Modeling of Household Waste
Generation and Treatment byBottom Up Approach• Takeshi Fujiwara, Kyoto University• Yuzuru Matsuoka, Kyoto University
The 7th AIM International Workshop 15-17, March 2002

Background• Material cycle has much relation to global
warming and atmospheric pollution.
• In the material production, transportation, andwaste treatment, GHG and atmospheric pollutants
are generated and emitted directly or indirectly.
• Analyzing and predicting the flow of material
cycle is important to reduce the global
environmental problem.
• To grasp the current situation of material cycle,
bottom up approach is effective as well as topdown approach.

Factors
Factors which can change material flow are :(1) Consumer’s preference: “Which goods does
the household purchase?”(2) Long time use: “When does the household
discard the goods as the waste?”(3) Waste treatment with low environmental
load: “How is the waste reused, recycled ortreated ?

Objective
To analyze and to predict the waste flow
through household, these three models aredeveloped.
(1) Consumer preference model(2) Household material balance model(3) Waste treatment modelBottom up model of household consumption and waste
Macro Economics
model
Income, product priceAmount of goods

Customer preference
Customer preference
modelmodelHouseholdconsumption goods

HouseholdHouseholdmaterial balancematerial balance
modelmodelAmount of waste
Household waste
Landfill cost
Utility cost
Recycle goods price
Facility cost
Running cost

Amount of the disposed

Waste treatment system model
Waste treatment system model
Facility
Facility
Planning
Planning

Landfill disposal

Amount of the recycled

RecyclingAmount of the industrial waste

Retired facility

Scenario of social &economic factors

Interindustry
relation
table

Research Researchonontimehousehold

Wasteelements
research

Treatment
Literature
Facility
dataCPIHousehold material balance model
Product price, Commodity production coefficient, Labor cost, Working hours

Consumer
Consumerpreference
preferencemodel
modelInterindustry
Relations
table

Product consumption modelHouseholdNon-durable
consumer
Goods

Container andpackage

Durableconsumergoods

Waste generation modelTransferfunction

Domestic waste

ResiduefunctionSuper structure of waste treatment system
House garbage (HG)

RefusederivedFuel (RDF)

Composting

Domestic waste (not HG)

Incineration

Gasificationandmelting
Fly ashCompostSolidfuelElectricPower
Bottom ashSlag

Fly ashAshmelting

Ash treatment
Landfill

Calculated waste flow of waste treatment system
House garbage (HG)

Domestic waste (not HG)
617

383

RefusederivedFuel (RDF)

Composting

Incineration

Gasification
andmelting

69.0
Fly ashCompostSolid
fuelElectric
Power

13900
Bottom ash

33.3

Slag

Fly ash

7.71

Ashmelting
79.6

Ash treatment
617

LandfillPlanning of waste treatment
Planning year

+5yearCompletion year

Predicted population Prediction
Predicted GDP

Total
Totalwaste
waste
volumevolumePlanning
Treatment
capacity+Consumer priceAge and capacityof all treatment
Facilities in Japan

Existing
Treatment
capacity

Active facility
Retired facility

Distribution
Capacity decided
from the viewpointof past result

Outputs

Industrial
waste
Kind and capacityof new facilities-Requiredadditional
capacity

Calculation of additional capacity
for all kinds of existing facility
Cost
Cost
minimization
minimization
Waste flow is
calculated

Waste
Wastetreatment
treatment
superstructure
super structure

Capacity decided
from the viewpointof cost performance
Property and cost
data for eachtreatment facility

Consumer preference modelSocial andeconomic factors

Free time+Time budget
constraint= 24hours

Essentialtime
Selection of goods/service

BudgetExpenditure constraint
is less equal thanhighlow

IncomeMaximum utility

Aging people ↑The # of children↓
Woman power ↑Technology ↑Housing↑Labor cost↑
Labor hours↑
Environment↑

Selection of action

Concept of consumer preference model
Cobb-Dougras-typeutility production
function

Commodity
Zi+1Z
Commodity
Benefit Zin

Utility
UtilityUU
Leontief-type commodity
Production function

Annualreport ofhousehold

財・サービス
財・サービス
財・サービス
財・サービス

Goods /Services Xi

budget constraint

時間
時間時間
時間

Time tiTime budget constraint

Full
Fullincome
incomeReport oflivinghours

Definition of benefit production
Production function of benefit (Leontief function)
Producedbenefit

Investment of money ∑ p ij x ij
 jz i = min ,Ai

Inestment of time∑tkikCoefficient of benefit
production

amusement
TV sethours to watch TVbooks

hours to read books

sports goods

hours to do sports

・・・・・・

Constraints for benefit production
Full income：money income when whole available time is spent
for labor.
Constraint of full income is regarded as integrated budge andtime budge constraints.
Labor costFullincome：

S=w T+K− V

Available total
IncomeExpenditure
timewithout labor excluding
consumption

Constraint： S=∑∑ p xijij

Investment
forgoods/service

ij+ w ∑∑ t ikik

Money income renounced
while the time is spentexcept for labor

Definition of utility production
Utility function (Cobb-Dougras function)
Base of benefit

Produced utilityu = ∏ (z i − β i ) α ii

Benefit

Maximize

Utility
EatingHouse

Sleep

Magnitude ofpreference・・・Amusement

Goods/ServiceTime

Each benefit isfixed

Full income is distributed
according toαi and βi

Full income

Prediction of household waste using‘Consumer preference model’
Scenario
Scenarioofofeconomic
economicgrowth
growthConsumer
Consumerpreference
preference
model
model
HouseholdHouseholdexpenditure
expenditureper
perperson
personforforagedagedhouseholds
householdsand
andthetheotherother

Scenario
Scenarioof
ofpopulation
population
changechangeandandaging
aging
HouseholdHouseholdexpenditure
expenditureof
ofwholewholeJapan
Japanininfuture
futurePrediction ofof JapaneseJapanesehouseholdhousehold waste
waste
in future
futureHouseholdHouseholdmaterialmaterialbalancebalancemodel
modelCategory of benefits
Categoryclotheatinghouseeducation
housework
healthBenefits
benefits by wearing clothes
benefits by eating dishes
benefits to get comfortable living
benefits by taking educations
benefits by housekeeping
benefits by maintaining healthy life

amusement benefits by enjoying amusement or recreations
sleep
benefits by sleeping
othersthe other benefits

Example of action
clothing
eatinghousing
going to schoolcleaning、washingtaking bath,washing face,going to a hospital
reading、sports、travel
sleeping
moving、communication

Total real living expenditure
1人当たり実質年間消費支出総額(1995 yearbased
106 yen/person)(1995年基準・円)

106

Prediction of living expenditure(total cost per person)

1.6

Economic
Economic
growthgrowth↓↓
Increase
Increaseincomeincome↓↓
Increase
Increase ofofhouseholdhouseholdexpenditure
expenditure

Aged household

The other household

1.2
Positive growth
積極ケース→ Prediction

中間ケース
Intermediate growth
停滞ケース
Zero growth

0.8
1980

1990

2000 Year年

2010

2020

Scenario of population change and aging
40%

Peak at 2007 year
Population

30%
125000

Ratio ofaged households

20%

120000

Ratio of 高齢者世帯率
aged households (%)

Population(103 persons)
人口(千人)

130000

10%
1995

2000

2005

2010

Year

年

2015

2020

2025

(国立社会保障 ・人口問題研究所)

家庭ごみ総量(t ) waste
Total weightof household(t)Prediction of household waste

24000

Peak at 2018 year
Effect ofpopulation
decrease

Peak at 2013 year

22000

Positive growth
積極ケース
Intermediate growth
中間ケース
Zero growth
停滞ケース

20000
1995

2005

年
Year

2015

2025

Ratio of the household garbage
家庭ごみ総量の占める割合
against the
total household waste (%)

Prediction of household garbage
62%

61%

60%

Positive growth
積極ケース
Intermediate growth
中間ケース
Zero growth
停滞ケース

59%

58%
1995

2005

年
Year

2015

2025

・In all households, the expenditure for ‘eating’ decreases.
・Household garbage, which is generated from the essential activity,
the ratio of garbage decreases even if the economic growth is high.

Ratio of the paper waste against
家庭ごみ総量の占める割合
the total household waste (%)

Prediction of paper waste
19%

18%

積極ケース
Positive
growth中間ケース
Intermediate
growthZerogrowth
停滞ケース

17%
1995

2005

年
Year

2015

・Increase of aged households.
・Expenditure for amusement in aged households increase.
・Papers have a relationship with the amusement.

2025

Conclusion• We developed sequential three models• Using a scenario considering aging problem,
the trend of waste in future was predicted.
• This models should be linked to the macro
economic model, AIM-Material.
• In the next step, a bottom up model ofindustrial waste will be studied.

Appendix(1) Commodity production function
Z n = f ( X 1 , X 2 , L , X M , t1 , t 2 , L , t M ; R )Z n : commodity
 : goods or service
Xi
ti : hour spent for X i
 R : other variables(5)Leontief − type " Commodity production function"
M∑ p j X j M 
Z i = min  j =1, ∑ ti i =1  Ai
Ai : Commodity production coefficient(6)Shadow price of the commodity(2)Budget constraintMMMMMi =1i =1i =1i =1i =1

S = ∑ pi X i + ∑ wi ti + V = ∑ Ai Z i + ∑ wZ i + V ≡ ∑ π i Z i + VM

I = ∑ pi X ii =1π i = Ai + w
π i : shadow price of commodity Z i

 I : Income pi : price of goods or service(7)Cobb - Douglas utility production fuction(3)Time budge constraint

NαnU = ∏ (Z n − β n ) , Z n ≥ β n ≥ 0Mt all = ∑ ti + t w

n =1i =1α n : marginal propensity to consume
 β n : base utility

t all : total hourt w : working hour(4)Full income
MMMi =1i =1i =1

S = ∑ pi X i + w∑ ti + V = wt w + w∑ ti + V = wt all + V
S : full income
V : other income
w : labor cost(8)Optimization problem to be solved
αnNmax U = max ∏ (Z n − β n )n =1subject toZn ≥ βn ≥ 0N

∑α = 1n =1nMS = ∑π m Zm
m =1MN→ max ∑ α n log(Z n − β n ) + λ  S − ∑ π m Z m m =1
 n =1(9) Utility demand function as the result of optimization
M





m =1

π n Z n = π n β n + α n  S − ∑π m β m 