J. Pack. Sci. Technol. Vol. 5 No. 2 (1996)

A Logistics Model for Post-Consumer
Waste Recycling

Masanobu ISHIKAWA*

In this paper, we propose a logistics model for post-consumer packaging waste recycling (GridCity Model). This model can predict the transport distance and the number of trucks needed to collect post-consumer packaging waste for recycling. The parameters needed are population, area, waste
discard unit, number of collection stations, size of a collection truck, frequency of collection. Tradeoff relation between the service level of waste collection and environmental load or the number oftrucks is explicitly described in the Grid City Model.
Both the unit transport distance (D/W) and the number of collection trucks per a unit waste (M/W)
are described as a sum of the "density effect" and the "scale effect": the "density effect depends onthe effective capacity of the collection truck (q) and independent of the waste discard unit (u) nor
the collection, frequency (f); the "scale effect" depends on both u and f and independent of q.
Both D/W and M/W of sorted collection of PET bottle is much larger than those of the household waste in a typical case.
Keywords: Recycling, Sorted collection, Logistics, Transportation, Model, Post-consumer waste,

Introduction

unit, on the environmental load of recycling, tocompare the inventory of different recycling sys-

This paper describes the essence of our model of logistics for post consumer waste packag-

tem; material recycling, thermal recycling, andchemical recycling.

ing (Grid City Model). The model was developed

The recycling was a key problem from the ear-by the author for a joint project sponsored by Japanly stage of LCA study (e.g. MRI, 1974; MRI,

Consumers' Co-operative Union and Environ-1975). Among LCA studies of recycling of post-

mental Agency (Anonymous, 1995), and con-consumer waste (hereafter referred to as PCW),

ducted by the Nomura Research Institute Ltd.

transportation process has been always an irksome(NRI). The objectives of the study were to exam-

process: because the environmental load of trans-

ine quantitatively the effect of characteristics ofa region; e.g. population density, waste discard

portation in the recycling is suspected to belarge and the transportation process in a recycling*Tokyo University of Fisheries, Department of Food Science and Technology, 4-5-7 Konan, Minato-ku, Tokyo,
108 Japan- 1 1 9 -

A Logistics Model for Post-Consumer Waste Recyclingof PCW was usually described by a simple sce-

the second part, we show how we determined thenario such as an assumption of the transportation

parameters based on data from 30 municipalities

distance; this means that results directly dependin Japan and compare the observed data and themodel predictions.

on the assumption.
In the present paper, the author attempts to giveModela clear and transparent structure to the collection
and transportation process for a LCA study.

A schematic diagram of the Grid City Model

The present paper can be divided into two parts.

is depicted in Figure 1. In this figure, each open

In the first part, we explain the key concepts ofthe model, and show the explicit expression. In

block are parameters or various , and arrows indi-Fig. 1 A schematic diagram of "Grid City Model"- 1 2 0 -

J. Pack. Sci. Technol. Vol. 5 No. 2 (1996)

cate causal relationships. In the largest grayfrom parameters of collection productivity, one

block, we collected the output variables; D, M,

will find that there is no causal path between trans-

D/W, M/W. The parameters which characterize

port distance and these parameters. Although every-

the city are in the top of the right column; A, £,one will agree that collection productivity should

P,W. This group of parameters should be given

be a major factor in the economy of collection sys-

for a certain city, however, an average value oftem, this means that the environmental load ofE, for 30 municipalities in Japan is given in this papertransport is independent from the collection pro-and the average value can be substituted to it. The

ductivity. This can be understood if we see theparameter in the top of the left column is p,: thewaste material flow from the Lagrangean point ofapparent density of the i-th waste in the collec-

view; when we observe the transport distance rid-tion trucks which was calculated from data on com-

ing on a certain waste discarded at a certain point,

position of household waste (Kyoto-shi Seisou-

the distance should depend on only state variables

kyoku, 1994). In the bottom of the left column,

such as geometric parameters.

policy variables are shown; q, N, f. We consider

Let us consider a city which has a regular gridthese variables are policy variables for improve-type configuration (Figure 2). In this city, a col-ment. We grouped the parameters which relate

lection truck starts from the recycling center whichto the collection productivity in the bottom of thelocates in the center of the square area drives toright column; v p , t L , k.
It may be interesting to trace the arrows start

the collection area. In the collection area, the truck
collects the waste at collection stations until its

Fig.2 The geometry of collection stations, collection center, and grid- 1 2 1 -

A Logistics Model for Post-Consumer Waste Recycling

maximum capacity: it means that a collection area

It is evident that the actual distance will differ

is dependent on the capacity of the truck. Afterfrom this value because the actual road config-

filling its load space, the truck returns to the recycling center. The collection truck repeats this col-uration is not a regular grid. We introduce a factor which correct this effect (ξ,: tortuosity factor).

lection trip several times a day.
The distance of a collection trip is expressed as:

(6)

(1)

In equation (6), D denotes total driving distanceIn equation (1), superscript G denotes grid cityof collection trucks of a recycling center permodel, subscripts 1 and 2 denote driving distance

year, superscript o denotes the observed value.

in the collection area, and the distance between
recycling center and the collection area, respec-

Since the total number of the collection trips a year
is given by W/q, tortuosity factor of the i-th city
i s g i v e n as :tively. The average value of d° can be obtained
as:

(7)
(2)

Therefore, if we have an average value of the
Similarly, the average value of dG1

tortuosity factor, we can estimate the total trans-is,port distance D from the equation below.
( 3 )

(8)

In equation (3), m denotes the number of colLet us introduce population (P) instead of W
using the waste discard unit (u).

lection stations which can be served in a trip, A
denotes area per a collection center, N denotes
the number of collection stations per a collection(9)

center. When we consider a macro balance of waste
When we substitute equation (9) into (8) anddivide it by W, we get:discarded and the waste collected a year, m canbe expressed by q, N, f, and Was:

V

( 4 )
(10)

Since A is equal to L2. , the average transport distance of a trip is described as:

From this equation, the transport distance
per a unit mass of waste is a decreasing functionof population density (P/A), when the ratio of the(5)number of collection stations and population(N/P) is kept constant. This equation can be inter-In the above equation,/denotes frequency ofcollection service.

preted as showing a quantitative trade-off relationship between the environmental load and- 1 2 2 -

J. Pack. Sci. Technol. Vol. 5 No. 2 (1996)

the service level of waste collection: when f or N

N/P is constant. As is expected, the increase inincrease, the service level will increase but theconsumer's convenience: increase in f or N,

environmental load will increase.

results in increase in M/W which can be inter-

Although the number of trucks (M) is independent of environmental load, it is important forpreted as a substitute variable of unit collection
c o s t .

the economy of the system. Let us consider what
determines M.

Identification of parameters

The time necessary for a collection trip (tt . ) isdefined as the sum of the driving time, loss

Model parameters: ξ, vp, tL, and k are determinedtime(tL. ) , and the loading time. Assuming that theby the data of 30 municipalities in Japan. The pop-

velocity is constant (v p. ), a certain amount ofulation of the cities vary from thirty thousand up

loss time is necessary per a collection station, andthe loading time is proportional to the amount of
the waste, we have an expression of tT as below

to three million: 3 cities over one million, 6 cities(11)

over five hundred thousand, 12 cities over two hundred thousand, 7 cities over fifty thousand, andremaining two cities are between twenty thousand
and fifty thousand.

From mass balance, the average number of col-The tortuosity factor of a certain city was cal-lection trips of a collection truck per a operation
day (n) is given as:

culated from equation (6), and a simple averageof the tortuosity factor was calculated.
The parameters which represent collection(12)

productivity: vp, tL, and k are determined by a multiple regression analysis. In order to reflect theT.

Since the product of n and t , M can be given as below from rearrangement of the product.

actual condition, the model was slightly modified
for analysis. Since the number of trips per aworking day (n) should be an integer, n' isdefined as:

(15)

(13)
/

Dividing equation (13) by (9) followed by substitution of (9) yields:

where Ceiling(x) denotes the minimum integer
which is not smaller than x. The number of stations collected in a collection trip (m) is expressed
by

n’

as:
(16)

(14)

This equation shows that the number of collection trucks per a unit mass of waste is adecreasing function of population density when

The actual driving distance of a trip (d0. ) can
be calculated from the observed data as- 1 2 3 -

A Logistics Model for Post-Consumer Waste Recycling

below.
(17)

We define the effective capacity of the collection
truck as:(18)

Substitution of equations (16), (17), and (18)
into (ll) and rearrangement yields:
value of vp which is derived from α, does not con-(19)

tradict our intuitive expectation.
In Table 3, we tabulated the results of our actu-

where

al observation of collection process. The observed
value of the loading rate coincided with theobservation. The observed value of velocity were(20)

somewhat smaller than the result of our analysis.
However, considering the low t-value of the paraa n dmeter, we are satisfied that the result was only
50% larger than the observed values.
Matsui also observed the actual collection(21)

activity in Uji city (Matsui, 1994). He obtained theloss time, the loading time, the driving velocity
between the collection center and the collection

In equation (19), parameters such as α, β, γ are
identified from regression analysis from theobserved data set (t Ti , x i , y i , z i ,).

area as well as the driving velocity in the collection
area. The loss time of our results (12.Is/station)
are extremely in good agreement with the average value (10 s/station) reported by Matsui

R e s u l t s(1994). The driving velocity of our results(31.5km/hour) is around 50% larger than those

The average tortuosity factor was 1.52
(δn-1=0.703).

reported by Matsui for drive between the collection
center and the collection area, and around 2.5 times

The results of multiple regression analysis arelisted in Table 1. The t-value of β and γ were large
enough to clear 1% significance. The parameters
calculated from the these parameters are given
in Table 2. Although the /-value of α was low, the- 1 2 4 -as much as the velocity reported for the drive inthe collection area.
The correlation between the observed data andthe predicted from equation (8) is depicted in Fig-

J. Pack. Sci. Technol. Vol. 5 No. 2 (1996)

ure 3. Considering the simplicity of the model,
the agreement is excellent.

of collection trucks was also in good agreementwith the observation.

The predicted number of trucks are correlated with the actual data in Figure 4. The number

Application
In order to examine the environmental and economic effects of selective collection of PCW, let
us calculate the actual cases and see what this model tells.
We take up two cases; sorted collection of PET
bottles and mixed collection of household waste.
Since PET bottles are one of the most bulky
PCW, the environmental and economic effects ofsorted collection of PCW are expected to be
most evident when compared to mixed collectionof household waste.
The values of para meters we assu med are
given in Table 4.
The unit transport distance (D/W) and the number of collection trucks per a waste (M/W) are
drawn as functions of the number of collection stations (N) for different collection frequency (f) in
Figures 5, 6, 7,and8.

Unit transport distance
As is expected, D/W increased with increaseof both N and f (Figures 5 and 6). However, D/W
of PET bottle was larger than that of house-holdwaste for 10 to 100 times depending on both N
a n d
f .

- 1 2 5 -

A Logistics Model for Post-Consumer Waste Recycling- 1 2 6 -

J. Pack. Sci. Technol. Vol. 5 No. 2 (1996)

Number of collection trucks
The results of calculation are given in Figures
7 and 8. Qualitatively, the results resemble to thoseof unit transport distance. M/W of PET.bottle ismuch larger than that of the household waste for
5 to 500 times depending on both N and f.

Discussion
Tortuosity factor
In our study, the average tortuosity factor
was 1.52 (δn-1.,=0.703). One of the reason why theaverage tortuosity factor was larger than unity may-127-

J. Pack. Sci. Technol. Vol. 5 No. 2 (1996)

be that the location of recycling center (waste treat-collection area, and not in the transport in the col-ment center) is likely to be in the peripheral area;

lection area looks to be peculiar. This is because

which will cause less collection efficiency than thatof the grid city model.

that the total transport distance in the collection
area can be described only by the total waste discarded: under a give collection frequency, one canModel performance

calculate the number of collection stations that

From comparison of the model prediction andthe actual data, we can conclude that, in average,

should be collected in a day, this means that thewaste discarded in these stations in a day should

the Grid City Model can predict the transport distance and the number of collection trucks. However, we should be careful to apply this model toa specific city, in such a case, we must accept somewhat large error shown in Figure 3 or 4. However,be collected in a day no matter how bulky the waste
might be, and this requires that the collection truck
should visit all the collection stations in thearea. Therefor the transport distance in the collection area is determined from only location ofeven in such a case, the Grid City Model has advan-

the collection stations.

tage over simple scenario approach because theGrid City Model can give the value of error of theprediction.

Similarly, the waste discard unit (u) only affectthe second term in equation (9). The reason
why we call this as "scale effect" is that this term
expresses the scale merit of collection. Consid-

Unit transport distance
D/W of PET bottle was larger than that of household waste for 10 to 100 times depending on both
N and f. This indicates that the environmental merit of recycling would be somewhat discounted by
the increase of transportation.

er the extreme case that the amount of waste discarded in one collection station is equal to the effective capacity of the collection truck, it is evident
that the transport distance in the collection area
should be minimal value of null.
The balance of these two effects depends on

The difference between PET and household
waste is explained by two reasons; one is the difference of effective density (hereafter we refer thiseffect as "density effect") and the other is the difference of waste discard unit (hereafter we refer
this effect as "scale effect").
The D/W is expressed as the sum of a constantterm and a N1/2. term. It is evident that the effective density affect only the first constant term, therefor this term describes the "density effect". The
fact that the "density effect" appear only in thetransport between the recycling center and thecases. In general, if the waste discard unit (u) islarge or the collection frequency (f) is small, D/W
would be mostly determined by the "density
effect", and D/W would be almost independentof the number of the collection stations (N) nor
the collection frequency (f); this is the case ofhousehold waste collection (Figure 6).
On the contrary, if the waste discard unit (u)is small or the collection frequency (f) is large,the "scale effect" would dominate in equation (10),and D/W would increase with the increase of N
and f; this is the case of sorted collection of PET-128-

A Logistics Model for Post-Consumer Waste Recycling

bottle (Figure 5). Please note that the asymptotic

between the service level of waste collection

values in Figures 5 and 6 are determined by the"density effect".

and the number of collection trucks are explicitly described in the Grid City Model.
Both the unit transport distance (D/W) and the

Number of collection trucks

number of collection trucks per a unit waste

M/W of PET bottle is much larger than that

(M/W) are described as a sum of the "densityof the household waste for 5 to 500 times depend-

effect" and the "scale effect": the "density effect"

ing on both N and f. This means that the sorted

depends on the effective capacity of the collec-

collection of PET bottle requires much larger costthan the conventional household waste collection.
It is evident that the increase in cost could betion truck, and independent of the waste discard

reduced by a simultaneous collection of several
selected wastes; since this increases the waste discard

unit

(u).

The difference between PET and household
waste can be similarly explained by the "density effect" and the "scale effect". The "density effect"

unit (u) nor the collection frequency (f); the"scale effect" depends on both the waste discard
unit (u) and the collection frequency (f), and independent of the effective capacity of the collection
truck.
Both D/W and M/W of sorted collection of PET
bottle is much larger than those of the household
waste in a typical case.

ofM/W is defined by the firstterm of the equation (14), and the "scale effect" of M/W is defined

Acknowledgmentby the sum of the terms except the first terms in
The author would like to thank Mr. Kanamori

the equation (14).
In the case of M/W, since the "scale effect"
includes a term proportional to N, M/W increases much fa ster with i n crease of N co mp a r ed
with the case of D/W (Figure 7).

and Mr. Motokawa for observation of the actual
collection. Part of the present work was financiallys u p p o r ted b y Ja p an C o n su me r 's Co -o pe r ati ve
U n i o n a n d E n v i r o n m e n t a l A g e n c y.

References
1) Anonymous: 'Housou haikibtsu no risaikuru ni
kannsuru teiryoutekibunnseki (A quantitative
analysis of the post consumer packaging waste recycle) '; Working Group and Nomura Research Institute, Ltd.; Tokyo 1995. (In Japanese)2) Kyoto-shi Seiso-kyoku (Cleaning Bureau of Kyoto):'Gomi Saisosei Chosa Houkokusho (Report on
detailed composition of waste) '; Kyoto-shi Seisok yo k u ; K y o t o 1 9 94
3) Shouichirou Matsui: 'Chuutoshi ni okeru gomi noConclusions
A model (Grid City Model) was developed, which
can predict the transport distance and the number of collection trucks from data such as population, area, tortuosity factor, waste discharge unit,
number of collection stations, size of a collection
truck, and frequency of collection.
Trade-off relation between the service level ofwaste collection and environmental load, and-129-

J. Pack. Sci. Technol. Vol. 5 No. 2 (1996)

haishutsu oyobi shuushuu no gennjyou ni kannsuru
kennkyuu (A research on the present status of thewaste discard and collection in medium sizecity) '; Graduate thesis of Department of Hygiene
Engineering, Faculty of Engineering, Kyoto University, 1994
4) MRI: 'Resource and Environmental Profile Analy-

sis of Nine Beer Container Alternatives': MRI Report MRI Project No. 3794-1); 1974
5) MRI: 'Resource and Environmental Profile Analysis of 10 Beer Container Systems': MRI Report MRI
Project No. 4021-D; 1975
(Received 1 November 1995)(Accep ted 25 Janu ary 1 996)

家庭系廃棄物リサイクルの輸送モデル

石川雅紀*

本論文では、家庭系から排出される包装廃棄物のリサイクルのための輸送モデル（Grid City
Model)を提案する。このモデルによれば、輸送距離と必要車両台数を予測できる。必要なパラメー
タは、人口、面積、廃棄物発生原単位、ステーション数、収集車容量、収集頻度である。収集のサービ
ス水準と環境負荷、収集車台数の間のトレードオフ関係がこのモデルによって明示的に記述された。
廃棄物当りの輸送距離（D/W）と廃棄物当りの収集車台数(M/W)は密度効果と規模効果にわけることができた。密度効果は、収集車の有効積載量のみで決まり、規模効果は、廃棄物発生原単位と、収集頻度で決まることが示された。典型的なケースにおいてPETボトルの分別収集のD/WとM/W
は、ともに家庭系廃棄物の混合収集に比較して遥かに大きかった。
キーワード：リサイクル、輸送、モデル、家庭系廃棄物、LCA*

東京水産大学（〒108

東京都港区港南4-5-7）-130-