The main objective of this research to develop a novel capacitated covering-based opti-mization model for public healthcare facility locations using adaptable Spatial Agent-Based modelling methodology, through the integration of different spatial, economic and social characteristics has been successfully achieved. Mainly, the research focus is to facilitate sustainable healthcare policies for universal coverage of healthcare and ease of access to health service. This subsequently serves as part of strategies for reducing health burden in Nigeria. The research has provided a cost-effective location-allocation measure that incorporates the population size in the type of facilities to be established, while ensuring complete health coverage for all citizens within a realistic travel time threshold. From the questions posed in Chapter 1, the achievements and results of this thesis confirms thus:
1. Spatial Agent-Based modelling analysis can support decision-making in health-care coverage.
2. Geographic Information System (GIS) and Agent-Based Model (ABM) can be integrated for geospatial accessibility and facility location analysis for health in-terventions.
The requirement for solving the central healthcare facility location problem is considerably data based, involving real-world geographic, environmental and socio-economic complexity and heterogeneity. Typically, these problems are solved using
O. Olowofoyeku 6.2. DISCUSSION
sophisticated mathematical or GIS models, or a combination of the two where the GIS provides the required spatial support. The mathematical model would require addi-tional equation for each feature or complexity added to the problem, while the GIS analysis is a static and rational representation of this complexity. Hence the need for the new integrated approach offered by this thesis, based on the Maximum Covering Location Problem (MCLP) that seeks to cover as much demand as possible with fixed number of facilities, p, within a predefined service distance, D, as a cost-effective con-sideration for limited resources. An alternative approach to ensure that the demands outside the coverage of D do not travel inconsiderable distance compared to D is to introduce a distance value, S, greater than D as a constraint in the objective function, beyond which no demand is expected to travel to reach its closest facility. To realise these MCLP with mandatory closeness constraints and objectives, the decision maker is faced with several other challenges identified in Chapter 2. These include knowing the values of p, D and S; and where to locate the p-facilities - without compromising full coverage and ease of access for resource availability. This research has provided a better cost-effective decision support that is flexible, adaptable and can ensure total health coverage. The capacity of the facility is integrated to propose a lower estab-lishment cost for facilities that are under-served. The value of D is the average travel distance in the region of focus, while multiple values of p and S, together with location configurations, are endogenously suggested by the model. The systematic approach and findings of this thesis are provided as follows:
• A loose coupling method was adopted for integrating GIS and ABM. Before the choice of this integration approach, this work tried using close coupling of Agent Analyst extension in the ESRI ArcGIS 10.0 software and discovered that the ex-tension is not compatible with subsequent versions of ArcGIS. The choice of loose coupling is considered to be the best approach such that the spatial data can be in-tegrated without restriction of a system into the other system’s programming en-vironment. Therefore, this synergy is completely independent of any GIS toolkit, either proprietary or open source.
• A methodological framework was developed in Chapter 3 to identify the required spatial data and agents, and the data acquisition processes. The algorithms for proximity and location-allocation analyses were also described. GIS data acquisi-tion and management capability was used to provide the data for the algorithms in ABM. Considering the limited time, technical and financial resources for this research – which is also usually the case in real-life decision-making processes, a budget-friendly and simple road data acquisition process was adopted for the travel-time analysis. Road networks were simply traced out on Google Earth Satellite imagery and converted to vector polyline dataset, considering that the open source ABM tool used does not require the level of accuracy and sophisti-cation that the GIS needs for road connectivity. This was after confirming con-siderable gaps in the available data used by the on-line routing and service area tools and the image data. To represent patients’ destinations, dwellings were
O. Olowofoyeku 6.2. DISCUSSION
randomly simulated in the ABM.
• The coverage of the existing public healthcare services was assessed with a prox-imity analysis. As an improvement to the buffer analysis in resource constrained circumstances, the travel-time model allowed autonomous and mobile agents to travel along road network using the shortest path, within a user-defined time threshold and travel-speed. The polygon joining the end of the agents’ journey formed the catchment of the existing healthcare facilities (HCFs). A straight-line measure was also included for the decision maker to simultaneously compare the two measures.
• The Adaptable Spatial Agent-Based Facility Location (ASABFL) technique pro-posed in this thesis has provided novel solutions to the covering problem by con-verting the continuous space into discrete points as potential facility locations, using meta-heuristics method. A Large Neighbourhood Search (LNS) algorithm was developed for which agents obeyed spatial rules such as: distance for deter-mining their closeness to other agents, containment that examines agents’ loca-tion within certain boundaries, adjacency where polygon features share bound-ary, connectivity for connecting demand locations to their closest HCFs, and in-tersection to check the occupancy of two agents on the same location. The agents take independent decisions while obeying these rules intelligently. Agents are either passive by not moving in the environment, or active by moving and chang-ing their locations - followchang-ing a suitability analysis of examinchang-ing their locations within the neighbourhood, and avoiding forbidding locations such as water bod-ies or committed zones.
The LNS meta-heuristic algorithm is a six-phased process – initialization for de-termining initial feasible solution with greedy random location of facilities; con-struction for relocating facilities after evaluation of conflicts of interest based on intersection and containment spatial rules; destruction for eliminating agents based on adjacency, containment, distance and intersection rules; repair for re-generating more agents based on capacity rules; sorting for classifying selected HCFs based on size of population served and proximity to other amenities within their catchments, and determining uncovered population; and lastly improve-ment and stopping for linking uncovered population to the closest facility, and returning the values of p and S.
• Chapter 4 describes the model verification and validation processes. The robust-ness and consistencies of the models were confirmed via multiple runs and pa-rameter variation. With 30 minutes travel limit at 48 m/min, real-life geographic locations of sets of origin (HCF) and destination (agent’s travel limit) were used as inputs for walking travel distance and time requests to the Google Maps Dis-tance Matrix Application Programming Interface (API). Evaluation of the re-sults with Paired T-Test for Equivalence using the two-one-sided test (TOST) con-firmed the equivalence of the Spatial-ABM travel-time model and Google Maps