Multicriteria Optimization Techniques for Understanding the Case Mix Landscape of a Hospital

Various medical and surgical units operate in a typical hospital and to treat their patients these units compete for infrastructure like operating rooms (OR) and ward beds. How that competition is regulated affects the capacity and output of a hospital. This article considers the impact of treating different patient case mix (PCM) in a hospital. As each case mix has an economic consequence and a unique profile of hospital resource usage, this consideration is important. To better understand the case mix landscape and to identify those which are optimal from a capacity utilisation perspective, an improved multicriteria optimization (MCO) approach is proposed. As there are many patient types in a typical hospital, the task of generating an archive of non-dominated (i.e., Pareto optimal) case mix is computationally challenging. To generate a better archive, an improved parallelised epsilon constraint method (ECM) is introduced. Our parallel random corrective approach is significantly faster than prior methods and is not restricted to evaluating points on a structured uniform mesh. As such we can generate more solutions. The application of KD-Trees is another new contribution. We use them to perform proximity testing and to store the high dimensional Pareto frontier (PF). For generating, viewing, navigating, and querying an archive, the development of a suitable decision support tool (DST) is proposed and demonstrated.

The Efficacy of Utility Functions for Multicriteria Hospital Case-Mix Planning

A new approach to perform hospital case-mix planning (CMP) is introduced in this article. Our multi-criteria approach utilises utility functions (UF) to articulate the preferences and standpoint of independent decision makers regarding outputs. The primary aim of this article is to test whether a utility functions method (UFM) based upon the scalarization of aforesaid UF is an appropriate quantitative technique to, i) distribute hospital resources to different operating units, and ii) provide a better capacity allocation and case mix. Our approach is motivated by the need to provide a method able to evaluate the trade-off between different stakeholders and objectives of hospitals. To the best of our knowledge, no such approach has been considered before in the literature. As we will later show, this idea addresses various technical limitations, weaknesses, and flaws in current CMP. The efficacy of the aforesaid approach is tested on a case study of a large tertiary hospital. Currently UF are not used by hospital managers, and real functions are unavailable, hence, 14 rational options are tested. Our exploratory analysis has provided important guidelines for the application of these UF. It indicates that these UF provide a valuable starting point for planners, managers, and executives of hospitals to impose their goals and aspirations. In conclusion, our approach may be better at identifying case mix that users want to treat and seems more capable of modelling the varying importance of different levels of output. Apart from finding desirable case mixes to consider, the approach can provide important insights via a sensitivity analysis of the parameters of each UF.