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Dynamic simulation of waste paper recycling system in japan
PAPER RECYCLING AND WASTE WATER Copyright © IFAC PRP 4 Automation, Ghent. Belgium 1980
DYNAMIC SIMULATION OF WASTE PAPER RECYCLING SYSTEM IN JAPAN T. Takamatsu*, I. Hashimoto*, F. Yoshida** and H. Ohno*** *Department of Chemical Engineering, Kyoto University, Kyoto, Japan **Osaka Prefectural Industrial Research Institute, Osaka, Japan ***Department of Chemical EngineenOng, Kobe University, Kobe, Japan
Abstract. The ainl of this paper is to make clear the prospects and policies for waste paper recycling and utilization in Japan. The waste paper recycling system is composed of ~any processes relevant to the production, distribution and consumption of paper and boa~d, and the generation, recovery and disposal of waste paper. A dynamic model of the national level is developed fi~st so as to <:;i:nulatp. the behaviour of the whole system and to clarify the real issue in this system. Then, the dynamic simulation on the future trend of waste paper recycling and utilization is carried out and at the same time the policy that will be the most promising in order to promote the waste paper recycling is made clear. The quantitative assessment of several practicalmeasuresfor the reconciliation of the problem of future waste paper supply and requirement is performed. As a result, it is conclu0ed that the most effective and desirable countermeasure for overcoming the anticipated shortage of waste paper supply in the future is to increase the recovery rate of waste paper up to 60% by revising and consolidating the collection sector. Keywords.
Waste paper recycling; modelling; system analysis; simulation
INTRODUCTION
the waste paper recovery and utilization, and at the same time to made clear what policy will be most promising in order to promote waste paper recycling.
In recent years, the recycle utilization of resources has been of great importance as an effective measure for the solution of energy, resources and environmental pollution problems. Within this context, the recovery and utilization of waste paper l have tended to
A rough material balance in the processes of the paper production, distribution, waste paper recovery and disposal in Japan is shown in Fig. 1. The paper and pulp industry in
increase in developed countries. Many studies have been published which have tried to explain why the recovery of waste paper and its utilization have increased and why and by how much it is expected to increase in the future. (OECD report, 1976; Glassery and Gupta, 1975; Clifford and Co-workers, 1978; Tunner, Grace and Pearce, 1978) The aim of the research reported here is to make clear the prospects and policies for waste paper recycling system in Japan. For this purpose, a dynamic model of the national level in Japan is first developed. This includes all the processes relevant to the production, distribution and consumption of paper and board, and the generation, recovery and disposal of waste paper. By using the developed model, the real issue in the promotion of waste paper recycling and utilization is clarified. By changing the assumptions about policy development which mayor may not be realized, many simulation calculations are performed to forecast the future trends of
Domestic Consumption (16.3)
Exports
rconsumer
.
!
'
(0.5)
IWho
th
Refuse ,(9.4) Waste Paper (6.9)
1e-;;l;;J
--f I
Imports
Waste Paper (6.9)
(0.3)
Domestic (9.1)
1
Fig. 1
Throughout this paper, the term waste paper also includes waste board. 271
Paper flow in Japan (million ton;1978)
T. Takamatsu et al.
272
Japan has grown very rapidly along with economic development since the 1960's. The actual production o~ paper and board exceeded 16 million tons, in 1978. The 'actual production of pulp is about 10 million tons, and the annual consumption of paper and board per capita is 141.6 kg. Almost all paper and board produced is domestically consumed. About 40% of the amount consummed is recovered. Of the remaining unrecovered 60%, about 10% is stored or utilized as a permanent stock such as books in libraries and building paper in construction etc. About 30% is used for some special type of paper and board such as paraffincoated paper for water-proofing etc. which is not suitable for recycled use and thus eventually becomes refuse. About 20% is also disposed of as refuse, even though it is still reusable. Recovered waste paper is a valuable raw material for the paper and board industry and is completely utilized for domestic demand. The importance of recovered waste paper as a raw material is growing due to the souring prices of both virgin pulp and imported pulp wood. (44% of the total necessary pulp wood came from imports, in 1979).
can be simply expressed as shown in Fig.3. From this figure, it is easily understood how and from what variables the major state variables are determined. As for the state variables Yl [Inventory of paper at the manufacturer] , y 2 [Inventory of paper at tre wholesaler] , Y4 [Inventory of waste paper at the recovery trader] and y [Inven:='C'ry of waste paper at the manufactur~r] in the differential equations of the model, the follo'.ving relation commonly holds; [Change of inventory] [Estimated s~les amount] + [Desirable month-end inventory] - [Present inventory] - [Actual sales amount] where for Y4 an~ yS' the ad~itional term related to the lnventory adJustment must be added to the right hand side of the equation. The differential equation with respect to y 3 [Paper stock in households] shows that the time derivative of the paper stock in consumers is equal to the difference of z [Amount of paper consummed by householJs] and z4 [Amount of paper discharged from househblds]. The differential equations of z4 shows that z has a time lag of the first . 4 order wlth respect to z3.
MODEL STRUCTURE The starting point of the analysis here is the simple material flow model, Fig.l. The recovery of waste paper is strongly influenced by business trends. Therefore, it is first necessary to examine the monthly changes of both the economic factors relating to waste paper recovery - (that is, the price of waste paper, gross national expenditure, private investment in plant and equipment, etc.), and the quantitative factors of paper, board and waste paper -(that is, amount of production, utilization rate, recovery rate and amount of stocks etc.) In order to build a mathematical model of such a large scale system as the waste paper recycling system at the national level, it is necessary to analyse the information available at present so as to make the relationship amo~g the variables clear. Then, a tentative model is built, and it is examined as to whether or not the model outputs can sufficiently explain the behaviour of the real data. If agreement between the model outputs and the real data can not be obtained, the tentative model is revised by changing the number and the kind of state variab lc;s so a:=: to decrease the discrepancy between the model outputs and the real data. By repeating the procedure explained above, the most updated model for the waste pC.per recycling system in Japan is obtained, as shown in Fig.2. The detailed mathematical expression of this model is given in Appendix 1, and the ~eaning of each equation is explained in Appendix 2. By eliminating auxiliary state variables xi (i=1-23) in the mathematical expression of the model, therathematical structure of the model
From this contracted mathematical model shown in Fig.3, the values of each state variable can be consecutively determined by perfoming the calculation according to the steps di-rected by the arrows in the figure.
SIMULATION Based on the dynamic model developed in the previous section, the calculation for the simulation is performed for the period of the past ten years (from 1968 through to 1977). The calculated values from the model are compared to the available real data. It is later shown that they agree quite well with each other. Judging from this good agreement, it may safely be said that the calculated values of the state variabl-:s the real da ta of which are not available could be a fairly good estimation of the past c}:angcs of these variables. The values of the parameters and external inputs (exogenous variables) used in the simulation calculation are shown in Appendix 3. The forecasting of the future trend ranging over from the present up to 2000 A.D. is performed by earring out the simulation for the several cases where the asslli~ptions on the future estimation of many economic and social factors are changed. The annual increases in t~e exogenous variables 9 [Actual gross national expenditure] and g 1 [Actual private plant and equipment inves€mentJ arc~ estimated as sho'I',rn in Table 1, based on the annual economic gro~th rate forecasted by the Japanese government and the economists.
Waste Paper Recycling System in Japan
rPM
Y,
____~ (
/ SIPP PJ
)
Fig. 2 Waste paper recycling model I.A.A.-T
273
T. Takamatsu et al.
274
external variables
g.1 (T) (i=l,Z) gj (t) (j=3,4,S,6)
~ ZlO=[k 1 /(1-k 1 )f 1 (gl,gZ)
- Y3=Z3(t)-Z4(t)
Z4=(Z3(t)-Z4)/P12 ~ ~Z3=PZfl(gl,gZ)/lOO
---
zZ=aZ(t)+bZ(t)-YZ(t)
---
+[kl/(1-kl)]fl(gl,g2)~
ilzl=a1(t)+b1(t)-Yl(t)J ~
z7=zl(t)f Z(gl,gZ",gS,g6)
~ z 8 =z1 (t) f 3 (g 1 ' g2 ' g 5' g6) zS=a 4 (t)+k 6 (b 4 (t)-Y4(t)) z 9 =z 4 (t)-z 5 (t)',--z6=a 5 et) +b 5 (t) - Y5 ( t ) +(1-k6)(Y4(t)~b4(t))
1-
~
YZ=a Z (t)+b 2 (t)-Z3(t)-yZ where a Z(t)=k 7 z 31 (t), b Z(t)=k 33 F1 (z3)' and z31=(z3(t)-z31)/P14
Yl=al(t)+bl(~)-Z2(t)-Yl
where al(~)-[Plfl(gl,g2)/lOO]/(1-kl)' and b 1 (t)-k Z3 F1 (zZ)
Y4=a 4 (t)+b 4 (t)-z6(t)-Y4+(I-k 6 )(Y4- b 4(t)) Ys=a S (t)+b S (t)-z7(t)-YS+(I-k 6 )(Y4- b 4(t)) where a s (t)=F 1 (z7)' b S (t)=k S3 F1 (z7) a 4 (t)=z4(t)f 4 (g3,g4) and b 4 (t)=k 43 F1 (z6)
--
I
w here ~ 1 (g 1 '
g2) = [(p 3+P6) g1+ (p 4+p 7) gZ+ (p 5+PS) ] / 12 , fZ(gl,g2,gS,g6)=[gS(P3g1+P4gZ+PS)+g6(P6g1+P7gZ+PS)]/IZf 1 , f 3 (gl,gZ,gS,g6)=(1-P 11 f 1 )/PIZ' f4(g3~g4)=P9+(PIO/IOO)(g4/gS)/16, (Xl
Fl(Zj)=i~1(S/6)
ir-l
. Zj(t-l)/6
Fig. 3 Computing procedure for the equations of the model The values between Table 1 Estimated Values 1979 and 1989 are esof gl and g2 timated by taking into account the yearly g2 gl Year change in business trends. The values 1.708 10.81 1978 after 1990 are esti1.911 11.84 1980 mated under the as2.134 13.03 1982 sumption that the eco2.402 14.54 1984 nomic growth rate is 2.620 15.84 1986 constant. 3.002 17.78 1988 3.386 19.58 1990 As for the parameters, 3.733 21.38 1992 4.115 (1) PI and P2 [Sea23.35 1994 sonal indices of paper 4.537 25.50 1996 production and paper 5.002 27.84 1998 consumption,respec30.41 ! 5.515 2000 tively] are fixed as 13 (10 yen/year) p = p = 100. Seas5nal ~erturbation is not taken into account. (2) p. (i=3-l4) [Regression coefficients], kj (j~2-5) [Inventory-sales ratios], k [Coefficient of inventory adjustment a~ the recovery trader] are assumed to be the same as in 1977. (3) Since the paper production is estimated to become 2.87 times the present during the 22 years from 1978 through to 2000, k [The 7
adjustment coefficient of estimated paper shipment from the manufacturer] is calculated as follows, i.e.
(k )264/ P 4 = 2.87, 7
k
7
= 1.00802
The following assumptions are set out in the simulation of three cases. Case I (1) The upper liP.lit of 1:he recvvery rate of waste paper (S)2 is 50%, i. e.
S ~ 50 (%) •
(2) The actual paper exp'"Jrt ratio (k ) is l kept at the present level, i.e.
k
= 0.024. l (3) The actual waste paper price (g4) changes in the following fo~r different ways.
-----------2 S [recovery rate of waste paper] is defined by the ratio of (z4/z5)XlOO.
Waste Paper Recycling System in Japan 3
Letting the time origin (t =0) be January, 1978, (No.l) g4 is constant after 1979. i.e.
is imported when the inventory-sales ratio (= Y4/z6) becomes less than 0.15 [month]
i.e.
g4 = 14.13 + 0.05887t
(No.3) g4 becomes 2 times during 10 years.
i.e.
g4 = 14.13 + 0.1177t
(NO.4) g4 becomes 3 times during 10 years. i.e.
g4 = 14.13 + 0.2355t
(4) There is no technological upper limit on the utilization ratio of waste paper. The utilization ratio of waste paper for paper p~oduction (g5) increases by 0.008% per annum. g
5
= 0.175 + 6.667 x 10-4 t
The utilization ratio of waste paper for board production (g6) increases by 0.0052 per annum. g
i.e.
6
= 0.731 + 4.333 x 10-4 t
Case ]I (1) The net paper export ratio (k ): l
(2) The actual waste paper price (g4): g4 becomes 2 times during 20 years. (3) The waste paper recovery rate (S) changes in the following rang~s: (No.2) S:S 50 (%) (1978-2000) (No.5)
(NO.6)
S S
:s 50(%) (1978-1984), ~
55(%)
(1985-2000),
S S
~
50(%) 55 (%)
(1978-1984), (1985-1990),
~
a = 0
(No.7)
a
(No. 8)
a = 5.0
(No.9)
a = 7.5
=
2.5
Case nI (1) The net paper eXFort ratio (k ) : l k = 0.0~4 l (2) The actual waste paper price (g ): 9 becomes . 4. 4 2 t~mes dur~ng 20 years. (3) The upper limit on Lho waste paper recovery rate (S) is kept at 50%.
RESULT AND DISCUSSION
4-1 Confirmation of the model by comparison with the real data The comparison of the calculated zl [Amount of paper production], z6 [Amount of waste paper purchased by the manufacturer] and Y5 [Inventory of waste paper in the manufacturer] ;"Ji th the actual data is shown in Fig.4. From these results of the simulation, it is safely con-
1 6 ,..---------------------------_~ ·
1 .4 1 .2 1 .0
0.6 0.4 0.2
o
1968
(4) As for the import policy of waste paper, the following cases are considered. That is, a % of the estimated purchasing amount of waste paper in the manufacturer t
1970
Fig. 4 Comparison
S ~ 50
3 rrhe unit of time
In Case I, the effect of the waste paper price trend on the waste paper supply trend which is anticipated to increase according to the rapidly rising demand for paper under the assumption that the upper limit of the recovery rate is fixed at 50%, is made clear. In Case ]I , the effect on the waste paper supply trend of changing the upper limit of the waste paper recovery rate is analysed. In Case nI, whether or not waste paper import will be effective as a measure for making up for the shortage of the waste paper supply which is anticipated to occur in the future is examined.
0.8
and it increases by 5% for 10 years after 1990.
i. e.
(No.2) g4 = 14.13 becomes 2 times during 20 years.
(No.2) g4
i.e.
275
is measured in months
1972
Year
1974
1976
1978
of calculated values and real data
eluded that the model developed here is confident.
4-2 The calculated values of the variables the real data of which t7!''? "ncn-exis tant An advantage of utilizing this kind of mathematical model is that it is possible to estimate the variables the real data of which are
T. Takamatsu et al.
276
not available, by using the calculated values from the model. As an example, the es tirnated values of z4 [Amount of paper discharged from households], z5 [Amount of waste paper collected by recovery trader], z [Amount of waste paper disposed of as refuse], y [paper stock in households] and y [Inventor~ of waste paper at recovery tr~derJ are shown in Fig.5. z4 and Y3 represent the same tendency
x10 6 ton
following measures are considered in order to further promote the recovery of waste paper: (i) To increase the collection of waste paper by steadily rising the price of waste paper; (ii) To increase the' recovery rate by consolidating the structure of the waste paper collection system; (iii) To compensate for the domestic shortage of waste raper by importing it from abroad.
1.8 ...- - - - - - - - - - - - - - - - - - - - - - - - - - - -.... 1 .6 1 .4
In order lo evaluate the availabili t:/ of such neasures m('llLj\~lll:(l '.i;)()Vi',
and to assess the en1.2 vironmental impacts which would result 1 .0 from the execution of these measures, it is 0.8 indispensable to quantitatively forecast 0.6 the future demand for the was tl~ paper by using such a dynamic 0.4 model as developed here and to carefully 0.2 examine the forecasted results. In this section, the results of 1968 1970 1972 1974 1976 1978 the many simulations Year used to forecast the Fig. 5 Simulation of Yl , Y , Y , z4: z5' and z9 3 4 future trend of waste paper utilization at the manufacturer dre shown and changes of the amount of waste in thier changes. Since z has the first order time lag with respec~ to z [Amount of paper collected, the dOInl·stic inventory of waste v~per and the amount of waste paper paper consumed by households], y3 shows a disposed of as refuse are estimated assuming larger increasing tendency when 60mpared to that these three measures are implemented in z4. [See Eqs. (3) and (8) in Appendix 1] Both the future. z and y increased yearly up to 1973 along w~th the 3 rapid incrase of z . After the oil In Fig.6 the simulation results of Case I crisis of 1973, however, th~y once decr<~Cls('d where only the price of waste paper is steadand then became almost unchanged. At present, they have shown a gradually increasing tendily increased by limiting the recovery rate within 50% are shown. From this figure, it ency. Until 1975, z5 also shows the same is clear what will Jlclppen in trJ.C supply of trend. as z4 since the recovery rate of waste and the demand for waste Lld per, and how the paper rema1ned almost unchanged, and conseamount of waste L!dper disposed of as refuse quently z9 i~crease~ annually. After 1976~ will change. Thi~; figure shows that the zr. has been 1ncreas1ng and, therefore, z 1S supply of waste I 'Cl per cannot catch up with c6nstant or sliCjhtlYdecreasing. f,-ou
o
Waste Paper Recycling System in Japan Fig.8 shnws the results of Case TII where the waste paper is imported from abroad in or·· der to compensate for the domestic shortage. As shown in this figure, the import of waste paper can delay the time when the shortage of the supply will start to occur, but it results in large fluctuations in the inventory of waste paper. Moreover, the amount of waste paper disposed of as refuse is very large as in Case I, which results in some environmental pollution problE:'Tls. From these viewpoints it is not good to depend on the import of waste paper in order to prevent shortage in the supply of wast.e paper. Judging from the results mentioned above, it can be easily understood that the most effective and desirable countermeasure to overcome the anticipated shortage of waste paper supply in the future is to increase the recovery rate of waste paper up to 60% by consolidating the collection system.
277
1.8 1 .6
1 .4 1 .2
o
1978
185
180
195
Year
Fig. 6 Forecasting of Y4'
2
6
, and
2
9
2000
in case I
x10 6 ton 2.0 1.8 -
z6(No.6)
hO. ?-::;:7\
1\./\
1.6 1.4
Zg(No.6)
1.2 .
-
1.0 0.8 0.6
~O.5) \
\\
\
\\
0.2 1978
~\
~'
2)(Y4 \(No.2)
0.4 .
0
6)
180
185
i
190
Fig. 7 Forecasting of Y4'
CONCLUSION In this report, the waste paper recycling system is taken up as a concrete example of a resource recycling system. A dynamic model was developed and, based on this model, the quantitative assessment of several measures for preventing the anticipated shortage of the supply of waste paper in the future is performed. The basic structure of the model developed is based on the material balance shown in Fig.l. By taking into account many controlling and
2
195
Year 6 , and
2
9
2000
in case 11
influencing factors and adding th~m to the basic model as information flows, the whole model structure was gradually developed, and finally obtained as shown in Fig.2. The fundamental structure which is obtained by rearranging the model equations according to the direction of the information flows, is shown in Fig.3. As is clear from this figure, the procedure for the simulation calculation proceeds from the exogenous variables related to economic factors to the opposite direction of the material flow. The prameters included in the model are
T. Takamatsu et al.
278
estimated from the real data, and the confidence of the model is confirmed by comparing the calculated values from the model with the real dat~ ranging over 10 ye~rs, (Fig.4. ) The model is first utilized for predicting the change of state variables the real data of which are not available. (Fig.S) Then, it is used to quantitatively assess three measures for preventing the anticipated shortage of the supply of waste paper in the future.
xl0 6 ton
2.0r-----------------------.. . 1 .8 1 .6 1 .4
1.2 1.0
0.8 0.6 0.4 .
0.2 185
190
195
Year
2000
Fig. 8 Forecasting of Y4' z6, and z9 in case III
From the results of the simulation (Fig.6-8), it was clarified that the increase in the recovery rate of Case TI is the most desirable among these three measures. The system approach based on the quanti ta ti vc model as shown in this paper, could be very helpful in evaluating and assessing many different measures intorduced to resolve issues not only in waste paper recycling systems, but also in many other large, complex, resources recycling systems.
APPENDIX 1 MATHEMATICAL MODEL (a) Equations related to Yi (i=l-S) dY (t) l
zl (t)
z2(t)
(1)
z2(t)
z3(t) - zlO(t)
(2)
z3(t)
z4(t)
(3)
zS(t)
z6(t)
(4)
~ = z6(t)
- z7(t)
(5)
~=
dY2(t) = dt dY3(t) _ ~-
ACKNOWLEDGEMENT
dY4(t)
The authors wish to acknowledge Mr. M. Arakawa for his valuable assistance.
~-
dYS(t) REFERENCES OECD Report (1976). "Prospects and Policies for Waste Paper Recycling in the Pulp and of Paper Industry". Glassery, C.R., an~ V.K. Gupta (196S). A lipear programming analysis of paper recycling. Studies in Management Science and Systems Vol.2. North-Holland. Chap.13, pp.273-292. Clifford, J.S., M.A. Laughton, T.S. McRoberts and P.V. Slee (1978). LP modelling in the paper industry as an aid to recycling decisions. Conservation & Recycling, ~ 97-109. Turner, R.K., R. Grace, and D.W. Pearce (1978). The economics of waste ~zper recycling. Resource Conservation, Social and Economic Dimensions of Recycling, Langaman Group Limited, London, Chap.16, pp.296343.
(b)
Equation related to z. (i=l-lO) l. zl (t) Pllz7(t) + P12 z 8(t) k z
z2(t)
7 31
(t)
x
9
(6)
(t) + ZlO(t)
w~ere z31 has the first order time lag Wl.th respect to z3'
i.e.
dZ P14
z3(t) =
1
31 dt
12
(t) + z31 (t) = z3(t) 1
(8)
x 17 (T)100 P2(t)
dz (t) 4 P13~ + z4(t) = z3(t) z5 (t)
z 4 (t.' {P9+P lOx
20
(9)
(t)} - k x (t) (10) 6 6
(12)
Waste Paper Recycling System in Japan X (t)X (t) 13 15
(13) x
14
(t)
1
x
(14)
z4 (t) - z5 (t)
279
(T) (x
2l
(T) g5 (t) +x
22
(T) g6 (t) }
17 x
(15)
15
(29)
(t)
_l_{l - Pllx14(t)} P12
(t)
-6lI . i-)65 i-I z 7 (t-i)
(T)
x
(30)
oo
(c) Equations related to xi
x
5 i-I
1\00
6L i=1 (6)
(t)
1
1
~z7 (t-l)
x
(i=1~23)
. z7(t-~)
x
+ 5x (t-l)} l
(16)
y 5 (t)
x
-
2
(~)i-lz (t-i)
~{z
(t-l) + Sx (t-l)} 6 4
(19)
(t)x (t) 4
(20) 1
6 :L=l 6
6
xs(t) w~ere
43
x x x
~I~
k
x
(IS)
(t)
17
19 20 2l 22 23
~=
(t)
(T) + x (T) 22 21 k l l-k x 17 (T) 1 1 1 16 100 g4(t)
(t)
~ x
XlS(T) x
where k (t) has the first order time lag S3 with respect to k (t). 5 i.e. dk 53 (17)2 T5~ + k 53 = k S
16
1
Xl (t)
(31) (32) (33) (34)
(t)
(35)
(t)
P3 g l (t) + P4 g 2(t) + PS
(36)
(t)
P6 g1 (t) + P7 g 2(t) + Ps
(37)
(t)
x
(38)
g3
17
19
(t) + x
18
(t)
6
APPENDIX 2 MEANING OF EACH EQUATION
(t) has the first order time lag 43 w~th respect to k (t) 4 i.e. dk 43 (20) 2 T4~ + k 43 = k 4 k
(21)
Y4(t) - x (t) 5 5 i-I
1\00
6Li=1 (6)
z3(t-i)
2-.-{z (t-l) + 5x (t-l)} 637
(22) (23)1
(a) Equation of Y i
(i=l-S)
Eqs. (1)-(5): The change of inventory with respect to time is equal to the difference of both amounts of the input and the output. For example, the time derivative of Y [the l inventory of paper at the manufacturer] is equal to the difference between z [Amount of . 1 ] and z2 paper product~on at the manufacturer [Amount of paper shipment from the manufacturer]. Here, y. is an unknown variable the value of which his to be calculated from the observed or estimated values of the material flow z. (t) (j=1-7,10) J
(b) Equation of zi (i=l-lO) where k (t) has the first order time lag with re~~ect to k (t), 3 i.e. dk 33 (23)2 T3~ + k 33 = k 3 (24)
x (t) = Y2(t) - xS(t) 9 1\00
xlO(t) =
5 i-I
6 Li=1 (6)
i
z2(t-i)
z2{ (t-ll + 5x
10
(t-ll}
(25) (26) 1
w~ere k (t) has the first order time lag 23 w1th respect to k (t). 2 i.e. dk T 23 k k (26) 2 2~ + 23 = 2
Yl (t) - XII (t)
(27)
1 1 100 PI (t)~23(T)
zl (t)
(2S)
Eq. (6): z
[Amount of paper production at the is equal to the sum of the two values which are calculated by multiplying each yield factor Pll and PI by z7 [Amount of waste paper consumption at the manufacturer] and z [Amount of pulp consumption at the manufactu~er], respectively.
manufactu~er]
Eq. (7): z2 [Amount of paper shipment from the manufacturer] is concurrently equal to the amount of paper purchased by the wholesaler. The wholesaler seems to forecast his purchasing amount by analysing the past trend of the amount of paper purchased by COnSlim0r. Here it is assumed that the estimated value of z , z , can be obtained from the differentia13equ~tion which has the first order time lag with respect to z . (The time constant p is assumed to be months.) The estimate~4value z 31 is modified by multiplping lYl a factor k used to compensate for the inade7 quacy in this estimation. The actual amount of paper purchased by the wholesaler (z2) is given by subtructing the variation of Ehe paper stock at the wholesalc)r (x ), due to 9
1
T. Takamatsu et al.
280
the inventory adjustment, from the modified estimated value of z (k z ) and adding the 3 7 31 amount of net paper export (z ). 10 Eq. (8): The amount of paper puchased by consumer (z3) is equal to the value which is obtained by mul tipl y ing t~le seasonal index of paper consumption (p ) by the average paper consumption per montt which is calculated by dividing the annual paper demand in the domestic market (x ) by 12. 17 Eq. (9): The paper purchased by the consumer is disposed of with a certain time lag with respect to the purchasing time. This time lag is assumed to be the first order whose' time constant P13 is onc month. Eq. (10): Zs [Amount of waste paper collected by the recovery trader] is assumed to be determined by adding the term relevant to the inventory adjustment to the product of z [Amount of paper discharged from househoids] and (P9+PlOx20) [Estimated recovery rate]. Where estlmaEed recovery rate is presumed to be a linear function of x [Auxiliary variable on the waste paper prfge]. The capability of the inventory adjustment of the recovery trader seems to be insufficient. Therefore, as a coefficient to express its weakness in adjustment ability, k [Coefficient of inventory adjustment in re80very trader] is introduced, and this coefficient is multiplied to x [Variation of the inventory of 6 waste paper at the recovery trader] . Eq. (11): z6 [Amount of waste paper purchased by the manufacturer] is determined by subtracting x [Variation of inventory of waste 3 paper at tne manufacturer] from x [Estimat' 16 by the ea~ pu~h aSlng amount 0 f waste paper manufacturer] and adding the supplementary amount of waste paper which is kept in stock to compensate for the weakness in the inventory adjustment ability of the recovery trader. Eqs. (12) (13): z7 and z [amounts of utilization of waste paper an~ virgin pulp, respectively] is determined by multiplying C3.ch utilization ratio (x ) or (x ) ~y x LS 13 14 [Planned monthly paper ~roauctlon]. Eq. (14): z9 [Amount of waste paper disposed of as refuse] is the amount of uncollected [ Amount of paper discharged frem house2 4 hold] . Eq. (IS): Since z [Monthly net paper export] . 10 1S very small compared to the paper production, zlO is assumed to be constant thoughtout a year and to be (1/12)xx [Annual pa18 per export]. (c) Equations of x.
1
(i=1-23)
Equations relevant to (x ,x ,x ), (x ,x 'x ), 4 S 6 2 l (x ,x ,x ) an~ (xlO,xll,X12) all have tne 7 8 same mat~ematlcal structure, and they are utilized to calculate the variations of the inventories.
Eq. (16) - (27): Variables x. (i=1.,.3), x. (j=4-6) are relevant to the inventories of waste paper at the manufacturer and at the recovery traders, respectively. x (k=7-9} and x k (e=10-12) are also relevant to the inve5tories of paper at the wholesaler and manufacturer, respectively. The average monthly utilization of paper or waste paper (x., i=1,4,7,lO) is calculated by smoothing the ~ast record in such a way that the older the data is, the smaller is the coefficient weighed by using an exponential type of wighting function. The standard value of each inventory of paper or waste paper (xi' i=2,~), 8,11) is expressed by the product of tne average utilization of paper or waste paper and the average inventorysales ratio of paper or waste paper (k ,k , S 4 k
3
,k ) . 2
When the average inventory-sales ratio changes, its change does not directly cause the variation of the standard level of the inventory, but its influence has a certain time lag. So, the average inventory-sales ratio in which the first order time lag is taken into account, is used here. The time constant of this time lag is assumed to be 3 months. The variation of each inventory of paper or waste paper (x., i=3,6,9,12) is tae difference between the actual inventory (y., i=S,4,2l) and its standard level. 1 Eq. (28): The planned monthly paper production (x ) is given by subtracting the variation of 13 the inventory due to the inventory adjustment from the product of the average planned monthly ~'aper production (x /l2) and the seasonal 23 index of paper productlon (PI). Eventually, this value becomes equal to the amount of paper production at the manufacturer (zl). Eq._(29): The utilization ratio of waste paper for paper and board (x 4) is obtained by dividing the. sum of the two products by the annual demand for all kinds of paper. The first product is obtained by multiplying the annual demand for paper by the utilization ratio of waste paper for paper production (g5)' and the second is the annual de~and for boara multiplied by the utilization ratio of waste paper for board production (g6)· Eq. (30): The utilization ratio of virgin pulp for paper and board (x ) is obtained from Eqs. (6), (12), (13) and e~e condition that zl=x 13 · Eq. (31): Estimated amount of purchased waste paper by the manufacturer (x ) is obtained by soomthing the past value of eRe amount of consumption of waste paper z (t-i) with an exponential type weighting flctor. Consequently, this value is equal to the average value of the waste paper consumption at the manufacturer (Xl). Eq. (32) : '~Lnnual domestic consumption of paper and board (x ) is the sum of the annual 17
281
Waste Paper Recycling System in Japan domestic consumption of paper (x ) and board 21 (x ). 22
[a] The seasonal index of paper production (p ) and the selsonal index Table B Values of PI and P2
Eq. (33): Annual paper export (x )is the net balance defined by the differen~~ between the amount of export and that of import. This value is calculated from Eq. (3S) by using the net paper export ratio k (=x /x ). lS 23 l
(1976-1977)
of paper consumption (P2) are given by the monthly values. The
Eq. (34): The price index of waste paper (x ) I9 is the ratio of the waste paper price trena (g ) with respect to the price in 1970. (The av~rage price of waste paper is ¥16)
PI
, i.Month
!
I
I
1 2
Eqs. (36) (37): Domestic demands of paper and board are both approximated by a linear function of the actual gross national expenditure (g ) and the actual private plant and equipme~t investment (g2).
2
90.8 92.2 100.8 99.9 100.8 101.5 102.0 100.4 103.3 104.8 102.2 101.4
values of PI 4 3 and p from 1965 to 1973 5 are constant. i 6 Taking into I 7 consideration 8 the influence 9 of the oil 10 crisis in 1974, 11 different 12 values are used, for 1974 and 1975. After1975, the constant values are used again, as shown in Table B. I
Eq. (35): An auxiliary variable of the pri~e of waste paper (x ) is defined by a ratio of the 2 price index of 8aste paper (x ) and the wholesale price index trend (g ). 11his variable . .ln d ex 0 f means the actual trend of 3 the prlce paper.
P
[b] p. (i=3-S) are regression coefficients. The r§gression analysis is performed in order to correlate g and g with the real data of the domestic c~nsumPtfons of paper and board. By using the regression coefficient obtained, annual demands for paper and for board are estimated. The regression coefficients are obtained as follows; p =566,OS, P =1415,2, P5=575.S5, R~=0.9922 34 2 P6= 253,76, P7=2469.2S, PS=409.92, R =0.9S16
Eq. (3S): The planned annual paper production (x ) is the sum of the annual paper demand 23 (x ) and the annual paper export (xIS)· 17 APPENDIX 3
3-1 Exogenous variables Table A Given Data Exogenous variables are set up as given r r ! conditions. The _Y--=::r_ I gl g2 I actual gross na~ r 1968 '5.749 1.0218i tional expenditure 1969 6.365 1.23781 trend (gl) and the 1970 7.061 1.4195 actual private 1 i 1971 7.583 1.4835 plant and equipi 1972 8.274 1.5670 ment investment I 1973 9.087 1.8566 trend (g2) are i 1974 8.973 1.6545 given by the value i 1975 9.197 1.4399 per annum, and I i 1976 9.740 1.4893 their values are 11977 10.248 1.5294 given in Table A. 13 Here "actual" means (10 yen/year) that the price increase from 1970 has been taken into account in the values.
Based on these values, x. (i=17, IS, 21,23) are estimated as shown in TaBle C.
j
r
1
I
The wholesale price index trend (g3) and the waste paper price index (g ) are glven as 4 monthly values. The price 0f corrugated card board, which is the most utilized among all of the kinds of waste paper, is taken as a representative value of the waste paper price. The utilization ratio of waste paper for paper and board (x ) calculated from the utilization ratio o!4waste paper for paper (g5) and the one for board (g ), is gradually increas. 6 lng up to 36-42% over a period of 10 years, for the period of which the simulation calculation in performed.
3-2 Parameters
Table C Comparison of the Estimated Values and the Real Data Year
I I
Estimated X
Real data of x
17
1968 i---9668 1969: 11012 1970 12289 1971 12965 1972 13856 1973 15648 1974 14769 1975 14119 1976 ' 14756 1977 15328
9957 11310 12973 12907 13638 15975 15646 13600 15394 15702
I
(10
,
l 3
If'
17
ton)
[c] P9' PI : The coefficient in relation to recovery rate (sI) and the auxiliary variable on the price of waste paper (x ) given by 20 sI (t) = P9 + PIOx 20
t~e estima~ed
are obtained by the regression analysis of the annual real data. The relationship between the price of waste paper and the estimated recovery rate is very complex due to the influences of the oil crisis of 1974, the active campaign for energy and resource saving since then, and the movement to collect waste paper previously brought from many places to one central place as opposed to house by house
T. Takamatsu et al.
282
collection. The regression calculation was therefore perfo:r-med independently in the following two periods. (i) Jan.l968-Dec.1974 (ii) Jan.1975-Dec.1977 [d] Pll' P12: The amount of consumption of waste paper and pulp is represented by a linear function of the amount of production of paper and board. The yield rate is calculated from the real data ranging over 10 years. The average values of p and p a r e obtained as follows, 11 12 Pll = 0.9029,
=
P12
0.9792
re] P13' ~14: The time constants of P13 and P14 are flxed as
=
P13
1,
P14 = 2
.
When P13=P14' z31 (t)=z (t) is obtained from the comparlson of EQs.i7)2 and (9). [f] 'r. (i=S, 4,3,2): Th(~ variables are all time eonstants. They are set as T
=
T.
1
=
3
[g] k : By taking the average of the past 10 l years, k is obtained as l k = 0.024 l rh] k. (i=2,3,4,5): By taking into account the otl crisis in 1974, each inventory-sales ratio is obtained as the following two different values before Feb. 1974 and after March 1974 by calculating the average values in each period. k k k S 2 3 4 0.47 0.34 0.25 0.67 k
period ~an.1968-Fab.1974
k.
10
Mar.1974-Dec.1977 kif 0.8
0.98
0.44 0.3
The actual inventory-sales ratio (k. ) is presumed to have the first order tiffi~ lag with respect to the step change of k ..
NOMENCLATURE A~-1PCM
Average Value of Waste Paper Consumption at the manufacturer SF?IM Standard Level of Waste Paper Inventory at the Manufac~urer VIWPM Variation of Inventory of Waste paper at the Manufacturer AWPPM Average Value of Waste Paper Purchased at the Manufacturer SWPIR Standard Level of Waste Paper Inventory VIWPR Variation of Inventory of Waste Paper at the Recovery Trader APSW Average Value of Paper Shipment from the Wholesaler SPIW Standard Level of Paper Inventory at the Wholesaler VIPW Variation of Inventory of Paper at the Wholesaler x APSM Average Value of Paper Shipment lO from the Manufacturer Standard Level of Paper Inventory xII SPIM at the Manufacturer VIPM x Variation of Inventory of Paper at 12 the Manufacturer x PMPPM Planned Monthly Paper Production 13 at the Manufacturer x URWPPB Utilization Ratio of Waste Paper 14 for Paper and Board Production XIS URVPP Utilization Ratio of Virgin Pulp for Paper and Board Production x EPWPM Estimated Purchasing Amount of 16 Waste Paper at the Manufacturer APDD x Annual Paper Demand in the Domestic 17 Market x APE Annual Paper Export l8 x PIWP Price Index of Waste Paper 19 x AVWPP Auxiliary Variable on Waste Paper 20 Price x ADCP Annual Domestic Consumption of 2l Paper x ADCB Annual Domestic Consumption of 22 Board x PAPPM Planned Annual Paper Production at 23 the Manufacturer
1
i.e. k i3
k.
10
+ (k. -k. ) {l-exp(-~)} lf 10 T.
IPM
1
where t is 1 for Mar. 1974.
IPW
[i] k : This is the coefficient of
inv0ntory k =1 means that the inventory adjustment i~ performed completely. In the simulation, it is assumed that k =0.7. 6
PSH IWPR
[j] k : During the 10 years from 1968 to 1977, the p~per production increased about 1.6 times. By taking into account the time constant of the delay (P14)' k is obtained from the relationship (k ) 120/p7 =1.6 as follows, 7 14 k = 1.11786 7 where P14=2.
PPM
adjus~ment in the recovery trader.
IWPM
PSM PCH PDH WPCRI WPPM WPCM
Inventory of Paper at the Manufacturer Inventory of Paper at the Wholesalers Paper Stock in Households Inventory of Waste Paper at the Recovery Trader Inventory of Waste Paper at the Manufacturer Amount of Paper Production at the Manufacturer Amount of Paper Shipment from the Manufacturer Amount of Paper Consumed by Households Amount of Paper Discharged from Households Amount of Waste Paper Collected by Recovery Traders Amount of Waste Paper Purchased by Manufacturer Amount of Waste Paper Consumption at the M~nufacturer
Waste Paper Recycling System 1n Japan Zs
VPCM
Zg
WPDR
zlO
NPE
Amount of Virgin Pulp Consumption at the Manufacturer Amount of Waste Paper Disposed of as Refuse Amount of Net Paper Export Actual Gross National Expenditure Actual Private Plant and Equipment Investment Wholesale Price Index Actual Waste Paper Price Utilization Ratio of Waste Paper for Paper Production Utilization Ratio of Waste Paper for Board Production
gl g2
AGNE APEI
g3 g4 gs
WPI AWPP URWPP
g6
URWPB
k l k 2
Net Paper Export Ratio Inventory-sales Ratio of Paper at the Hanufacturer ISRPW Inventory-sales Ratio of Paper at the Wholesaler ISRWPR Inventory-sales Ratio of Waste Paper at the Recovery Trader ISRWPM Inventory-sales Ratio of Waste Paper at the Manufacturer Coefficient of Inventory AdjustCIAR ment at the Recovery Traders ACPSM Adjustment Coefficient of Paper Shipment from the Manufacturer
k k
3 4
k k
S 6
k
7
NPER ISRPM
P
SIPP Seasonal Index of Paper Production .SIPC Seasonal Index of Paper Consumption p. (1=3-10) Regression Coefficients p1 YFWP Yielc Factor of Waste Paper P~2l YFUP Yield Factor of Virgin Pulp p. (j=13,14) Time Constants
p~
]
RR
S
Recovery Rate
T. (i=2-S)
Time Constants
t T
month year
1
283
DYNAMIC SIMULATION OF WASTE PAPER RECYCLING SYSTEM IN JAPAN T. Takamatsu*, I. Hashimoto*, F. Yoshida** and H. Ohno*** *Department of Chemical Engineering, Kyoto University, Kyoto, Japan **Osaka Prefectural Industrial Research Institute, Osaka, Japan ***Department of Chemical EngineenOng, Kobe University, Kobe, Japan
Abstract. The ainl of this paper is to make clear the prospects and policies for waste paper recycling and utilization in Japan. The waste paper recycling system is composed of ~any processes relevant to the production, distribution and consumption of paper and boa~d, and the generation, recovery and disposal of waste paper. A dynamic model of the national level is developed fi~st so as to <:;i:nulatp. the behaviour of the whole system and to clarify the real issue in this system. Then, the dynamic simulation on the future trend of waste paper recycling and utilization is carried out and at the same time the policy that will be the most promising in order to promote the waste paper recycling is made clear. The quantitative assessment of several practicalmeasuresfor the reconciliation of the problem of future waste paper supply and requirement is performed. As a result, it is conclu0ed that the most effective and desirable countermeasure for overcoming the anticipated shortage of waste paper supply in the future is to increase the recovery rate of waste paper up to 60% by revising and consolidating the collection sector. Keywords.
Waste paper recycling; modelling; system analysis; simulation
INTRODUCTION
the waste paper recovery and utilization, and at the same time to made clear what policy will be most promising in order to promote waste paper recycling.
In recent years, the recycle utilization of resources has been of great importance as an effective measure for the solution of energy, resources and environmental pollution problems. Within this context, the recovery and utilization of waste paper l have tended to
A rough material balance in the processes of the paper production, distribution, waste paper recovery and disposal in Japan is shown in Fig. 1. The paper and pulp industry in
increase in developed countries. Many studies have been published which have tried to explain why the recovery of waste paper and its utilization have increased and why and by how much it is expected to increase in the future. (OECD report, 1976; Glassery and Gupta, 1975; Clifford and Co-workers, 1978; Tunner, Grace and Pearce, 1978) The aim of the research reported here is to make clear the prospects and policies for waste paper recycling system in Japan. For this purpose, a dynamic model of the national level in Japan is first developed. This includes all the processes relevant to the production, distribution and consumption of paper and board, and the generation, recovery and disposal of waste paper. By using the developed model, the real issue in the promotion of waste paper recycling and utilization is clarified. By changing the assumptions about policy development which mayor may not be realized, many simulation calculations are performed to forecast the future trends of
Domestic Consumption (16.3)
Exports
rconsumer
.
!
'
(0.5)
IWho
th
Refuse ,(9.4) Waste Paper (6.9)
1e-;;l;;J
--f I
Imports
Waste Paper (6.9)
(0.3)
Domestic (9.1)
1
Fig. 1
Throughout this paper, the term waste paper also includes waste board. 271
Paper flow in Japan (million ton;1978)
T. Takamatsu et al.
272
Japan has grown very rapidly along with economic development since the 1960's. The actual production o~ paper and board exceeded 16 million tons, in 1978. The 'actual production of pulp is about 10 million tons, and the annual consumption of paper and board per capita is 141.6 kg. Almost all paper and board produced is domestically consumed. About 40% of the amount consummed is recovered. Of the remaining unrecovered 60%, about 10% is stored or utilized as a permanent stock such as books in libraries and building paper in construction etc. About 30% is used for some special type of paper and board such as paraffincoated paper for water-proofing etc. which is not suitable for recycled use and thus eventually becomes refuse. About 20% is also disposed of as refuse, even though it is still reusable. Recovered waste paper is a valuable raw material for the paper and board industry and is completely utilized for domestic demand. The importance of recovered waste paper as a raw material is growing due to the souring prices of both virgin pulp and imported pulp wood. (44% of the total necessary pulp wood came from imports, in 1979).
can be simply expressed as shown in Fig.3. From this figure, it is easily understood how and from what variables the major state variables are determined. As for the state variables Yl [Inventory of paper at the manufacturer] , y 2 [Inventory of paper at tre wholesaler] , Y4 [Inventory of waste paper at the recovery trader] and y [Inven:='C'ry of waste paper at the manufactur~r] in the differential equations of the model, the follo'.ving relation commonly holds; [Change of inventory] [Estimated s~les amount] + [Desirable month-end inventory] - [Present inventory] - [Actual sales amount] where for Y4 an~ yS' the ad~itional term related to the lnventory adJustment must be added to the right hand side of the equation. The differential equation with respect to y 3 [Paper stock in households] shows that the time derivative of the paper stock in consumers is equal to the difference of z [Amount of paper consummed by householJs] and z4 [Amount of paper discharged from househblds]. The differential equations of z4 shows that z has a time lag of the first . 4 order wlth respect to z3.
MODEL STRUCTURE The starting point of the analysis here is the simple material flow model, Fig.l. The recovery of waste paper is strongly influenced by business trends. Therefore, it is first necessary to examine the monthly changes of both the economic factors relating to waste paper recovery - (that is, the price of waste paper, gross national expenditure, private investment in plant and equipment, etc.), and the quantitative factors of paper, board and waste paper -(that is, amount of production, utilization rate, recovery rate and amount of stocks etc.) In order to build a mathematical model of such a large scale system as the waste paper recycling system at the national level, it is necessary to analyse the information available at present so as to make the relationship amo~g the variables clear. Then, a tentative model is built, and it is examined as to whether or not the model outputs can sufficiently explain the behaviour of the real data. If agreement between the model outputs and the real data can not be obtained, the tentative model is revised by changing the number and the kind of state variab lc;s so a:=: to decrease the discrepancy between the model outputs and the real data. By repeating the procedure explained above, the most updated model for the waste pC.per recycling system in Japan is obtained, as shown in Fig.2. The detailed mathematical expression of this model is given in Appendix 1, and the ~eaning of each equation is explained in Appendix 2. By eliminating auxiliary state variables xi (i=1-23) in the mathematical expression of the model, therathematical structure of the model
From this contracted mathematical model shown in Fig.3, the values of each state variable can be consecutively determined by perfoming the calculation according to the steps di-rected by the arrows in the figure.
SIMULATION Based on the dynamic model developed in the previous section, the calculation for the simulation is performed for the period of the past ten years (from 1968 through to 1977). The calculated values from the model are compared to the available real data. It is later shown that they agree quite well with each other. Judging from this good agreement, it may safely be said that the calculated values of the state variabl-:s the real da ta of which are not available could be a fairly good estimation of the past c}:angcs of these variables. The values of the parameters and external inputs (exogenous variables) used in the simulation calculation are shown in Appendix 3. The forecasting of the future trend ranging over from the present up to 2000 A.D. is performed by earring out the simulation for the several cases where the asslli~ptions on the future estimation of many economic and social factors are changed. The annual increases in t~e exogenous variables 9 [Actual gross national expenditure] and g 1 [Actual private plant and equipment inves€mentJ arc~ estimated as sho'I',rn in Table 1, based on the annual economic gro~th rate forecasted by the Japanese government and the economists.
Waste Paper Recycling System in Japan
rPM
Y,
____~ (
/ SIPP PJ
)
Fig. 2 Waste paper recycling model I.A.A.-T
273
T. Takamatsu et al.
274
external variables
g.1 (T) (i=l,Z) gj (t) (j=3,4,S,6)
~ ZlO=[k 1 /(1-k 1 )f 1 (gl,gZ)
- Y3=Z3(t)-Z4(t)
Z4=(Z3(t)-Z4)/P12 ~ ~Z3=PZfl(gl,gZ)/lOO
---
zZ=aZ(t)+bZ(t)-YZ(t)
---
+[kl/(1-kl)]fl(gl,g2)~
ilzl=a1(t)+b1(t)-Yl(t)J ~
z7=zl(t)f Z(gl,gZ",gS,g6)
~ z 8 =z1 (t) f 3 (g 1 ' g2 ' g 5' g6) zS=a 4 (t)+k 6 (b 4 (t)-Y4(t)) z 9 =z 4 (t)-z 5 (t)',--z6=a 5 et) +b 5 (t) - Y5 ( t ) +(1-k6)(Y4(t)~b4(t))
1-
~
YZ=a Z (t)+b 2 (t)-Z3(t)-yZ where a Z(t)=k 7 z 31 (t), b Z(t)=k 33 F1 (z3)' and z31=(z3(t)-z31)/P14
Yl=al(t)+bl(~)-Z2(t)-Yl
where al(~)-[Plfl(gl,g2)/lOO]/(1-kl)' and b 1 (t)-k Z3 F1 (zZ)
Y4=a 4 (t)+b 4 (t)-z6(t)-Y4+(I-k 6 )(Y4- b 4(t)) Ys=a S (t)+b S (t)-z7(t)-YS+(I-k 6 )(Y4- b 4(t)) where a s (t)=F 1 (z7)' b S (t)=k S3 F1 (z7) a 4 (t)=z4(t)f 4 (g3,g4) and b 4 (t)=k 43 F1 (z6)
--
I
w here ~ 1 (g 1 '
g2) = [(p 3+P6) g1+ (p 4+p 7) gZ+ (p 5+PS) ] / 12 , fZ(gl,g2,gS,g6)=[gS(P3g1+P4gZ+PS)+g6(P6g1+P7gZ+PS)]/IZf 1 , f 3 (gl,gZ,gS,g6)=(1-P 11 f 1 )/PIZ' f4(g3~g4)=P9+(PIO/IOO)(g4/gS)/16, (Xl
Fl(Zj)=i~1(S/6)
ir-l
. Zj(t-l)/6
Fig. 3 Computing procedure for the equations of the model The values between Table 1 Estimated Values 1979 and 1989 are esof gl and g2 timated by taking into account the yearly g2 gl Year change in business trends. The values 1.708 10.81 1978 after 1990 are esti1.911 11.84 1980 mated under the as2.134 13.03 1982 sumption that the eco2.402 14.54 1984 nomic growth rate is 2.620 15.84 1986 constant. 3.002 17.78 1988 3.386 19.58 1990 As for the parameters, 3.733 21.38 1992 4.115 (1) PI and P2 [Sea23.35 1994 sonal indices of paper 4.537 25.50 1996 production and paper 5.002 27.84 1998 consumption,respec30.41 ! 5.515 2000 tively] are fixed as 13 (10 yen/year) p = p = 100. Seas5nal ~erturbation is not taken into account. (2) p. (i=3-l4) [Regression coefficients], kj (j~2-5) [Inventory-sales ratios], k [Coefficient of inventory adjustment a~ the recovery trader] are assumed to be the same as in 1977. (3) Since the paper production is estimated to become 2.87 times the present during the 22 years from 1978 through to 2000, k [The 7
adjustment coefficient of estimated paper shipment from the manufacturer] is calculated as follows, i.e.
(k )264/ P 4 = 2.87, 7
k
7
= 1.00802
The following assumptions are set out in the simulation of three cases. Case I (1) The upper liP.lit of 1:he recvvery rate of waste paper (S)2 is 50%, i. e.
S ~ 50 (%) •
(2) The actual paper exp'"Jrt ratio (k ) is l kept at the present level, i.e.
k
= 0.024. l (3) The actual waste paper price (g4) changes in the following fo~r different ways.
-----------2 S [recovery rate of waste paper] is defined by the ratio of (z4/z5)XlOO.
Waste Paper Recycling System in Japan 3
Letting the time origin (t =0) be January, 1978, (No.l) g4 is constant after 1979. i.e.
is imported when the inventory-sales ratio (= Y4/z6) becomes less than 0.15 [month]
i.e.
g4 = 14.13 + 0.05887t
(No.3) g4 becomes 2 times during 10 years.
i.e.
g4 = 14.13 + 0.1177t
(NO.4) g4 becomes 3 times during 10 years. i.e.
g4 = 14.13 + 0.2355t
(4) There is no technological upper limit on the utilization ratio of waste paper. The utilization ratio of waste paper for paper p~oduction (g5) increases by 0.008% per annum. g
5
= 0.175 + 6.667 x 10-4 t
The utilization ratio of waste paper for board production (g6) increases by 0.0052 per annum. g
i.e.
6
= 0.731 + 4.333 x 10-4 t
Case ]I (1) The net paper export ratio (k ): l
(2) The actual waste paper price (g4): g4 becomes 2 times during 20 years. (3) The waste paper recovery rate (S) changes in the following rang~s: (No.2) S:S 50 (%) (1978-2000) (No.5)
(NO.6)
S S
:s 50(%) (1978-1984), ~
55(%)
(1985-2000),
S S
~
50(%) 55 (%)
(1978-1984), (1985-1990),
~
a = 0
(No.7)
a
(No. 8)
a = 5.0
(No.9)
a = 7.5
=
2.5
Case nI (1) The net paper eXFort ratio (k ) : l k = 0.0~4 l (2) The actual waste paper price (g ): 9 becomes . 4. 4 2 t~mes dur~ng 20 years. (3) The upper limit on Lho waste paper recovery rate (S) is kept at 50%.
RESULT AND DISCUSSION
4-1 Confirmation of the model by comparison with the real data The comparison of the calculated zl [Amount of paper production], z6 [Amount of waste paper purchased by the manufacturer] and Y5 [Inventory of waste paper in the manufacturer] ;"Ji th the actual data is shown in Fig.4. From these results of the simulation, it is safely con-
1 6 ,..---------------------------_~ ·
1 .4 1 .2 1 .0
0.6 0.4 0.2
o
1968
(4) As for the import policy of waste paper, the following cases are considered. That is, a % of the estimated purchasing amount of waste paper in the manufacturer t
1970
Fig. 4 Comparison
S ~ 50
3 rrhe unit of time
In Case I, the effect of the waste paper price trend on the waste paper supply trend which is anticipated to increase according to the rapidly rising demand for paper under the assumption that the upper limit of the recovery rate is fixed at 50%, is made clear. In Case ]I , the effect on the waste paper supply trend of changing the upper limit of the waste paper recovery rate is analysed. In Case nI, whether or not waste paper import will be effective as a measure for making up for the shortage of the waste paper supply which is anticipated to occur in the future is examined.
0.8
and it increases by 5% for 10 years after 1990.
i. e.
(No.2) g4 = 14.13 becomes 2 times during 20 years.
(No.2) g4
i.e.
275
is measured in months
1972
Year
1974
1976
1978
of calculated values and real data
eluded that the model developed here is confident.
4-2 The calculated values of the variables the real data of which t7!''? "ncn-exis tant An advantage of utilizing this kind of mathematical model is that it is possible to estimate the variables the real data of which are
T. Takamatsu et al.
276
not available, by using the calculated values from the model. As an example, the es tirnated values of z4 [Amount of paper discharged from households], z5 [Amount of waste paper collected by recovery trader], z [Amount of waste paper disposed of as refuse], y [paper stock in households] and y [Inventor~ of waste paper at recovery tr~derJ are shown in Fig.5. z4 and Y3 represent the same tendency
x10 6 ton
following measures are considered in order to further promote the recovery of waste paper: (i) To increase the collection of waste paper by steadily rising the price of waste paper; (ii) To increase the' recovery rate by consolidating the structure of the waste paper collection system; (iii) To compensate for the domestic shortage of waste raper by importing it from abroad.
1.8 ...- - - - - - - - - - - - - - - - - - - - - - - - - - - -.... 1 .6 1 .4
In order lo evaluate the availabili t:/ of such neasures m('llLj\~lll:(l '.i;)()Vi',
and to assess the en1.2 vironmental impacts which would result 1 .0 from the execution of these measures, it is 0.8 indispensable to quantitatively forecast 0.6 the future demand for the was tl~ paper by using such a dynamic 0.4 model as developed here and to carefully 0.2 examine the forecasted results. In this section, the results of 1968 1970 1972 1974 1976 1978 the many simulations Year used to forecast the Fig. 5 Simulation of Yl , Y , Y , z4: z5' and z9 3 4 future trend of waste paper utilization at the manufacturer dre shown and changes of the amount of waste in thier changes. Since z has the first order time lag with respec~ to z [Amount of paper collected, the dOInl·stic inventory of waste v~per and the amount of waste paper paper consumed by households], y3 shows a disposed of as refuse are estimated assuming larger increasing tendency when 60mpared to that these three measures are implemented in z4. [See Eqs. (3) and (8) in Appendix 1] Both the future. z and y increased yearly up to 1973 along w~th the 3 rapid incrase of z . After the oil In Fig.6 the simulation results of Case I crisis of 1973, however, th~y once decr<~Cls('d where only the price of waste paper is steadand then became almost unchanged. At present, they have shown a gradually increasing tendily increased by limiting the recovery rate within 50% are shown. From this figure, it ency. Until 1975, z5 also shows the same is clear what will Jlclppen in trJ.C supply of trend. as z4 since the recovery rate of waste and the demand for waste Lld per, and how the paper rema1ned almost unchanged, and conseamount of waste L!dper disposed of as refuse quently z9 i~crease~ annually. After 1976~ will change. Thi~; figure shows that the zr. has been 1ncreas1ng and, therefore, z 1S supply of waste I 'Cl per cannot catch up with c6nstant or sliCjhtlYdecreasing. f,-ou
o
Waste Paper Recycling System in Japan Fig.8 shnws the results of Case TII where the waste paper is imported from abroad in or·· der to compensate for the domestic shortage. As shown in this figure, the import of waste paper can delay the time when the shortage of the supply will start to occur, but it results in large fluctuations in the inventory of waste paper. Moreover, the amount of waste paper disposed of as refuse is very large as in Case I, which results in some environmental pollution problE:'Tls. From these viewpoints it is not good to depend on the import of waste paper in order to prevent shortage in the supply of wast.e paper. Judging from the results mentioned above, it can be easily understood that the most effective and desirable countermeasure to overcome the anticipated shortage of waste paper supply in the future is to increase the recovery rate of waste paper up to 60% by consolidating the collection system.
277
1.8 1 .6
1 .4 1 .2
o
1978
185
180
195
Year
Fig. 6 Forecasting of Y4'
2
6
, and
2
9
2000
in case I
x10 6 ton 2.0 1.8 -
z6(No.6)
hO. ?-::;:7\
1\./\
1.6 1.4
Zg(No.6)
1.2 .
-
1.0 0.8 0.6
~O.5) \
\\
\
\\
0.2 1978
~\
~'
2)(Y4 \(No.2)
0.4 .
0
6)
180
185
i
190
Fig. 7 Forecasting of Y4'
CONCLUSION In this report, the waste paper recycling system is taken up as a concrete example of a resource recycling system. A dynamic model was developed and, based on this model, the quantitative assessment of several measures for preventing the anticipated shortage of the supply of waste paper in the future is performed. The basic structure of the model developed is based on the material balance shown in Fig.l. By taking into account many controlling and
2
195
Year 6 , and
2
9
2000
in case 11
influencing factors and adding th~m to the basic model as information flows, the whole model structure was gradually developed, and finally obtained as shown in Fig.2. The fundamental structure which is obtained by rearranging the model equations according to the direction of the information flows, is shown in Fig.3. As is clear from this figure, the procedure for the simulation calculation proceeds from the exogenous variables related to economic factors to the opposite direction of the material flow. The prameters included in the model are
T. Takamatsu et al.
278
estimated from the real data, and the confidence of the model is confirmed by comparing the calculated values from the model with the real dat~ ranging over 10 ye~rs, (Fig.4. ) The model is first utilized for predicting the change of state variables the real data of which are not available. (Fig.S) Then, it is used to quantitatively assess three measures for preventing the anticipated shortage of the supply of waste paper in the future.
xl0 6 ton
2.0r-----------------------.. . 1 .8 1 .6 1 .4
1.2 1.0
0.8 0.6 0.4 .
0.2 185
190
195
Year
2000
Fig. 8 Forecasting of Y4' z6, and z9 in case III
From the results of the simulation (Fig.6-8), it was clarified that the increase in the recovery rate of Case TI is the most desirable among these three measures. The system approach based on the quanti ta ti vc model as shown in this paper, could be very helpful in evaluating and assessing many different measures intorduced to resolve issues not only in waste paper recycling systems, but also in many other large, complex, resources recycling systems.
APPENDIX 1 MATHEMATICAL MODEL (a) Equations related to Yi (i=l-S) dY (t) l
zl (t)
z2(t)
(1)
z2(t)
z3(t) - zlO(t)
(2)
z3(t)
z4(t)
(3)
zS(t)
z6(t)
(4)
~ = z6(t)
- z7(t)
(5)
~=
dY2(t) = dt dY3(t) _ ~-
ACKNOWLEDGEMENT
dY4(t)
The authors wish to acknowledge Mr. M. Arakawa for his valuable assistance.
~-
dYS(t) REFERENCES OECD Report (1976). "Prospects and Policies for Waste Paper Recycling in the Pulp and of Paper Industry". Glassery, C.R., an~ V.K. Gupta (196S). A lipear programming analysis of paper recycling. Studies in Management Science and Systems Vol.2. North-Holland. Chap.13, pp.273-292. Clifford, J.S., M.A. Laughton, T.S. McRoberts and P.V. Slee (1978). LP modelling in the paper industry as an aid to recycling decisions. Conservation & Recycling, ~ 97-109. Turner, R.K., R. Grace, and D.W. Pearce (1978). The economics of waste ~zper recycling. Resource Conservation, Social and Economic Dimensions of Recycling, Langaman Group Limited, London, Chap.16, pp.296343.
(b)
Equation related to z. (i=l-lO) l. zl (t) Pllz7(t) + P12 z 8(t) k z
z2(t)
7 31
(t)
x
9
(6)
(t) + ZlO(t)
w~ere z31 has the first order time lag Wl.th respect to z3'
i.e.
dZ P14
z3(t) =
1
31 dt
12
(t) + z31 (t) = z3(t) 1
(8)
x 17 (T)100 P2(t)
dz (t) 4 P13~ + z4(t) = z3(t) z5 (t)
z 4 (t.' {P9+P lOx
20
(9)
(t)} - k x (t) (10) 6 6
(12)
Waste Paper Recycling System in Japan X (t)X (t) 13 15
(13) x
14
(t)
1
x
(14)
z4 (t) - z5 (t)
279
(T) (x
2l
(T) g5 (t) +x
22
(T) g6 (t) }
17 x
(15)
15
(29)
(t)
_l_{l - Pllx14(t)} P12
(t)
-6lI . i-)65 i-I z 7 (t-i)
(T)
x
(30)
oo
(c) Equations related to xi
x
5 i-I
1\00
6L i=1 (6)
(t)
1
1
~z7 (t-l)
x
(i=1~23)
. z7(t-~)
x
+ 5x (t-l)} l
(16)
y 5 (t)
x
-
2
(~)i-lz (t-i)
~{z
(t-l) + Sx (t-l)} 6 4
(19)
(t)x (t) 4
(20) 1
6 :L=l 6
6
xs(t) w~ere
43
x x x
~I~
k
x
(IS)
(t)
17
19 20 2l 22 23
~=
(t)
(T) + x (T) 22 21 k l l-k x 17 (T) 1 1 1 16 100 g4(t)
(t)
~ x
XlS(T) x
where k (t) has the first order time lag S3 with respect to k (t). 5 i.e. dk 53 (17)2 T5~ + k 53 = k S
16
1
Xl (t)
(31) (32) (33) (34)
(t)
(35)
(t)
P3 g l (t) + P4 g 2(t) + PS
(36)
(t)
P6 g1 (t) + P7 g 2(t) + Ps
(37)
(t)
x
(38)
g3
17
19
(t) + x
18
(t)
6
APPENDIX 2 MEANING OF EACH EQUATION
(t) has the first order time lag 43 w~th respect to k (t) 4 i.e. dk 43 (20) 2 T4~ + k 43 = k 4 k
(21)
Y4(t) - x (t) 5 5 i-I
1\00
6Li=1 (6)
z3(t-i)
2-.-{z (t-l) + 5x (t-l)} 637
(22) (23)1
(a) Equation of Y i
(i=l-S)
Eqs. (1)-(5): The change of inventory with respect to time is equal to the difference of both amounts of the input and the output. For example, the time derivative of Y [the l inventory of paper at the manufacturer] is equal to the difference between z [Amount of . 1 ] and z2 paper product~on at the manufacturer [Amount of paper shipment from the manufacturer]. Here, y. is an unknown variable the value of which his to be calculated from the observed or estimated values of the material flow z. (t) (j=1-7,10) J
(b) Equation of zi (i=l-lO) where k (t) has the first order time lag with re~~ect to k (t), 3 i.e. dk 33 (23)2 T3~ + k 33 = k 3 (24)
x (t) = Y2(t) - xS(t) 9 1\00
xlO(t) =
5 i-I
6 Li=1 (6)
i
z2(t-i)
z2{ (t-ll + 5x
10
(t-ll}
(25) (26) 1
w~ere k (t) has the first order time lag 23 w1th respect to k (t). 2 i.e. dk T 23 k k (26) 2 2~ + 23 = 2
Yl (t) - XII (t)
(27)
1 1 100 PI (t)~23(T)
zl (t)
(2S)
Eq. (6): z
[Amount of paper production at the is equal to the sum of the two values which are calculated by multiplying each yield factor Pll and PI by z7 [Amount of waste paper consumption at the manufacturer] and z [Amount of pulp consumption at the manufactu~er], respectively.
manufactu~er]
Eq. (7): z2 [Amount of paper shipment from the manufacturer] is concurrently equal to the amount of paper purchased by the wholesaler. The wholesaler seems to forecast his purchasing amount by analysing the past trend of the amount of paper purchased by COnSlim0r. Here it is assumed that the estimated value of z , z , can be obtained from the differentia13equ~tion which has the first order time lag with respect to z . (The time constant p is assumed to be months.) The estimate~4value z 31 is modified by multiplping lYl a factor k used to compensate for the inade7 quacy in this estimation. The actual amount of paper purchased by the wholesaler (z2) is given by subtructing the variation of Ehe paper stock at the wholesalc)r (x ), due to 9
1
T. Takamatsu et al.
280
the inventory adjustment, from the modified estimated value of z (k z ) and adding the 3 7 31 amount of net paper export (z ). 10 Eq. (8): The amount of paper puchased by consumer (z3) is equal to the value which is obtained by mul tipl y ing t~le seasonal index of paper consumption (p ) by the average paper consumption per montt which is calculated by dividing the annual paper demand in the domestic market (x ) by 12. 17 Eq. (9): The paper purchased by the consumer is disposed of with a certain time lag with respect to the purchasing time. This time lag is assumed to be the first order whose' time constant P13 is onc month. Eq. (10): Zs [Amount of waste paper collected by the recovery trader] is assumed to be determined by adding the term relevant to the inventory adjustment to the product of z [Amount of paper discharged from househoids] and (P9+PlOx20) [Estimated recovery rate]. Where estlmaEed recovery rate is presumed to be a linear function of x [Auxiliary variable on the waste paper prfge]. The capability of the inventory adjustment of the recovery trader seems to be insufficient. Therefore, as a coefficient to express its weakness in adjustment ability, k [Coefficient of inventory adjustment in re80very trader] is introduced, and this coefficient is multiplied to x [Variation of the inventory of 6 waste paper at the recovery trader] . Eq. (11): z6 [Amount of waste paper purchased by the manufacturer] is determined by subtracting x [Variation of inventory of waste 3 paper at tne manufacturer] from x [Estimat' 16 by the ea~ pu~h aSlng amount 0 f waste paper manufacturer] and adding the supplementary amount of waste paper which is kept in stock to compensate for the weakness in the inventory adjustment ability of the recovery trader. Eqs. (12) (13): z7 and z [amounts of utilization of waste paper an~ virgin pulp, respectively] is determined by multiplying C3.ch utilization ratio (x ) or (x ) ~y x LS 13 14 [Planned monthly paper ~roauctlon]. Eq. (14): z9 [Amount of waste paper disposed of as refuse] is the amount of uncollected [ Amount of paper discharged frem house2 4 hold] . Eq. (IS): Since z [Monthly net paper export] . 10 1S very small compared to the paper production, zlO is assumed to be constant thoughtout a year and to be (1/12)xx [Annual pa18 per export]. (c) Equations of x.
1
(i=1-23)
Equations relevant to (x ,x ,x ), (x ,x 'x ), 4 S 6 2 l (x ,x ,x ) an~ (xlO,xll,X12) all have tne 7 8 same mat~ematlcal structure, and they are utilized to calculate the variations of the inventories.
Eq. (16) - (27): Variables x. (i=1.,.3), x. (j=4-6) are relevant to the inventories of waste paper at the manufacturer and at the recovery traders, respectively. x (k=7-9} and x k (e=10-12) are also relevant to the inve5tories of paper at the wholesaler and manufacturer, respectively. The average monthly utilization of paper or waste paper (x., i=1,4,7,lO) is calculated by smoothing the ~ast record in such a way that the older the data is, the smaller is the coefficient weighed by using an exponential type of wighting function. The standard value of each inventory of paper or waste paper (xi' i=2,~), 8,11) is expressed by the product of tne average utilization of paper or waste paper and the average inventorysales ratio of paper or waste paper (k ,k , S 4 k
3
,k ) . 2
When the average inventory-sales ratio changes, its change does not directly cause the variation of the standard level of the inventory, but its influence has a certain time lag. So, the average inventory-sales ratio in which the first order time lag is taken into account, is used here. The time constant of this time lag is assumed to be 3 months. The variation of each inventory of paper or waste paper (x., i=3,6,9,12) is tae difference between the actual inventory (y., i=S,4,2l) and its standard level. 1 Eq. (28): The planned monthly paper production (x ) is given by subtracting the variation of 13 the inventory due to the inventory adjustment from the product of the average planned monthly ~'aper production (x /l2) and the seasonal 23 index of paper productlon (PI). Eventually, this value becomes equal to the amount of paper production at the manufacturer (zl). Eq._(29): The utilization ratio of waste paper for paper and board (x 4) is obtained by dividing the. sum of the two products by the annual demand for all kinds of paper. The first product is obtained by multiplying the annual demand for paper by the utilization ratio of waste paper for paper production (g5)' and the second is the annual de~and for boara multiplied by the utilization ratio of waste paper for board production (g6)· Eq. (30): The utilization ratio of virgin pulp for paper and board (x ) is obtained from Eqs. (6), (12), (13) and e~e condition that zl=x 13 · Eq. (31): Estimated amount of purchased waste paper by the manufacturer (x ) is obtained by soomthing the past value of eRe amount of consumption of waste paper z (t-i) with an exponential type weighting flctor. Consequently, this value is equal to the average value of the waste paper consumption at the manufacturer (Xl). Eq. (32) : '~Lnnual domestic consumption of paper and board (x ) is the sum of the annual 17
281
Waste Paper Recycling System in Japan domestic consumption of paper (x ) and board 21 (x ). 22
[a] The seasonal index of paper production (p ) and the selsonal index Table B Values of PI and P2
Eq. (33): Annual paper export (x )is the net balance defined by the differen~~ between the amount of export and that of import. This value is calculated from Eq. (3S) by using the net paper export ratio k (=x /x ). lS 23 l
(1976-1977)
of paper consumption (P2) are given by the monthly values. The
Eq. (34): The price index of waste paper (x ) I9 is the ratio of the waste paper price trena (g ) with respect to the price in 1970. (The av~rage price of waste paper is ¥16)
PI
, i.Month
!
I
I
1 2
Eqs. (36) (37): Domestic demands of paper and board are both approximated by a linear function of the actual gross national expenditure (g ) and the actual private plant and equipme~t investment (g2).
2
90.8 92.2 100.8 99.9 100.8 101.5 102.0 100.4 103.3 104.8 102.2 101.4
values of PI 4 3 and p from 1965 to 1973 5 are constant. i 6 Taking into I 7 consideration 8 the influence 9 of the oil 10 crisis in 1974, 11 different 12 values are used, for 1974 and 1975. After1975, the constant values are used again, as shown in Table B. I
Eq. (35): An auxiliary variable of the pri~e of waste paper (x ) is defined by a ratio of the 2 price index of 8aste paper (x ) and the wholesale price index trend (g ). 11his variable . .ln d ex 0 f means the actual trend of 3 the prlce paper.
P
[b] p. (i=3-S) are regression coefficients. The r§gression analysis is performed in order to correlate g and g with the real data of the domestic c~nsumPtfons of paper and board. By using the regression coefficient obtained, annual demands for paper and for board are estimated. The regression coefficients are obtained as follows; p =566,OS, P =1415,2, P5=575.S5, R~=0.9922 34 2 P6= 253,76, P7=2469.2S, PS=409.92, R =0.9S16
Eq. (3S): The planned annual paper production (x ) is the sum of the annual paper demand 23 (x ) and the annual paper export (xIS)· 17 APPENDIX 3
3-1 Exogenous variables Table A Given Data Exogenous variables are set up as given r r ! conditions. The _Y--=::r_ I gl g2 I actual gross na~ r 1968 '5.749 1.0218i tional expenditure 1969 6.365 1.23781 trend (gl) and the 1970 7.061 1.4195 actual private 1 i 1971 7.583 1.4835 plant and equipi 1972 8.274 1.5670 ment investment I 1973 9.087 1.8566 trend (g2) are i 1974 8.973 1.6545 given by the value i 1975 9.197 1.4399 per annum, and I i 1976 9.740 1.4893 their values are 11977 10.248 1.5294 given in Table A. 13 Here "actual" means (10 yen/year) that the price increase from 1970 has been taken into account in the values.
Based on these values, x. (i=17, IS, 21,23) are estimated as shown in TaBle C.
j
r
1
I
The wholesale price index trend (g3) and the waste paper price index (g ) are glven as 4 monthly values. The price 0f corrugated card board, which is the most utilized among all of the kinds of waste paper, is taken as a representative value of the waste paper price. The utilization ratio of waste paper for paper and board (x ) calculated from the utilization ratio o!4waste paper for paper (g5) and the one for board (g ), is gradually increas. 6 lng up to 36-42% over a period of 10 years, for the period of which the simulation calculation in performed.
3-2 Parameters
Table C Comparison of the Estimated Values and the Real Data Year
I I
Estimated X
Real data of x
17
1968 i---9668 1969: 11012 1970 12289 1971 12965 1972 13856 1973 15648 1974 14769 1975 14119 1976 ' 14756 1977 15328
9957 11310 12973 12907 13638 15975 15646 13600 15394 15702
I
(10
,
l 3
If'
17
ton)
[c] P9' PI : The coefficient in relation to recovery rate (sI) and the auxiliary variable on the price of waste paper (x ) given by 20 sI (t) = P9 + PIOx 20
t~e estima~ed
are obtained by the regression analysis of the annual real data. The relationship between the price of waste paper and the estimated recovery rate is very complex due to the influences of the oil crisis of 1974, the active campaign for energy and resource saving since then, and the movement to collect waste paper previously brought from many places to one central place as opposed to house by house
T. Takamatsu et al.
282
collection. The regression calculation was therefore perfo:r-med independently in the following two periods. (i) Jan.l968-Dec.1974 (ii) Jan.1975-Dec.1977 [d] Pll' P12: The amount of consumption of waste paper and pulp is represented by a linear function of the amount of production of paper and board. The yield rate is calculated from the real data ranging over 10 years. The average values of p and p a r e obtained as follows, 11 12 Pll = 0.9029,
=
P12
0.9792
re] P13' ~14: The time constants of P13 and P14 are flxed as
=
P13
1,
P14 = 2
.
When P13=P14' z31 (t)=z (t) is obtained from the comparlson of EQs.i7)2 and (9). [f] 'r. (i=S, 4,3,2): Th(~ variables are all time eonstants. They are set as T
=
T.
1
=
3
[g] k : By taking the average of the past 10 l years, k is obtained as l k = 0.024 l rh] k. (i=2,3,4,5): By taking into account the otl crisis in 1974, each inventory-sales ratio is obtained as the following two different values before Feb. 1974 and after March 1974 by calculating the average values in each period. k k k S 2 3 4 0.47 0.34 0.25 0.67 k
period ~an.1968-Fab.1974
k.
10
Mar.1974-Dec.1977 kif 0.8
0.98
0.44 0.3
The actual inventory-sales ratio (k. ) is presumed to have the first order tiffi~ lag with respect to the step change of k ..
NOMENCLATURE A~-1PCM
Average Value of Waste Paper Consumption at the manufacturer SF?IM Standard Level of Waste Paper Inventory at the Manufac~urer VIWPM Variation of Inventory of Waste paper at the Manufacturer AWPPM Average Value of Waste Paper Purchased at the Manufacturer SWPIR Standard Level of Waste Paper Inventory VIWPR Variation of Inventory of Waste Paper at the Recovery Trader APSW Average Value of Paper Shipment from the Wholesaler SPIW Standard Level of Paper Inventory at the Wholesaler VIPW Variation of Inventory of Paper at the Wholesaler x APSM Average Value of Paper Shipment lO from the Manufacturer Standard Level of Paper Inventory xII SPIM at the Manufacturer VIPM x Variation of Inventory of Paper at 12 the Manufacturer x PMPPM Planned Monthly Paper Production 13 at the Manufacturer x URWPPB Utilization Ratio of Waste Paper 14 for Paper and Board Production XIS URVPP Utilization Ratio of Virgin Pulp for Paper and Board Production x EPWPM Estimated Purchasing Amount of 16 Waste Paper at the Manufacturer APDD x Annual Paper Demand in the Domestic 17 Market x APE Annual Paper Export l8 x PIWP Price Index of Waste Paper 19 x AVWPP Auxiliary Variable on Waste Paper 20 Price x ADCP Annual Domestic Consumption of 2l Paper x ADCB Annual Domestic Consumption of 22 Board x PAPPM Planned Annual Paper Production at 23 the Manufacturer
1
i.e. k i3
k.
10
+ (k. -k. ) {l-exp(-~)} lf 10 T.
IPM
1
where t is 1 for Mar. 1974.
IPW
[i] k : This is the coefficient of
inv0ntory k =1 means that the inventory adjustment i~ performed completely. In the simulation, it is assumed that k =0.7. 6
PSH IWPR
[j] k : During the 10 years from 1968 to 1977, the p~per production increased about 1.6 times. By taking into account the time constant of the delay (P14)' k is obtained from the relationship (k ) 120/p7 =1.6 as follows, 7 14 k = 1.11786 7 where P14=2.
PPM
adjus~ment in the recovery trader.
IWPM
PSM PCH PDH WPCRI WPPM WPCM
Inventory of Paper at the Manufacturer Inventory of Paper at the Wholesalers Paper Stock in Households Inventory of Waste Paper at the Recovery Trader Inventory of Waste Paper at the Manufacturer Amount of Paper Production at the Manufacturer Amount of Paper Shipment from the Manufacturer Amount of Paper Consumed by Households Amount of Paper Discharged from Households Amount of Waste Paper Collected by Recovery Traders Amount of Waste Paper Purchased by Manufacturer Amount of Waste Paper Consumption at the M~nufacturer
Waste Paper Recycling System 1n Japan Zs
VPCM
Zg
WPDR
zlO
NPE
Amount of Virgin Pulp Consumption at the Manufacturer Amount of Waste Paper Disposed of as Refuse Amount of Net Paper Export Actual Gross National Expenditure Actual Private Plant and Equipment Investment Wholesale Price Index Actual Waste Paper Price Utilization Ratio of Waste Paper for Paper Production Utilization Ratio of Waste Paper for Board Production
gl g2
AGNE APEI
g3 g4 gs
WPI AWPP URWPP
g6
URWPB
k l k 2
Net Paper Export Ratio Inventory-sales Ratio of Paper at the Hanufacturer ISRPW Inventory-sales Ratio of Paper at the Wholesaler ISRWPR Inventory-sales Ratio of Waste Paper at the Recovery Trader ISRWPM Inventory-sales Ratio of Waste Paper at the Manufacturer Coefficient of Inventory AdjustCIAR ment at the Recovery Traders ACPSM Adjustment Coefficient of Paper Shipment from the Manufacturer
k k
3 4
k k
S 6
k
7
NPER ISRPM
P
SIPP Seasonal Index of Paper Production .SIPC Seasonal Index of Paper Consumption p. (1=3-10) Regression Coefficients p1 YFWP Yielc Factor of Waste Paper P~2l YFUP Yield Factor of Virgin Pulp p. (j=13,14) Time Constants
p~
]
RR
S
Recovery Rate
T. (i=2-S)
Time Constants
t T
month year
1
283