The Kebab Challenge: spatial optimisation of sales networks

Location decisions are often made by experience: a good spot, plenty of footfall, acceptable rent. What that does not assess is the interplay – how several locations influence each other, how much demand the competition already captures, and which combination of locations delivers more than the sum of their individual qualities.

That, precisely, is an optimisation problem with spatial structure. It can be computed, and the result is often not the spot one would have picked intuitively. As our example we chose a fictitious entrepreneur wanting to enter the kebab business in Berlin – the kebab capital, and home of Supper & Supper GmbH.

Three datasets, all publicly available:

• coordinates of vacant shop premises in Berlin – the available options
• positions of other kebab shops – the demand already captured
• coordinates of Berlin clubs – as a proxy for the distribution of demand at the relevant hours

The third dataset is the interesting one. Demand appears in no dataset; it has to be approximated through an observable quantity. That choice shapes the result more than any optimisation method – and it is a domain decision, not a technical one.

Four parameters pulling against each other. The optimisation took in: budget for acquiring the property, distance to the demand points, proximity to competitors, and their market shares. A location close to demand is expensive and usually contested; a cheap location reaches less demand. The task is finding the balance between all four.

Locations compete with each other. Two locations that are both well placed can take demand from each other. A network's market share is therefore not the sum of the individual shares – which is why the combination has to be optimised, not the single location.

The spatial optimisation was implemented with ArcGIS. What was assessed were not individual spots but combinations of locations against the four parameters – with the goal of maximising the market share of the network as a whole.

Two locations – in Friedrichshain and Moabit – reach a market share of 30% with two purchases.

The statement behind it is the more interesting one: the best network need not consist of the best individual spots. Two locations that complement each other spatially can beat two that are each optimal on their own.

Location and network optimisation is one of the oldest applications of spatial analysis, and in many industries it is the same calculation: branch and service networks, charging infrastructure, sites for collection points and depots, distribution of mobile services, coverage in healthcare, siting of generation plants. The most important insight transfers too: the hardest part is not the optimisation but the question of which observable quantity to approximate demand with.

Demand modelling is the part with the most room for improvement. Where club locations served as the proxy back then, there are now movement and footfall data, accessibility analyses over real street networks instead of straight-line distance, and small-area population data. The optimisation itself we would not set up much differently; the established location models are still the right tool, complemented by a sensitivity analysis showing how stable a recommendation is against assumptions about demand. That is the point that matters in practice: a location recommendation that flips under a slightly changed demand assumption is not a recommendation.