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A. Horni and F. Ciari (2009) Modeling Shopping Customers & Retailers with the Activity-based Multi-agent Transport Simulation MATSim, CCSS Seminar, Zurich, April 2009.
Customer Shopping Location Choice
F. Ciari & A. Horni
IVT, ETH Zurich
Status Update & Open Questions
Modeling Shopping Customers & Retailers with the Activity-based Multi-agent Transport Simulation MATSim:-
Retailer Location Choice
Link loadsTravel distancesTravel times…Location choice:Catchment areaNumber of visitors…
3
MATSim: Model Purpose
Purpose: Model patterns of people’s activity scheduling and participation behavior at high level of detail.
Goal: Average working day of Swiss resident population (> 7.5 M) in „reasonable“ time
→ 2009 (KTI project)
Dynamic,Disaggregated
Method: Coevolutionary, agent-based algorithm adopted
MATSim: Structure → Iterative4
initial demand
analysesexecution scoring
replanning
Fixed attributes e.g. home location, census data
Utility function f (t):activity participation, travel
Share x of agents (usually 10%):Time, route, location choice
Exit conditon:„Relaxed state“, i.e. equilibrium
Agents‘ day plans
MATSim: Structure5
initial demand
analysesexecution scoring
replanning
Share x of agents (usually 10%):Time, route, location choice
replanning
Exit conditon:„Relaxed state“, i.e. equilibrium
Utility function f (t):activity participation, travel
Agents‘ day plans
Fixed attributes e.g. home location, census data
MATSim: Structure6
Controler → Replanning
replanning
StrategyManagerperson.removeWorstPlan();strategy.run(person);
PlanStrategy
this.planSelector.selectPlan(); person.copySelectedPlan();this.plans.add(plan);
PlanStrategyModule.handlePlan(plan);
for all persons who are chosen to make replanning
e.g. selectExpBeta: selection dependent on plan score
i.e., route, time or location choice
Nash eq. = stable state in sim→ Exit condition
Local opt. ≠ Nash eq.→ Probabilistic p(score)
Interpretation
7
MATSim - Coevolution
Agent i
Plan 0
Plan 1
Plan 2
Plan 3
Individual learning
Agent j
Plan 0
Plan 1
Plan 2
Plan 3
species iIndivid. i,0
Plan 0
Individ. i,1
Plan 1
Individ. i,2
Plan 2
Individ. i,3
Plan 3
species jIndivid. j,0
Plan 0
Individ. …
Plan ..Competition on the infrastructure
→ Score (fitness)
Weakest die→ Generations
person.removeWorstPlan()Agent …
Plan ..
Coevolution: „The evolution of two or more interdependent species, each adapting to changes in the other. […]“The American Heritage Dictionary of the English Language
Evolution: „(Biology): Change in the gene pool of a population from generation to generation by such processes as mutation, natural selection, and genetic drift. […]“ „www.dictionary.com“
8
What are we searching & How are we searching?
Iterate until „relaxed state“ is reached
Equilibrium
≠ Network equilibrium Wardrop (tt)
Planningequilibrium =? Nash
Multilateral (but uncoordinated) changes in a replanning step! → coalition-proof eq.?
What are we searching & How are we searching?
Iterate until „relaxed state“ is reached
Equilibrium
≠ Network equilibrium Wardrop (tt)
Planningequilibrium =? Nash
Multilateral changes in a replanning step But: Not coordinated.→ No coalition-proof eq.
Non-cooperative, coordination game (non-zero-sum)
10
What are we searching & How are we searching?
Non-cooperative, coordination game (non-zero-sum)
Pure Mixed
? ?
Equilibrium
Existence
Uniqueness
Yes
?No
Yes?Existence conditions
Results:e.g. link volumes
Results: Prob. of e.g. link volumes
Selection of plan for execution:
p(score) → mixed│agent‘s memory│ << #possible strategies of an agent
Score and hence p not stable between iterations
Battle of the sexes
Player 1
Store 0
Store 10,0c,d
a,b0,0
Refinements?Closest to SO?Largest basin of attraction? …
Player 0
11
What are we searching & How are we searching?
#locations#activities × tper iteration. Search space prohibitively large to be searched exhaustively or – even worse – globally at random.
Idea: Adapt local search techniques from optimization (e.g. simulated annealing).
Location Choice in MATSim - Status
First results: • Local search• Improvement of realism by competition on the activities
infrastructure
Future work:• Impr. local search & capacity restraints• Validation• Utility function extension• Analyzing existence and uniqueness of solution
13
Local Search Adopted to Coevolutionary Systems
Tie together location choice and time choice (t) p(accept bad solutions) > 0
Day plan
Aktivity i - WorkLocationStart time, duration…
Aktivity i+1 - ShoppingDuration
Aktivity i+2 - HomeLocationStart time, duration…
Location Set:Locations consistent with time choice (ttravel ≤ tbudget)
Travel time budget
Time GeographyHägerstrand
14
r = tbudget/2 * v
Check all locationsttravel ≤ tbudget
→ choice set
Check ∑ttravel ≤ tbudget
Random choice
Based on PPA-Algorithm Scott, 2006
„Implicit choice set“Chains of consecutive shopping activities
Location Choice in MATSim - Status
First results: • Local search• Improvement of realism by competition on the activities
infrastructure
Future work:• Impr. local search & capacity restraints• Validation• Utility function extension• Analyzing existence and uniqueness of solution
Time-dependent
capacity
Penalty funtion
Power function (cost-flow function for roads, BPR)
(load/capacity) : parameters
16
Competition on Activities Infrastructure
Micro-census 2005
17
Simulation Scenario
Region Zurich: 30 km radius circle, center Bellevue; 10% sample
Initial location assignment: Region Zurich
Location Choice in MATSim – Conclusions I
First results: • Local search:
Local search productive (w/ same computational effort per iteration).
• Competition on the activities infrastructure:
Balanced facility load → number of implausibly overloaded facilities reduced
Location Choice in MATSim – Conclusions II
Future work:• Local search
• Improvements + extended analysis
• Activity location competition• Diversification of capacity restraint functions
• Utility function extension• Influencing factors + activity classification
• Validation• Counting data, GPS (FCD), Micro census
• Analyzing existence and uniqueness of computed solution• Exit condition
Application of estimated modelsHypothesis testing
27
Who are Retailers in MATSim?
from www.wikipedia.org:
Retailer: “In commerce, a retailer buys goods or products in large quantities from manufacturers or importers, either directly or through a wholesaler, and then sells smaller quantities to the end-user.“
In MATSim:
Retailer: “Person or entity having the control on one or more shopping facilities”
28
Motivations & Tasks
Motivations:
• First step to a fully agent-based representation of the system • Correctly predict the location choices of retailers under a
given policy scenario• Estimate a benchmark value for retailers (# customers,
turnaround, etc…) under a given policy scenario
Tasks:
• Define/implement retailer agents in the MATSim framework• Enrich individual agents (customer aspect)
29
Individual Agent Framework
Individual Agent
Personal attributes
• Age
• Gender
• Home location
• Work location
• Driving License
• Car availability
• Transit tickets ownership
• Income
• Household
Knowledge
• Memory of previous plans (score)
• Shop Attributes (Price, Quality, Parking, etc.)
Objective function
• Time based
• Utility based with budget constraints
Location choice methodology
• Not optimized
• Optimized in time and space
Current MATSim
Next Stage
30
Individual Agent Framework
Individual Agent
Personal attributes
• Age
• Gender
• Home location
• Work location
• Driving License
• Car availability
• Transit tickets ownership
• Income
• Household
Knowledge
• Memory of previous plans (score)
• Shop Attributes (Price, Quality, Parking, etc.)
Objective function
• Time based
• Utility based with budget constraints
Current MATSim
Next Stage
Location choice methodology
• Optimized in time and space
32
Common Methods and Tools in Retail Location Planning
Technique/s Subjectivity CostTechnical
experience required
Computing and data
needs
rules of thumb,
checklists,
ratio and analogue methods
multiple regression
discriminant analysis,
cluster analysis,
gravity models
Expert systems,
neural networks
Ada
pte
d fr
om H
ern
ande
z an
d B
enni
nson
, 20
00
33
Practice in Location Choices
Extensive literature research
11 explorative interviews accomplished in Germany and Switzerland in 2008
Results:
Location strategies vary both between and within different retail sectors
Location choices are still heavily based on experience and intuition, particularly those decisions at the micro scale
Simpler methodologies are still predominant, more sophisticated are sometimes used as a posterior confirmation
34
Retailer Agent Framework
Retailer Agent
Attributes
• Type
• Facility portfolio
• Price level
• …
Knowledge
• Customers
• Competitors
• Land Prices
• Land use regulation
Objective
• Max. Customers
• Max. Revenue
• Max. Market share
Location choice methodology
• Market ratio
• Catchment area
• Checklists
35
Retailer Agent Framework
Retailer Agent
Attributes
• Type
• Facility portfolio
• Price level
• …
Knowledge
• Customers
• Competitors
• Land Prices
• Land use regulation
Objective
• Max. Customers
• Max. Revenue
• Max. Market share
Location choice methodology
• Market ratio
• Catchment area
• Checklists
•…
Refinements
36
Retailer agents – Relocation steps
A new random link is proposed
The ratio # residents / #shopsin the new area is higher
Stay on the current linkNo
The daily traffic volume on the new link is higher
No
Yes
Move to the new link
Yes
NEXT
ITERATION
The retailer already owns a shop in this area
Yes
No
Global search
37
Simulation Inputs and Parameters
Inputs: • Retailers file:
List of retailer agents and shop facilities controled by them
• Links file
• Links allowed for the relocation of shop facilities
Parameters:
• Frequency of retailers relocation
• Catchment area dimension
MATSim: Actual framework38
initial demand
analysesexecution scoring
replanning
Share x of agents (usually 10%):Time, route, location choice
Fixed attributes Utility function f (t)
replanning
Exit conditon:„Relaxed state“, i.e. equilibrium
MATSim: Framework with Retailer Agents39
initial demand
analysesexecution scoring
Fixed attributes Utility function f (t)
replanning
Exit conditon:„Relaxed state“, i.e. equilibrium
Retailer agents‘ facilities:Location choice
Retailers replanning
40
Results: Simulation Scenario - Region Zurich
• Number of shops relocating: 80
0
20
40
60
80
100
120
0 5 10 15 20 25 30 35 40 45 50
ITERATION
Cu
sto
mer
s
AV.Customers
41
Issues and possible solutions
Simulations with different combination of input parameters: No relaxation is observed
Real Optimization Technique (e.g. SA)?
Same story as before: Search space prohibitively large ...
Alternative: Adapt local search techniques …• In each iteration• Outer loop
→ Replanning of person agents → relaxed state → local search
Interpretation
42
Customers & retailers – Coevolution
Agent i
Plan 0
Plan 1
Plan 2
Plan 3
Agent j
Plan 0
Plan 1
Plan 2
Plan 3
species iIndivid. i,0
Plan 0
Individ. i,1
Plan 1
Individ. i,2
Plan 2
Individ. i,3
Plan 3
species jIndivid. j,0
Plan 0
Individ. …
Plan ..
Weakest die→ Generations
person.removeWorstPlan()
Agent u
Plan 0
Plan 1
Plan 2
Plan 3
- - - - - - - - -
Agent v
Plan 0
Plan 1
Plan 2
Plan 3
species uIndivid. u,0
Plan 0
Individ. …
Plan ..
species vIndivid. v,0
Plan 0
Individ. …
Plan ..
retailer.removeWorstPlan()
Main limitations
• The land market is not represented• Introduction of monetary costs for activities and taking into
account prices for them • Retail shops are undifferentiated• Persons behavior on Saturday is different than during the week
-> Simulating only Mo-Fr retailers’ location decision are biased • …
Conclusions and future work
Conclusions:
• The new retailer agents have been introduced in MATSim, but their behavior still has many limitations and a strategy to produce meaningful and easily interpretable results hasn‘t been found yet
Future work:
• Try to use a local search• Define an exit condition• Overcome some of the limitations (e.g. take into account
different types of retail shops, account for monetary costs, etc…)
45
THANK YOU FOR YOUR ATTENTION !
MATSim project page: www.matsim.orgFurther publications: http://www.ivt.ethz.ch/vpl/publications/reports
Activity Classification & Utility Function
Store load – store capacity
Activity classificationshop, leisure
Status quo
(Shopping) location choice
Utility function
TimeTime & route choice
Alternative (Store) This summer (data set available)• Store size, local store density Later:• Parking, Product range, Price level
Situation…
Person Age, Income,Education
Next steps
Micro census (e.g. shopping)
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