topography. The authors used Genetic Algorithm-based multi-objective optimization in locating HCFs and allocating demand to the HCFs.

Decisions for establishing HCFs is typically a long-term commitment of substan-tial resources - technology, equipment, human and infrastructure. Such decisions may be very difficult to reverse or change after it has been implemented. Static facility lo-cation may result in waste of scarce resources and redundant expenditure due to in-equity in spatial circumstances. HCF planning should possess adaptation to changing socio-economic and geographic conditions. Due to the complexity of such decision making in site selection for HCFs, integrating GIS and ABM as proposed in this thesis provides alternative adaptable solutions to aid decision making that combines such factors. The heterogeneous spatial characteristics and population distribution are con-sidered to flexibly suggest the number and location of HCFs, and the service distance or travel time. Agents are capable of sensing and adapting to changes in the environment.

For example, changes in the population size, changes from land to water, changes from committed to uncommitted zones. As opposed to static modelling, HCFs represented by mobile agents can change their locations. The emergent behaviour from these in-teraction with environment changes results in different service area, service distance, HCF network, including location and number of HCFs. This adaptability also makes it possible for the agents to change their states, reflecting the current HCF capacity that