A stochastic programming approach to perform hospital capacity assessments.

This article introduces a bespoke risk averse stochastic programming approach for performing a strategic level assessment of hospital capacity (QAHC). We include stochastic treatment durations and length of stay in the analysis for the first time. To the best of our knowledge this is a new capability, not yet provided in the literature. Our stochastic programming approach identifies the maximum caseload that can be treated over a specified duration of time subject to a specified risk threshold in relation to temporary exceedances of capacity. Sample averaging techniques are applied to handle probabilistic constraints, but due to the size and complexity of the resultant mixed integer programming model, a novel two-stage hierarchical solution approach is needed. Our two-stage hierarchical solution approach is novel as it combines the application of a meta-heuristic with a binary search. It is also computationally fast. A case study of a large public hospital has been considered and extensive numerical tests have been undertaken to highlight the nuances and intricacies of the analysis. We conclude that the proposed approach is effective and can provide extra clarity and insights around hospital outputs. It provides a way to better calibrate hospitals and other health care infrastructure to future demands and challenges, like those created by the COVID pandemic.

An Overview of Hospital Capacity Planning and Optimisation.

Health care is uncertain, dynamic, and fast growing. With digital technologies set to revolutionise the industry, hospital capacity optimisation and planning have never been more relevant. The purposes of this article are threefold. The first is to identify the current state of the art, to summarise/analyse the key achievements, and to identify gaps in the body of research. The second is to synthesise and evaluate that literature to create a holistic framework for understanding hospital capacity planning and optimisation, in terms of physical elements, process, and governance. Third, avenues for future research are sought to inform researchers and practitioners where they should best concentrate their efforts. In conclusion, we find that prior research has typically focussed on individual parts, but the hospital is one body that is made up of many interdependent parts. It is also evident that past attempts considering entire hospitals fail to incorporate all the detail that is necessary to provide solutions that can be implemented in the real world, across strategic, tactical and operational planning horizons. A holistic approach is needed that includes ancillary services, equipment medicines, utilities, instrument trays, supply chain and inventory considerations.

Analysis of uncertainty in the surgical department: durations, requests and cancellations.

Objective Analytical techniques are being implemented with increasing frequency to improve the management of surgical departments and to ensure that decisions are well informed. Often these analytical techniques rely on the validity of underlying statistical assumptions, including those around choice of distribution when modelling uncertainty. The aim of the present study was to determine a set of suitable statistical distributions and provide recommendations to assist hospital planning staff, based on three full years of historical data. Methods Statistical analysis was performed to determine the most appropriate distributions and models in a variety of surgical contexts. Data from 2013 to 2015 were collected from the surgical department at a large Australian public hospital. Results A log-normal distribution approximation of the total duration of surgeries in an operating room is appropriate when considering probability of overtime. Surgical requests can be modelled as a Poisson process with rate dependent on urgency and day of the week. Individual cancellations could be modelled as Bernoulli trials, with the probability of patient-, staff- and resource-based cancellations provided herein. Conclusions The analysis presented herein can be used to ensure that assumptions surrounding planning and scheduling in the surgical department are valid. Understanding the stochasticity in the surgical department may result in the implementation of more realistic decision models. What is known about the topic? Many surgical departments rely on crude estimates and general intuition to predict surgical duration, surgical requests (both elective and non-elective) and cancellations. What does this paper add? This paper describes how statistical analysis can be performed to validate common assumptions surrounding surgical uncertainty. The paper also provides a set of recommended distributions and associated parameters that can be used to model uncertainty in a large public hospital's surgical department. What are the implications for practitioners? The insights on surgical uncertainty provided here will prove valuable for administrative staff who want to incorporate uncertainty in their surgical planning and scheduling decisions.