A mathematical framework for regional hospital case mix planning and capacity appraisal

This article considers current capacity issues in health care and the development of quantitative techniques to facilitate a high-level strategic assessment of hospital activity within a region. In providing that assessment, a variety of decision problems are foreseen, and we test the notion that it is useful to provide decision support for those. To achieve that support, several optimization models are developed and tested. In theory the presented models may help health care planners organise hospital resources and activity better, to treat more patients. The first model that we propose identifies a maximal caseload that meets the patient type proportions specified in a regional case mix imposed by a planner, executive or manager. The second model identifies how spatially distributed demand can best be met amongst the different hospitals, such that travel distance and unmet demand are minimised. The third model identifies how individual hospitals can jointly achieve their goals with the help of outsourcing. Each of the models has been implemented and tested on some demonstrative examples of a smaller nature, before a larger study is presented. Our case study demonstrates that appropriate data can be collected, and the proposed decision models can provide a rational appraisal of regional capacity and utilization.