The South African Social Security

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1 Visualisation Spatial optimisation of the SA Social Security Agency service offices by Larry Zietsman, Geographical Systems Research Bureau, and Cobus van Doorn, SITA Location-allocation modelling provides a methodology for optimising accessibility by creating a spatially equitable and efficient distribution of service locations at lower overall costs. The South African Social Security Agency (SASSA) strives to provide an optimal service of social benefits and welfare grants to the population of South Africa. One of the areas identified by SASSA for improvement relates to public accessibility to its service office locations and the services rendered at these points. The current distribution pattern has grown historically by incremental and fragmental adaptation and may contain over or underserved areas. A thorough investigation into the rationality and optimality of the existing distribution pattern of service offices was called for. The agency provides services at about 900 service offices in the RSA. Service offices have direct contact and interaction with the beneficiary population. Grant applications, interviews, queries, assistance etc. are handled at these offices. Three types of service points are currently in operation, i.e. service offices, satellite offices and mobile sites serviced by vehicles. Fig. 1: Location-allocation modelling procedures, inputs and outputs. (Source: A Naude, CSIR (Adapted).) The purpose of this paper is to describe the development of a spatial optimisation model for service offices. The model utilises travel time and incorporates topographical effects and mobility variations between different regions. Modelling methodology The basic premise on which the spatial optimisation modelling is based is that the service distribution network is a public good and that spatial efficiency should therefore not be achieved at the cost of equity. This means that a methodology should be developed that would provide a distribution network of service locations that would optimise coverage but which is constrained by a certain maximum travel distance or time. From a public authority perspective, optimisation of coverage to service as many beneficiaries as possible with the least number of service points is required to use funds as efficiently as possible. A time constraint was imposed to ensure that all individuals are within a predetermined travel time from a service point in order to adhere to the service standards adopted by the agency. This will ensure an equitable solution. Alternative locationallocation scenarios were investigated and a solution selected that is most acceptable to the agency and the public at large. The steps displayed in Fig. 1 were followed to derive an optimised distribution of service locations. Accordingly, the various input datasets required were: Geographical distribution of social grant beneficiaries (demand) Potential destinations for social service offices (supply) Travel time matrix linking all demand and supply locations (road network) Determination of the beneficiary population and spatial distribution As previous estimates of the beneficiary population numbers in South Africa were based on the 2001 Population Census, it was necessary to update the figures. The StatsSA 2007 Community Survey was used for this purpose. PositionIT Nov/Dec

2 Population density Grid size = 5 people per sq km 10 x 10 km ڤڤ 5,1 25 7,5 x 7,5 km 25,1 50 5,0 x 5,0 km 50, ,5 x 2,5 km > 500 people per sq km 1,0 x 1,0 km Table 1: Population density categories and grid cell sizes used for modelling beneficiary demand. Fig. 2: Extract of grid with varying resolution used for spatial modelling. Fig. 3: Distribution of estimated social grant beneficiaries in South Africa (2008). to the changed legislation which will extend child support grants (CSGs) from 14 to 18 years of age and old age pensions (OAPs) for males from 65 years to 60 years. Due to limited space the methodology followed is not discussed in this paper. The spatial distribution of the beneficiary population was required in order to determine where the optimum locations of service points should be. A spatial framework of varying resolution was developed for modelling service offices as it provides a much more realistic representation of spatial variations than a uniform grid. The grid that was generated was based on variations in population densities at municipality level. Four levels of population densities were defined in non-metropolitan areas using Jenk s method to find natural breakpoints in the population densities per municipality. A fifth level was allocated to metropolitan areas. Table 1 lists the population density levels and spatial grid sizes used to spatially model the numbers of beneficiaries. Fig. 2 shows an extract from the resultant spatially varying grid. As the location-allocation model was to be run on a spatially varying gridded mesh for the entire country it was necessary to determine the number of beneficiaries per grid cell. This was done by spatially intersecting the GIS layer of data containing the 2001 population census Small Area Layer (SAL) boundaries and adjusted beneficiary totals derived from the StatsSA 2007 Community Survey with the boundaries of the gridded mesh. The beneficiary data in the intersected resultant layer of information was then recomputed per grid cell by redistributing the population figures proportionally to the area of grid cell in relation to the area of the SAL of which it formed part. Once this has been done the beneficiary totals per polygon were re-aggregated (summed) per grid cell to obtain the final spatial distribution of demand based on the spatially varying grid making up the country. Fig. 3 shows the distribution of the estimated beneficiary population in the country and Fig. 4 the density distribution. The 2007 Community Survey undertaken by Statistics South Africa provided estimates of the size of the population as well as the number of people receiving social grants at a municipal level. The survey tabulated social grants by type. The StatsSA number of beneficiaries per municipality per grant type (old age pension, child support grants, other) were expressed as a proportion of their respective StatsSA national grant type totals. These ratios were then applied per municipality using the SASSA national totals per grant type to obtain updated 2008 estimates of the number of beneficiaries per grant type at a municipal level. As these figures pertain to the current legislative situation a further step was required to estimate the expected increases in beneficiary numbers due Determination of potential service point sites All existing SASSA service offices (excluding regional and district) were considered as potential locations for service office sites. In addition Thusong Centres, Home Affairs offices, vacant post offices and sub-places identified by the 2001 population census located further than 2 km from service points were incorporated into the spatial 50 PositionIT Nov/Dec 2009

3 news modelling framework for consideration. In total more than potential sites were identified as possible locations for service offices. Fig. 5 shows the distribution of these locations across the country. Road network data Location-allocation modelling can be applied to a road network. In which case optimal sites are found by computing shortest travel times from demand origins to service destinations through the network. The most comprehensive and up-to-date road network data available for the country was obtained for the model. This consists of about 1,6-million road segments (Fig. 6). This road network dataset also included tertiary and lower order road classes. This is important especially for more accurately modelling accessibility in rural and remote areas. Another advantage of the road network was the availability of travel speeds from which travel times could be computed. Fig. 4: Density distribution of the estimated beneficiary population (2008). Feed links As most centroids of demand cells and potential destination points do not fall directly on roads it was necessary to link these points to the network by means of shortest distance links. These were added to the network in order to comply with the spatial model s requirements. Fig. 7 shows an extract of these links in Eastern Cape. The ESRI modelling software has a limitation of 255 links per node. Consequently where the spatial resolution of the demand grid is too fine and the roads too sparse this limit can be exceeded. This factor had to be kept in mind when designing the spatial modelling framework. Fig. 5: Potential locations for service offices. Modification of travel times The roads are categorised into various classes with different mean travel times attached to these different road classes. The data provided was modified to incorporate topographical effects and mobility variations between different regions of the country. To include the effect of terrain on travel times and thus accessibility a slope map was prepared for South Africa. The SRTM 90 m resolution digital elevation data obtainable from the US Geological Survey at the EROS Data Centre was used. The resulting slope dataset was much too detailed for use at the scale of this analysis and it had to be generalised to three slope classes. This was done by reclassification into slopes below 10,0, 10,01 to 30 and above 30,0. The reclassified image was repeatedly filtered using a modal filter of various sizes ranging from 3 x 3 to 9 x 9 Fig. 6: Road network used for location-allocation modelling. 52 PositionIT Nov/Dec 2009

4 of access times, but as maximum distance limits. Consequently maximum distance limits were re-specified in terms of maximum access times and the modelling done using travel times. Specification of location-allocation model parameters The ESRI ArcInfo model was used to optimise spatial locations of service offices in South Africa. This model provided most of the functionality required and had sufficient capacity to handle the large number of spatial units required by the application. The time used to complete a single run of the model was also acceptable. This allowed investigation of alternative scenarios, before choosing a final preferred solution. Fig. 7: Feed links to road network. To run the model required certain inputs that needed to be determined a priori, such as which locations will be considered as "fixed" and which candidate locations as "mobile". Additionally, the type of model, the allocation heuristic and total number of points to be allocated had to be specified. In this particular case the maximum coverage model was selected, so that it was also necessary to specify a maximum time and desired time constraint. These values have an effect on the number of points to be allocated and are discussed in the following sections. Fig. 8: Generalised gradients in South Africa. (Fig. 8). Average road speeds for the different road classes were reduced by 25% and 50% if they traversed the second and third slope classes. The second factor that was considered in modifying travel times was the developmental nature of the area through which roads passed. Two classes were distinguished, namely former homelands (tribal areas) and the rest of the country. Road speeds in the formal homeland areas were reduced by a further 20%. This was done to model the effects of stray animals, dense rural populations, weaker road infrastructure and lower mobility levels of the population. Feed links were handled in a similar fashion. Initial travel speeds assigned to feed links also distinguished between former homeland areas and the rest of the country. Speeds of 20 and 30 km/h were allocated respectively and travel times subsequently reduced in accordance to the rules which applied to slope classes. The current norms and standards adopted by the Department of Social Development are not specified in terms Optimisation criterion The maximum coverage model was selected because the purpose of the analysis is to determine where SASSA should provide permanent infrastructure and facilities to service the beneficiaries at service offices. As large capital expenditures are involved it is therefore more important to find a more affordable and efficient solution. Equity is achieved by specifying maximum desired travel times. Candidacy status The location-allocation model used in this analysis allowed identification of certain locations as being "fixed" and others as "mobile" or "selectable" and others as "non-selectable". This specification is referred to as the candidacy status. The model developed for service offices used the following candidacy specifications: All Thusong Centres were given fixed candidacy as these will be used where available. PositionIT Nov/Dec

5 Scenario Current System Number of service offices Average travel time (min) Weighted average travel time (min) Demand beyond 60 min % Demand within 60 min travel zone ,8 19, ,6 Model ,2 14, ,9 Table 2: Summary of overall location-allocation results. Travel times to nearest service point Beneficiaries < 5 min <10 min < 15 min < 30 min < 60 min < 120 min Current Number system % 24,7 44,4 56,3 78,8 95,6 99,8 Model Number % 21,0 42,4 61,9 90,4 99,6 100,0 Table 3: Comparison of coverage between current and modelled service point distributions. for services. The modelling process was refined in a similar fashion. Using the population density classes previously defined, the LAM was run separately on five subsets of data, using different maximum travel time and desired travel time thresholds for each of these classes. Spatial optimisation results It is clear from the statistics in Table 2 that the country as a whole stands to gain by applying the results of the analyses. Another potential benefit of using the results of the model in decision-making would be to promote equity of service delivery infrastructure between regions. Fig. 9: Travel times to current social grant service offices. The following locations were regarded as selectable for assignment, namely existing SASSA service offices, Home Affairs offices, vacant post offices and centroids of sub-places. In the case of sub-places, locations should be seen as indications of where service offices could be located and not necessarily for use of the actual facilities. Number of service points and maximum travel times The existing numbers of service offices were used to specify the required number for the model. The reason for this decision is that the intention of SASSA is not to reduce their level of service but to redistribute resources to more optimal locations. The number of service offices may be reduced or increased if indicated by the results of the analyses. Large regional differences in population densities and variations in the distribution of service offices across the country require regionalisation of the model. No single set of parameters would provide satisfactory results in all parts of the country. Regional differences have already been catered for in terms of the varying resolutions of spatial units used for capturing the demand Table 2 shows that the modelled distribution of service offices is more accessible to more people than the current distribution. Both average travel times and weighted average travel times are reduced from the current 26,8 min and 19,0 min to 20,2 min and 14,4 min respectively for the model. The weighted average travel time differs from the average travel time measure as it considers the number of people affected. The demand beyond 60 min travel time is reduced from beneficiaries to In the modelled system fewer beneficiaries travel long distances than is currently the case (0,4% vs 4,4%). Table 3 shows that the modelled optimised distribution of service offices is more equitable than the current system. The proposed locations are more dispersed than the current distribution pattern. The number of beneficiaries that are currently unfairly favoured by very close locations to service offices (less 54 PositionIT Nov/Dec 2009

6 However, the results cannot be accepted uncritically. Sound judgment should prevail in the final decision-making process. Other factors not included by the model should be considered. Sites indicated by the model and provisionally accepted by the regions must be evaluated with respect to local conditions. The proposed locations should be seen as an indication of the general area in which a service point should be established. If the location is within a reasonable distance from an existing service point, the latter should be retained, especially if building infrastructure is adequate. Fig. 10: Travel times to optimised social grant service offices. than 10 min travel times) are reduced from 44,4% to 42,4%. Beneficiaries living further than 10 min from a service point will all gain (about 2,2-million people). Two maps showing the existing situation and that proposed by the model are presented in Figs. 9 and 10 respectively. inequities between regions and reduce unnecessary duplication of services. It could bring service point locations closer to the population thereby improving accessibility. Implementation of the results should lead to improved overall service efficiency at a lower cost. A process of regional consultation followed and the results of the model were adjusted where necessary based on local feedback, the results of which are not reported in this paper. Acknowledgement This paper is based on an unpublished report to the South African Social Security Agency. Contact Contact Larry Zietsman, GSRB, Tel , hlzietsman@gmail.com A comparison of the two maps (Figs. 9 and 10) shows that the model has aligned the distribution of service points more equitably and more efficiently to the distribution of the beneficiary population (see Figs. 3 and 4). The more equitable re-alignment is most visible in the arid parts of the country, such as in the Karoo areas of the Western Cape and especially Northern Cape. The more efficient re-alignment is more visible in the more densely populated eastern parts of the country. This is a direct result of the maximal coverage principle on which the model is based, as it seeks to optimise travel times by relocating service locations to cover as many people with the least number of points in areas with greater demand. The cost of servicing areas with low demand is offset by locating services closer to areas with higher demand to improve overall efficiency. A careful inspection of the maps reveals that in most cases more densely populated regions also show an improvement in accessibility. Final comments The results of the spatial optimisation model were satisfactory. The model produced a service office network that can potentially improve accessibility of beneficiaries, reduce spatial PositionIT Nov/Dec