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? Withinunit variation ? Crossborder ? Limitations ? Straightline ? SD beyond radius 2step floating catchment area: 2SFCA ? Scale availability at each supply location ? Sum up accessible supplies around each demand location 2SFCA Recap 1a. For each supply location j, select all demand locations k within a travel time range from j (catchment Cj). 1b. Compute the supply to demand ratio within Cj: 2a. For each demand location i, search all supply locations j within the travel time range from i (catchment Zi). 2b. Sum up the supply to demand ratios at these supply locations: ???jCkkjj PSR /? ??? ????i ji Zj CkkjZjji PSRA )/(Generalizing “distance decay” ? as a continuous function ? a power or exponential function ? a Gaussian function ? as a discrete variable ? dichotomous as in 2SFCA ? multiple as in E2SFCA ? a hybrid approach ? a kernel density function ? a threezone approach Generalizing “distance decay” Validation ? Modeling actual supplydemand interactions ? Individual travel behavior ? Aggregated travel pattern Optimization ? Towards equal accessibility ? Formulated as a planning problem ? minimizing accessibility gaps among demand locations by adjusting the amounts of supplies at given supply locations. A Quadratic Programming Approach ? Subject to ? ?? ???minj jijj aVdS1 12)(m in???S 1 ? S 2 ? ... ? S n ? S???? mkkjkj dDV1?where Value of optimization ? Emphasizing the equality issue ? Identifying over and undercapacity of supply ? Guiding planning and public policy in closing the gap Application in Healthcare Access: HPSA designation ? . ranks behind in health performance ? deep disparities in access to care and health out