Understanding waiting lists as the matching of surgical capacity to demand: are we wasting enough surgical time?

If surgical 'capacity' always matched or exceeded 'demand' then there should be no waiting lists for surgery. However, understanding what is meant by 'demand', 'capacity' and 'matched' requires some mathematical concepts that we outline in this paper. 'Time' is the relevant measure: 'demand' for a surgical team is best understood as the total min required for the surgery booked from outpatient clinics every week; and 'capacity' is the weekly operating time available. We explain how the variation in demand (not just the mean demand) influences the analysis of optimum capacity. However, any capacity chosen in this way is associated with only a likelihood (that is, a probability rather than certainty) of absorbing the prevailing demand. A capacity that suitably absorbs the demand most of the time (for example, > 80% of weeks) will inevitably also involve considerable waste (that is, many weeks in which there is spare, unused capacity). Conversely, a level of capacity chosen to minimise wasted time will inevitably cause an increase in size of the waiting list. Thus the question of how to balance demand and capacity is intimately related to the question of how to balance utilisation and waste. These mathematical considerations enable us to consider objectively how to manage the waiting list. They also enable us critically to analyse the extent to which philosophies adopted by the National Health Service (such as 'Lean' or 'Six Sigma') will be successful in matching surgical capacity to demand.