Unit Mix Optimisation

Think Piece by our valued client, Christopher Beech

 

A feature of planning guidance is a set of requirements for the approximate percentages of private, intermediate, and social units. Within those categories will be a set of requirements for proportions of 1/2/3/4 bedroom apartments.

Often these requirements will be rather vague as Camden’s Development Policy ‘DP5 — Homes of different sizes’ demonstrates.

Unit Mix Optimization

 

What is the best way to maximise Gross Development Value (GDV) whilst meeting requirements? Which is to say, what is the best way to optimise the number of each apartment type within that matrix?

Having seen planning feasibility studies for sites other than my own, I’m often rather surprised when developers leave the unit mix choice to their architects. This is far too important an aspect of the developer’s job to be left unquestioned.

For a time I thought that this was a yield management problem just like an airline selling inventory. However, yield management concerns different people paying different prices for the same type of inventory. Whilst selling units off-plan and post-completion may be a yield management problem, unit mix optimisation is not.

In fact unit mix optimisation is a linear programming problem. Recognising this, I was very surprised to find only one academic conference paper on the subject, “Optimal Residential Property Development And Linear Programming”.

Linear programming problems can easily be solved with the appropriate mathematical tool. Excel’s Solver is not bad but other more sophisticated plug-ins and software packages are available.

Linear programming problems require a set of inputs and constraints, in this case: overall gross internal area, maximum density, sales prices for each type of apartment, ideally build costs for each type of apartment, Community Infrastructure Levy for each type of apartment, etc. As many variables as possible can be added to the mathematical model, however, the more variables, the longer it may take to solve.

There are number of limitations that I’ve recognised running linear programming models:

  • The solution may not return integer values for the number of each unit type (even though you asked it to), manual tweaking of the solution may be required.
  • Architectural constraints:
    • It’s not always possible to fit as many units into a site as the model may suggest. Hence using a linear programming model as a guide to my analogue cut outs has worked well.
    • The problem is sometimes a combination of optimising the individual unit mix using a set of possible floor plans. For example, a given floor could 2 x 1 bed units & 2 x 3 bed units, or 4 x 2 bed units. A mix of floors may not return the optimal unit mix.
  • Housing Association constraints: The Registered Provider may have their own specific requirements.
  • Local Authority Planning Officer preferences: The negotiating process can change the ideal unit mix.

However, in all cases it is always best to start from your best possible unit mix and accept that the final solution may be less than the optimal maximum GDV.

Finally, although not strictly a yield management or linear programming problem, I was once very impressed by how one developer sought to address differing consumer preferences.

Unit Mix Optimization

Unit size (sqm) and type at Kingsgate Place

Unit Mix Optimization

Sales prices (around 2010) for 1, 2 and 3 bed units at Kingsgate Place

 

Christopher Beech is a long-standing client of InsideOut, working with us on two different multi-unit housing schemes, Passivhaus Apartments – Camden and Kilburn Apartments – Camden.