Demand and Capacity Modelling of Acute Services Using Simulation and Optimization Techniques

Abstract

The level of difficulty that hospital management have been experiencing over the past decade in terms of balancing demand and capacity needs has been at an unprecedented level in the UK. Due to shortage of capacity, hospitals are unable to treat patients, and in some cases, patients are transferred to other hospitals, outpatient referrals are delayed, and accident and emergency (A&E) waiting times are prolonged. So, it’s time to do things differently, because the current status quo is not an option. A whole hospital level decision support system (DSS) was developed to assess and respond to the needs of local populations. The model integrates every component of a hospital (including A&E, all outpatient and inpatient specialties) to aid with efficient and effective use of scarce resources. An individual service or a specialty cannot be assumed to be independent, they are all interconnected. It is clear from the literature that this level of generic hospital simulation model has never been developed before (so this is an innovative DSS). Using the Hospital Episode Statistics and local datasets, 768 forecasting models for the 28 outpatient and inpatient specialties are developed (to capture demand). Within this context, a variety of forecasting models (i.e. ARIMA, exponential smoothing, stepwise linear regression and STLF) for each specialty of outpatient and inpatient including the A&E department were developed. The best forecasting methods and periods were selected by comparing 4 forecasting methods and 3 periods (i.e. daily, weekly and monthly) according to forecast accuracy values calculated by the mean absolute scaled error (MASE). Demand forecasts were then used as an input into the simulation model for the entire hospital (all specialties). The generic hospital simulation model was developed by taking into account all specialties and interactions amongst the A&E, outpatient and inpatient specialties. Six hundred observed frequency distributions were established for the simulation model. All distributions used in the model were based on age groups. Using other inputs (i.e. financial inputs, number of follow ups, etc.), the hospital was therefore modelled to measure key output metrics in strategic planning. This decision support system eliminates the deficiencies of the current and past studies around modelling hospitals within a single framework. A new output metric which is called ‘demand coverage ratio’ was developed to measure the percentage of patients who are admitted and discharged with available resources of the associated specialty. In addition, a full factorial experimental design with 4 factors (A&E, elective and non-elective admissions and outpatient attendance) at 2 levels (possible 5% and 10% demand increases) was carried out in order to investigate the effects of demand increases on the key outputs (i.e. demand coverage ratio, bed occupancy rate and total revenue). As a result, each factor is found to affect total revenue, as well as the interaction between elective and non-elective admissions. The demand coverage ratio is affected by the changes in outpatient demands as well as A&E arrivals and non-elective admissions. In addition, the A&E arrivals, non-elective admissions and elective admissions are most important for bed occupancy rates, respectively. After an exhaustive review of the literature we notice that an entire hospital model has never been developed that combines forecasting, simulation and optimization techniques. A linear optimization model was developed to estimate the required bed capacity and staff needs of a mid-size hospital in England (using essential outputs from forecasting and forecasting-simulation) for each inpatient elective and non-elective specialty. In conclusion, these results will bring a different perspective to key decision makers with a decision support tool for short and long term strategic planning to make rational and realistic plans. This hospital decision support system can become a crucial instrument for decision makers for efficient service in hospitals in England and other parts of the world.