The Maths Model

Here is a slightly more technical description of a more ‘accurate’ demand and capacity model. To make it work in real life you will need really, really good data – which we certainly don’t have. The usefulness of it is that, if you find you are out of balance, then the model describes all the variables that might be contributing to this.

The Model

The demand comes from the number of referrals accepted AND the hours you use in Choice and in Core Partnership for those referrals.

Choice

  • The number of referrals accepted
  • The number of clinical hours used in each Choice.

Core Partnership

  • The percentage of service users who transfer from Choice to Core Partnership
  • The average number of clinical appointments in Core Partnership and
  • The Percentage Co-therapy rate.

So Demand = Accepted Referrals x (Choice hours + Percentage transferring to Core Partnership x (Core Partnership hours x (1 + Percentage Co-therapy rate)))

TIP: note that if any of the above five variables increase the demand increases

The capacity provided comes from:

  • The team FTE (full-time equivalent) in half days (FTE x 10 half-days per FTE)
  • The percentage of that which provide Choice and Core Partnership time
  • The number of clinical appointments that can be provided per half day
  • The percentage of each period of time that is actually worked (obviously less than 100% due to leave, study leave etc.).

And so Capacity = FTE x 10 x Percentage capacity in Choice and Core Partnership x Appointments per half-day x % time worked

Note: again if any of the above decreases the capacity decreases

So if the service is in balance then the capacity for Choice and Core Partnership will meet the accepted demand.

Simple! Maybe!

What does the maths tell us?

We can put these factors into a table and note which of them are large and how much under our control (see next page).

Why?

  • We want to know which variables are the ones with big effects as those would be a good variable to change and
  • We also want to know which are under our control so that these are the ones we can actually change in any reasonable timescale.

Have a look at this table...

Little Small
Potential Size of Changing variable How much is under our control?
Choice
The number of referrals accepted Big Little
The number of clinical hours used in each Choice SmallLarge
The percentage of service users who transfer from Choice to Partnership BigLarge
Partnership
The average number of clinical appointments in Core Partnership MediumLarge
The Percentage Co-therapy rate BigLittle
Capacity Factors
The team FTE (full-time equivalent) in half days (FTE x 10 half days per FTE)BigLittle
The percentage of service that provides Choice and Core Partnership time BigLarge
The number of clinical appointments that can be provided per half day SmallLarge
The percentage of each period of time that is actually worked SmallMedium

It’s interesting to note that there are three factors that are big and under our control. These will make the greatest difference to our busyness and we can do something about them!

Two are demand factors:

The transfer percentage and

The number of appointments offered per client.

One is a capacity item:

The percentage of the service in Core Partnership.

So if you have CAPA in play but feel under pressure these are the big 3 to monitor and change.