School of Geography something FACULTY OF ENVIRONMENT OTHER

School of Geography something FACULTY OF ENVIRONMENT OTHER Extending spatial interaction models with agents for understanding relationships in a dynamic retail market §Alison Heppenstall & Mark Birkin §University of Leeds §Presenter: Andrew Evans

School of Geography FACULTY OF ENVIRONMENT Overview §An agent-based retail model – review §An agent-based retail model – extension §Experiments with an extended ABRM §Future plans and reflections

School of Geography FACULTY OF ENVIRONMENT Complex Geographical Systems § Characteristics of a geographical system: • Dynamic, nonlinear relationships among a multitude of components • Complex, recursive or highly iterative interactions among components • Evolve dynamically over time and space • Exhibit chaotic and potentially self-organising behaviour Retail Petrol Market §Highly competitive and sensitive market. §Complex system: • Internal, external factors. Effects of locality. • Petrol brands operate unique rule sets? • Networks of information geographically constrained?

School of Geography FACULTY OF ENVIRONMENT Spatial Diffusion: Price Drop

School of Geography FACULTY OF ENVIRONMENT

School of Geography FACULTY OF ENVIRONMENT Agent-based retail model About 1000 people

School of Geography FACULTY OF ENVIRONMENT Agent-based retail model Weighting for price and distance Portion of total fuel sold in this ward The greater the distance and price, the closer the weighting to zero

School of Geography FACULTY OF ENVIRONMENT Agent-based retail model

School of Geography FACULTY OF ENVIRONMENT ‘What if? ’ analysis: aggressive drop t 1 t 2 t 3 t 4

School of Geography FACULTY OF ENVIRONMENT Agent-based retail model: Version 2 §New agent rules • Attraction = floorspace, not price • Standard retail model as prices unknown – floorspace proxy for competitiveness. • Adjustment mechanism based on provision (‘floorspace’) rather than price • If operation is profitable then expand, otherwise contract. • This has the advantage that unprofitable stations will close naturally. • Retail agents not dispersed but homogeneous

School of Geography FACULTY OF ENVIRONMENT ABRM: Version 2 Set floorspace Evaluate profit Spatial Interaction Model Profit >0? Increase floorspace Reduce floorspace

School of Geography FACULTY OF ENVIRONMENT Agent-based retail model Attractiveness Price effect Accessibility Set the effect of price to neutral. Introduce a new weighting associated with floorspace Wj α : Wj is adjusted in line with profits.

School of Geography FACULTY OF ENVIRONMENT ABRM: Version 2 §Experiment 1 – • Rectangular lattice of 27 x 27 zones • Even distribution of population and accessibility • Explore variations in provision (at equilibrium) for alternative configurations of accessibility (beta) and attractiveness (alpha) • Adjustment mechanism: • Wj = Profits / constant • Means stations with negative profits shrink to nothing and gain no consumers.

School of Geography Attractiveness more important FACULTY OF ENVIRONMENT Distance harder to travel Agent-based model Competition increases with ease of travel and attractiveness

School of Geography Attractiveness more important FACULTY OF ENVIRONMENT Distance harder to travel Spatial Interaction Model

School of Geography FACULTY OF ENVIRONMENT ABRM: Version 2 §Significance of this result: • Exactly parallels the simulations of Wilson & Clarke (1983), following Harris and Wilson (1978) • Further applications to • Residential location (Clarke & Wilson, 1984) • Industrial location (Birkin & Wilson, 1986 a, b) • Agricultural location (Wilson & Birkin, 1987)

School of Geography FACULTY OF ENVIRONMENT ABRMV 2: Further Experiments §A) Move to real geography Distribution of petrol stations comes from the Catalist data §B) Add demographics Distance travelled comes from a paper by Haining and Plummer §C) Calibrate model

School of Geography Attractiveness more important FACULTY OF ENVIRONMENT Distance harder to travel Agent-based model

School of Geography FACULTY OF ENVIRONMENT Where is the real world in this solution space?

School of Geography FACULTY OF ENVIRONMENT What happens if we mess with the real world? EPS = sensitivity to profit Higher EPS = faster reaction to market = more instability =less survival

School of Geography FACULTY OF ENVIRONMENT Models § started with a model in which changes in both the interactions and petrol station profits were dictated by changing prices; but stations never closed. § then we created a classical model in which the dynamics are determined by changes in retail floorspace. Stations could shrink. § Now we want to look at a third model in which prices and floorspace (i. e. Location) are both changing simultaneously.

School of Geography FACULTY OF ENVIRONMENT Eps 1 (price sensitivity) =0. 1 Eps 2 (floorspace sensitivity) =0. 1

School of Geography FACULTY OF ENVIRONMENT Price constraint low, Floorspace important Price constraint medium, Floorspace neutral Price constraint high Floorspace unimportant

School of Geography FACULTY OF ENVIRONMENT Future directions §Variable patterns of price and location adjustment §Discrete changes in strategy or provision §Reactive behaviour and agent interactions

School of Geography FACULTY OF ENVIRONMENT Summary and conclusions §Agent-based modelling breathes new life into classical approaches §Spatial interaction model emphasises the potential for practical deployment of simulation methods §Extension of this work to agent-based models of consumer behaviour is the obvious next step