This paper first measures the accessibility to RCFs at the subdistrict level in Beijing. The spatial optimization model is developed to maximize equal access to residential care resources by minimizing the total square difference between the accessibility score of each demand location and the weighted average accessibility measure. The standard variation of accessibility at each demand location is 0.0066 in our results. The optimal results show that more RCF beds (34,762 beds, 51% of the total) should be allocated to the suburban districts, and less in the central and periphery districts (22,413 and 11,262 beds, 33% and 16% of the total, respectively).
The results also show the gaps between the existing and optimal layouts, which suggest that RCF beds should be increased in the suburban districts (5,961 beds). The RCF beds in some subdistricts located in the central and peripheral districts, however, are oversupplied (5,253 and 1,584 beds respectively). The gaps imply that the existing large supply in some subdistricts seems irrational under the maximum equity objective. The oversupply in most subdistricts with large RCFs is considerable compared to the existing bed numbers. For example, the Shisanling Township in Changping District had 5,350 RCF beds in 2013. It was the subdistrict with the largest absolute number of beds among all the subdistricts, but the optimal number is only 329. The RCFs in 24 of the 30 subdistricts that have more than 600 RCF beds are oversupplied for more than half of the existing RCFs beds. More efforts, however, are needed to confirm whether the existing RCF clusters are irrational indeed. On-site investigations to find out if the occupancy rate of RCFs located in existing clusters is low would be helpful for confirming the over-supply suggested by the modeling results.
The Beijing Municipal Commission of Urban Planning and the Beijing Civil Affairs Bureau issued a special plan for the development of RCFs . It claimed that the new increases in RCFs should mainly be allocated in the suburban districts. According to the special plan, 39.8%, 40.8% and 19.4% of RCF beds will be located in central city, new towns and rural areas respectively. Considering that the new towns in the special plan refer to the urban areas of the suburban and periphery districts or counties, planned distribution of RCF beds is quite similar to the results of this study. The plan recommended enlarging existing RCFs or renovating other types of public facilities to make them into RCFs to maximize the potential capacity instead of building new ones in the central districts. New RCFs are planned in the outer region of the central districts to meet local demand. Relatively more new RCFs are planned for the suburban districts with the goal of providing residential care resources for the elderly population living in the central districts. The optimized results of this study correspond to the municipal special plan. The results of this study therefore confirm that the layout proposed will meet the equality in accessibility to RCFs criterion to a great extent.
The optimization objective in this study differs from the traditional optimization studies of facility locations. The former aims to maximize equality in accessibility to facilities by minimizing the disparity in accessibility of each demand location , while most of the existing studies aim to maximize the efficiency of the facility allocation. The formulations of the two types of optimization objectives are different. The traditional objectives usually take a linear form, but the maximum equality objective is nonlinear . Both types of optimization objectives are important and significant for the planning of facility locations.
The methods used in this paper also improve on the measurement of accessibility to facilities in optimization studies of facility locations. The traditional location-allocation models usually adopt a dichotomous distance-decay form, namely, accessibility to facilities is assumed to be homogeneous within a certain threshold distance and inaccessible beyond the threshold distance. Moreover, traditional models do not take the capacity of facilities and difference in demand at locations into account. To measure accessibility more accurately, this study takes a 2SFCA form with a distance-decay function.
This research is one of the first studies to apply the optimization model maximizing equity in accessibility to residential care facilities considering different utilization behaviors in residential care services and health care services. The PSO method is used rather than a traditional quadratic programming method to solve the location optimization problem, which is found to be more effective than the traditional method. We also compare the optimization results with the distribution of RCF beds proposed by the special plan. The results show that the government’s plan on RCFs will meet the equality in accessibility to RCFs criterion to a great extent.
There are some limitations to this study. First, the geographical and socio-economic factors of elderly people’s preferences for RCFs are not considered in the optimization model. Second, the most recent population census data are only available for 2010, and the smallest scale of census data is only available at the subdistrict level (the average number of elderly population in subdistricts is 5,268). The census data at a smaller geographical scale would improve the accuracy of our findings.
In the future, we will strive to obtain smaller-scale or predicted elderly population data for better optimization results. Moreover, various optimization objectives (both maximum equality and efficiency) will be adopted to compare optimization results and costs in various optimization scenarios. As a first step, the findings of the current research, however, offer support for knowledge-based policy-making and planning of residential care facilities in Beijing, as well as in other regions in China and developing countries, where there is still in a great shortage of facilities and services for the elderly population.