Cost and Capacity Issues in Small Hospital Departments, Difficulties in Estimating Future Demand, the Impact of Seasonality, and the Cost Reduction (If Any) from Reducing Length of Stay

Queuing theory and the Erlang equation are directly applicable to small hospital departments such as maternity and pediatrics. Bed capacity tables can be easily generated linking annual births/admissions to the required available beds, using expected births/admissions and length of stay (LOS). Two bed calculators are provided. For example, in maternity the total bed days includes any admissions during pregnancy and after birth, i.e., excluding the time spent in the birthing unit. It is emphasized that bed days must be calculated using real time length of stay as opposed to the usual midnight figure. The bed occupancy margin is directly linked to size and not ‘efficiency’. Based on the Erlang B equation which links available beds, occupied beds and turn-away, a figure of 0.1% turn-away has been chosen as the minimum acceptable number of beds, 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 obstetric, maternity, midwife-led, birthing wards and neonatal unit bed capacity. Specific issues relating to neonatal critical care bed capacity are highlighted. The negative effects of turn-away are likely to be context specific, hence, critical care > theatres > birthing unit > maternity unit. The far greater uncertainty regarding future births is discussed along with the variable nature of seasonality in births. For pediatrics much of bed demand is also influenced by the trend in births. Suggestions are made for a pragmatic approach to bed planning. Evidence is presented which suggests that for maternity (and other relative 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. Several lines of evidence point to the minimum cost per patient in maternity (antenatal + postnatal) lying greater than 30 beds (plus associated labor/birthing beds), and the minimum economic size around 12 beds. Around 30 beds probably mark the point where it is possible to make small cost savings by reducing LOS. Allocating total organizational costs to individual units and then to patients is far less precise than is realized and can be done in different ways which all heavily rely on the steady-state assumption. The real world of daily arrivals, case mix and clinical severity is never in steady state. Below 20 to 30 beds Poisson statistical plus environment induced randomness in daily arrivals imply that staff costs become increasingly fixed irrespective of LOS. 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? Finally, a list of nine ‘never do this’ catastrophic pitfalls are given for doctors to identify dubious capacity advice from managers and external ‘experts’.