A little while ago, I was presenting some of my geeky stats to a room full of people. We were reviewing how variable the workload coming into a planning department is – much more than you’d imagine. My argument is that simple performance measures (*we will validate 90% of applications on the same day*) are pointless and act to demotivate people. Anyway. As it happened, a couple of authorities in the room were planning to combine their back offices. They asked a really basic question – “Would combining our workloads smooth out the peaks and troughs, or make them worse ?”. It’s an important question. At the time, we eyeballed it and reckoned that the answer was “no, it would probably make things worse”.

What with the formation of “super” authorities in the news recently, when another person asked me a similar question recently I thought I’d try to answer it properly. Like many simple-sounding questions it actually is quite tricky to pin down. This is my attempt, and given that I’m not a professional statto your comments and criticism is welcome. Let’s find out whether there is an economy of scale to planning applications.

**Not an opinion, let’s use some data**

If you want to play along, I’ve left some sample data on our forum over at PASland. It’s in excel, along with some workings to give you a headstart. It assumes three authorities are thinking of joining up – they’ve given me the number of applications received each week in the calendar year 2009-2010.

Now you can see how wiggly the work coming in is. No wonder many people think that validation is often “broken”. In fact, it’s just the first place you notice that you’ve not been flexible enough in the way you deploy resource to meet a variable workload. Anyway. The question is, I think, does the job of resourcing the work get easier as it scales up. If you had these three workstreams together, is it any less wiggly ?

**Standard distribution**

The eyeballs can tell you it’s still wiggly, and xmas gets quiet, but not much more than that. I decided to tackle this in two steps. The first step is to understand not how things occur over time (as is presented above) but to understand how often things occur. The distribution of events is what makes resourcing tricky. You can tell a validator to expect somewhere between 4 and 6 applications a day (say). They can cope with this level of variability by working harder/faster/slower as appropriate. When they only get 1 or 2 they might be scratching around. When 10 or 12 appear we’re in trouble. This is as true for teams as it is for individuals.

So, we calculate the standard deviation for the four lists.

Slightly technical aside. You may want to revisit the theory. The results are:

Charlie 17

India 17

Lima 18

So, my novice interpretation of these results is that the number of applications for Charlie can be expected to vary by 17 around the mean – using this sample data this is +/- 17 around 68. The leader of the team should expect (not on a freaky week, but on a normal week) to receive anywhere between 51 and 85 applications. [nb Because of the actual numbers involved, while it looks as if India has the same degree of variability it’s actually more wiggly because it’s calculated from a smaller volume of work. This is doubly true when we add all three together. ]

Standard deviation for Charlie+India+Lima = 41. It’s a bigger number, but then it reflects a bigger volume of work. Is it proportionally smaller ? Yes. The standard deviation as a proportion of mean varies from 24 to 34% for each authority. When taken together it’s 21%.

Bingo ! Proof that there is a benefit to scaling up and we should all immediately start glueing our back offices together ! [*ed – do not stop reading here. This is being said for dramatic effect.*]

**Lies, damn lies**

I can only grok things when I see them in a picture. It’s a numerical deficiency of mine, as you’ll discover if you ever play poker against me. Here are the workloads looked at in frequency terms. Not laid out over the year, but how often we receive a certain number in a week. [*if you look at the excel data I’ve used bins of 5 which give slightly different answers to the bins I’ve used to make these pretty pictures.*]

I’m starting to frown a bit now. Imagine I’m the teamleader at Charlie. I look at what’s coming in, and I ignore the very high and the very low. I figure the very low is christmas, and I can plan for that, and that if the numbers get ridiculous I’ll go running next door and ask for help. As long as I can gear myself up for 46 weeks out of the 52 we’ll cope. Mentally I’m doing something like this:

I am gearing myself and everyone up for a workload between 45 and 85 applications. The most common number will be 65. There are 7 weeks I’ve scribbled over, and we’ll have to have a plan to cope with them, but everything else is business as usual.

Now, imagine I’m the teamleader at the new super council. I look at the distribution, and attempt to do the same thing:

Suddenly, 17 weeks have become unusual. This is a big fat spread of work to try and cover, and I don’t think this is a binning issue or other kind of quirk. From this, there appears to be more of a problem resourcing a bigger authority – it’s true, though that you may have more staff to throw at the problem and move around.

**So, what’s the answer ?**

My last go at this returns to the data spread over time. After all, this is how we’re going to experience the ebb and flow of work. I took these ideas together, and said that a “normal” week is one where the work received fell within the standard deviation. I call it the “comfort zone”. Easier to show than explain:

So, they grey rectangle represents the upper and lower limits suggested by the standard deviation. Everytime you receive workload outside these margins you get hassle. If you count the red dots you’ll see that the super authority gets hassle for 18 weeks in the year, compared to 16 for a stand-alone Charlie and 15 weeks for both India and Lima.

**My conclusions**

The simple answer to the simple question is “adding these back office functions together will make things worse, not better”. Probably a more helpful response is that nothing magic happens when you add services together. This analysis shows that resourcing them becomes more difficult. The peaks are peakier, troughs troughier and normal weeks rarer. It’s definite but not catastrophic. Making super authorities will only make your life easier if you can compensate for this in some way. Perhaps you have a bigger pool of people to move around, perhaps while going through the organisational pain you also introduce more flexible methods of employing people.

So. Best to go into this with eyes open and not just hoping. Final caveat – I’ll try to talk this through with a proper statto, just to ensure I’m not exposing myself and/or lying to you all.

Pingback: The comfort zone for improvement « Planning Advisory Service