Capacity Planning for Small Hospitals and Departments Illustrated Using Maternity and Paediatrics Departments: Roles for Weighted Population Density, Seasonality and Size, Myths Around Length of Stay and Factors Influencing Costs and Funding.

The Erlang B equation is directly applicable to smaller hospital departments such as maternity and paediatrics departments. The bed occupancy margin is directly linked to size and not 'efficiency'. A figure of 0.1% turn-away has been recommended as a planning target, i.e., only 1 in a thousand admissions suffer a delay before a bed can be found. Two bed calculators are provided which can be used for paediatric, obstetric, maternity, midwife-led, birthing wards and neonatal/paediatric critical care capacity. The negative effects of turn-away are likely to be context specific, hence, critical care > theatres > birthing unit > maternity unit. The uncertainty regarding future births is discussed along with the variable nature of seasonality in births. For paediatrics, much of bed demand is also influenced by the trend in births. Weighted population density (WPD) is associated with the size distribution of hospitals/units within countries and regions. This influences the average cost per birth/admission. The USA has a low WPD and a significant problem with small hospitals/departments. Only 10% of countries have WPD higher than England. Some countries choose to operate with even more hospitals than needed and this acts to elevate costs. Suggestions are made for a pragmatic approach to bed planning, especially where a dispersed population dictates a need for small hospitals, and hence, issues regarding size and costs. For maternity/paediatrics admissions (and other relatively short-stay admissions) the majority of overhead/indirect costs and most staffing costs should be apportioned based on admissions, and not LOS. Apportionment based on LOS creates the spurious illusion that LOS is the major cost driver and that reducing LOS will immediately save costs. Below 20 beds, Poisson statistical variation plus environment-induced randomness in daily arrivals imply that staff costs may become increasingly fixed irrespective of LOS. Around >30 beds, it looks possible to save costs by reducing LOS. Allocating total organizational costs to individual units and then to patients is less precise than realized and can be done in different ways, which all heavily rely on the steady-state assumption. When bed availability is the bottleneck, then reducing LOS may increase throughput per bed and increase income; however, is this for the benefit of the patient or for the benefit of the organization, and does it lead to higher unanticipated total costs including patient harm? The older economy-of-scale literature has been demonstrated to be flawed, with a recent focus on economy of scale at the department level being entirely consistent with the application of the Erlang B equation. A list of nine catastrophic pitfalls is given for doctors to identify dubious capacity advice from managers and external experts.