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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 Ch emical Engineen'n g, Kob e University, Kobe, japan
Abstract. The aim of this paper is to mak e c l ea r the p rosi,e cts and po licies for waste paper r ecyc ling and utilization in Japan . The was t e p a pe r r ecy cling sys t em is composed of wany p roc e sses rel evan t to the p roducti on , dis tribution and cor6umption of pape r and boa~d, and the gene rati o n , recovery and dis posal of wa ste p a pe r. A dy namic model of the national leve l i s devel oped fi:- ;; ': Sf) as to <;i::lU lat c> th e behaviour of th e who le system and to c l arify the real i ssue in this system. Then , the dynamic simul a ti on on th e futur e trend of waste pape r r ecycling and uti l ization i s carri e d o ut and at t he same time th e po l icy that will be th e most p romising in order t o p romot e t he was t e p a pe r r ecyc ling is made clear . The quantitative assessmen t of several p ra c t i ca l measu r es for th e r e conci l iation of t he p ro b lem of futur e waste p a pe r supp l y and requir e men t is pe r formed . As a r es ult , i t i s conc l u ." ed that th e most effective and desirab l e counte rmeasur e for overcoming t he antici pa t e d sho r tag e of waste p a pe r supply in the futur e i s to increase the r ecove ry rat e of waste p a pe r up to 60% by revisin g and consolidating the co ll ec tion sec tor . Ke ywords .
Waste pape r r e cyc l ing; mode l ling ; system anal ys i s ; s i mulation
INTRODUCTION
th e was t e p a pe r r eco v e ry and uti l ization , and at t he same time to made clear wh at po licy wi l l be most p romi si ng in order t o p romote waste pape r r ecycljng,
In r e cent ye ars , the .recycle utilization of r esources has been of g r e at impor tanc e as an effective measure for the solution of energy , re s ources and env i ronmental po llution p rob lems . Within t h is conte xt , the recover y and utilization of wa ste p a pe r l h ave tended to increase in developed countries. Many s tudi es h ave been pub l ished wh ic h h a ve tried to e x p l ain why th e recove ry of was t e p a pe r a nd its util i zation have inc r e as ed and why and by how much it is expected to increase i n t he futur e . (OECD r eport , 1 976 ; Glassery and Gup ta , 1 9 7. 5 ; Cliff o rd and Co - wo rkers , 1 9 78; Tunne r , Grace and Pearce , 1 978 ) The ai m o f th e r ese arch r epo rt e d he r e i s to mak e clea r th e p rospects and p o l icies for waste pape r recyc l ing system in Japan . For this p~ rpose , a dynamic model of the national level in Jap an is first d eve loped . This includes a ll t he p rocesses rel evant to th e p roduction, distribution and consumption of p a pe r a nd board , and th e generation , r eco v e r y and dis posal of waste p a pe r . By using the d e v eloped mode l, the real issue i n t he p romotion of waste paper rec yc ling and utilization i s clar i fi e d . By changing t he assumptions a bo ut po l ic y developme nt wh ic h mayo r way no t be realized, many s imulation calculations are pe rformed to f o recast the future tr e nds of
A rough materia l balance in t he p rocess es of the pape r p rodu ction , distribution, wast e p a pe r r ecove ry and disposal in Jap an is shown in Fig. 1 . The p aper and p ul p industry in
DO"7estic CO>lsu",;,ticm
( 16 . 3)
r.
I~ ."Iefuse (9.4)
c-o-n-s-u-m-e...Jrc.-,~
(6.9)
(0.5)
- ---,-J
IWho1e-s~l ;;
(6 . 9) ( 0 . 3)
I
YManufacturer fJ A A
:':,, ~:: (9 . 1) Fig. 1
1 Throug hout t .n ~. s p a pe r , t h e t e rm waste p a pe r a l so inc l udes was t e b oard . 271
-.J
L ?-.A l::
I '";:; cY'tec!.
0. 3) Paper f l ow in Japan (mil l ion ton; 1 978)
272 Jap an has grown very rapidly along ',:i th eco nomic deve l opment since th e 1 9 6 0 ' s . The ac tual product io n 0 ' pape r and boa rd exc, ",c, ' c 16 mi llion tons , in 1978. The'actual production of pu l p is about 1 0 I ~. i l l i o n tons , and the an nual consumption of pape r and board pe r cap ita is 141. 6 kg. Almost al l pa p er and boa rd p ro duced is domestically consumed. About 40 % of t he amount consummed is r ecovered . Of th e r emain ing unrecovered 60% , about 1 0% i s stored or utilized as a p ermanent stock such as books i n libraries and b uild i ng p a p e r i n construction etc. About 30 % i s us e d for some s p ecial t ype of pape r and board such as pa r affin coated pape r for wate r- p roofi ng etc . which is not suitab l e f o r recycled use and t hus even tual l y becomes refuse . About 20 % is also dis posed of as refuse , even thou ';" it is still r eusab l e . Recovered was t e p a p e r is a valuab l e raw mate rial f or the pape r and boa rd i ndustry and is comp l e t ely utili z ed f o r domestic de mand . The im; 'orta ;-,c C' o f r eco v ered was t e paper as a raw mate ri a l is g r owing due to the sour ing pr i ces of both v irgin p ul p and imported pulp wood . (44 % of the t otal nec e ssary p ul p wood came fr om i mports , i n 19 79) .
can b e simp ly e xp r e ss e d as s ho·.,·!"! i n Fig . 3 . From this figur e , it j~ easil~' und e rstood ~O~ and from what variab l e s the ~ajor state v~ria bles ar e d e t e ~in e d . As for t he state varia bl e s Yl [ Inventory of r a r er at t he ~a n uf ac tu r e r 1 ' Y2 [Inve ntor y of pal)e r at t :-- e ·..:".o l e sa le r ] , Y4 ! I nv e ntor y of wast e pape r at t ~e r e covery trad e r 1 and 1" , [Inve :: ', 'c ' of ·. :a s t e p aper at t'1e manufact~r~r] in the d iff e r e :'tial equations of t he mod e l, the f o 11 0· . :ing relation commonly holds; [Chang e of inven tory ] [Estinat e d s:l l e s a::lount] + [De sira b le month - end inve ntory ] - [Pr e s e n t inve ntory] - [Actual s .l e s amount] where for y and y_, the additio ~a l t e r ::l r e lated to th e inv~ ntory adju s tne nt must b e adde d to the ri ght h and side of t h e eq uation . Th e diff e rential e quation wit h r e s pect to y 3 [Pape r stock in hous e ho l d s ] s hows that t h e time d e rivat i v e of th e p a pe r s tock in con sumers is equa l to t he d'.ff e r e nc e of z [Amount o f pa pe r consumrne d b~' l: o useholJs] and z4 [Amount of p a pe r disc h arged fro n h ous e holds] . The diff e r e ntial equati o ns of z4 shows that z h as a time l a g of t he first . 4 o r der w1th res pect to z3 '
MODEL STRUCTURE The sta rting po int of the anal y sis he r e i s the s i mp l e mate rial flow mode l, Fig.l . The r e covery o f waste paper is strongly influenced by business trend s . Therefore , it i s first nec essary to e xamine the month l y changes of both t he economic factors re l ating to waste pap er recovery - (that i s , the price of waste p a pe r , gross national expend iture , private investmen t in plant and equipment , e t c . ) , and the quanti:·..::tive factors of paper , board and waste pape r - (that i s , amo u nt of produc ti on , utiliz at i on rat e , recovery rat e and amount of stocks e t c . ) In order to build a mathematical model of such a l arge scale system as the wast e p a , n r r _, cling system at the natio nal level , it is nec essary t o analyse the information available at present so as t o mak e the r e lationshi p amo ng the variab l es c l ear. Then, a t e ntat i ve mod e l is bui lt, and it is examin e d as to wheth e r or not t h e model out p ut s can sufficiently e xp lain the behaviour of the real data . If agre e ment between t c',,-, model o utp uts and the r eal data can not b e o b tained, the tentative mod e l is revised by c h anging the numbe r and the i-.i:,d of state va r iab l"~s ,",O::i- to d e cre as e the discre l) anc y between the mod e l out p uts a nd th e r e al data . By repe ating the p rocedure exp lain e d above , t he most updat e d mod e l for the -."aste p < ce r r e cycling syste m in Jap an is o b tai ne d , as s h own in Fig . 2. The d e tailed math e matical exp r ess ion of t h is model is given in App e ndix 1, and t he ~ean in g of each equation is e xplained i n App endix 2.
From this contracte d mathemati c al model s hown in Fi g . 3 , th e values of e ac h s tat e varia b l e can b e consecutivel y de t e rni ne d by pe rfoming the calculation according to t he step s di · r ecte d by the arrows in th e fi g ur e .
SPi ULATI ON Bas e d on t: ,,· d y namic mod e l d e v e lope d in t he previous sect i on , t o,. calculation for t l~ e simulat i on is p e rformed for th e p eriod of th e p ast ten years (from 1968 t h roug h to 1977). The calculate d valu e s fro m t he ~o d e l ar e comIt i s p are d to the availab le r e al d at a . la t e r s h o~n t h at t hey agr ee qu i te ~ e ll wit h e ac h oth e r. Judging from t h i s good a g r eeme nt , it may safely b G s aid that th e ca lculat e d valu e s o f the state varia bl .s t h e r e al da t~ of wh ic h ar e ~ o t ava ila b l e cou l d be a fairl y go od es tiMati on o f t ;-: e :::,a s t. r o f L -:esc: varia l:: l e s . ,"l"
7h e valu e s of t he ~a r a~ e t e r s a ~~ e xt e rnal i np uts (e xogenous vari ab l e s) US Gd in th e sinulation calculati o:, ar e sh o~ ~ i ~ ~ rpe njix 3. T~~e
ove r
for e casti~ g o ~ fro~
~ ~~e
~utu~ c
~ r ese~ t ~ ~
t:1e
; 'e rf o r:-1 e d b":-' c a rri:)~
O 'Jt
to
tr end
ra~ g i ~g
~:SC ~ . ~ .
is
t:-.e s i:-:-::.ll ation f o r
t:-. e s e v e ral cas es '..::~e r e t:~ e a ssu::'l: tior,s o~ t~ e futur e e sti ~ ati o ~ o f ~ a ~~' e c o~ o~ic and s oc ial factors ar e c~ a n g e j . The annual ir,c r -2a s es i;: - :- e x ogc :10'J.S va r i a bl es gl fActual g r o s s nationa l e X P G~ditur e ] ~~ ~ 9, [~ct',Jal ; r~vat e ?la~t anj e ~ui9~ e ~t ir.\;!2 sE::1e :lt] :J!:-
j a sed o n By e l im i nating auxiliar y state variabl e s Xi (i =1 - 23) in the math e matical e xp r e ssion of t h e model , the' at ",<'!'la ti ca l structure of t'1 e model
:
t~1 e
e sti~at e d as
ar.:l ua l
0 c o ~o:-:-:i =
S:-.O",-::--. i1. -:a ;:' l e 1 , g r o ~t~
rat e
f o r e cast ed jy :' :-.12 Ja ;:~ ar. e s ·~ go \"e r :1:-l-2 :-.t :s. :1j
e conon ists.
t: ':e
Waste Pa per Recyclin g System·in Japan
--"
/ SIPP PJ
)
Fig. 2 Waste paper recv_ c 1·~ng model I.A .A . - T
273
T. Takama t s u e t al .
274
exte.nal variables g. (T) (i=1,2) 1
~ZlO=[kl/(l-kl)fl(gl,gZ) Z4=(Z3(t)-Z4)/PIZ
~
Y3- Z 3(t)-Z4(t)
~Z3 PZf1(gl,gZ)/lOO
YZ=a Z (t)+b Z (t)-z3(t)-yZ
where a Z (t)=k 7 z 31 (t), b Z (t)=k 33 F 1 (z3)'
zZ=aZ(t)+bZ(t)-YZ(t)
+[kl/(l-kl))fl(gl,gZ)~ r l z -a (t)+b (t)-y (t) 1 1 1 1
where a,(:)'[p",(g"g,)/100)/(l-k,), and b
1
(t)-k Z3 F (zZ) 1
y
~Zg=zl(t)f3(gl,gZ,gS,g6)
Z9=z4(t)-zS(t) 1
and z31=(z3(t)-z31)/P14
Yl = a1(t)+b1(t)-zZ(t)-Y 1
~
z7=zl(t)f Z (gl, g Z,gS,g6)
zS=a 4 (t)+k (b (t)-Y4(t)) 6 4
(j=3,4,S,6)
g j (t)
4 =a 4 ( t)+b 4 (t)-z6(t)- Y4+(1-k 6 ) ( Y4- b 4(t)) YS=aS(t)+bS(t)-z 7 (t)- YS+(1-k 6 )( Y4 - b4(t))
~
where a s (t)=F 1 (z7)' b S (t)=k S3 F 1 (z7) a 4 (t)=z4(t)f 4 (g3,g4)
z6=a S (t)+b
(t)-YS(t) S +(1-k ) ( Y4(t)-b (t)) 6 4
and b
4
(t)=k
F (z6) 43 1
I
where fl(gl,gZ)=~P3+P6)gl+(P4+P7)gZ+(PS+Pg))/lZ, fz(gl, g Z, g S,g6) = [gS(P3g1+P4gZ+PS)+ g 6(P6g1+P7gZ+Pg))/lZf
1
,
f 3 (gl, g Z, g S,g6)=(1-P 11 f 1 )/PIZ' f4 (g3 ,g4)=P9+ (PI0/100) (g4/gS) /16, "" i-I Fl ( Zj ) = i h (S/6) Zj (t-i)/6 Fig. 3 Compu t i n g p r oced ure f o r th e equ3 t ion s of th e mod e l Tab l e The va l ues be t wee n Es t ima t ed Val u es 19 79 and 1989 are es of gl an d g 2 timat e d by taking into account the ye a r l y g2 gl Ye a r change in business tr e nds. The va l ues 1.708 10 .81 19 78 after 1990 a r e esti 1.911 11 .84 19 80 mat ed under the as 2.134 13.03 19 82 sumption tha t the eco 2.40 2 14.54 19 84 nomic growth rat e is 2.6 20 15 . 84 19 86 constant . 3.00 2 17.78 19 88 3 . 38 6 19.5 8 1990 As fo r the parameters, 3 .7 33 21. 38 1992 (1) p and P2 [Sea4.115 2 3. 35 199 4 1 sonal ind i ces of pape r 4.5 37 25.50 1996 p roduction and p a pe r 5.00 2 2 7 . 84 1998 consumption,respec 30.41 I 5 . 515 2000 tive ly ] a r e f i xe d as 13 p = p = 100 . Sea (10 y en/ yea r) 1 2 b at ~" on ~ s not tak sonal pertur e n '~nto account. (2 ) p . (i= 3- l 4) [Reg r ess ion coef fi cients ], kj (j~2 -S ) [ I nventor y - sa les ratios ], k [Coeff i cient of inventory adjustmen t a~ th e recove r y trad e r] are a ss umed to be the same as in 19 77 . (3) Since the pape r p r odu c ti on is estimat ed to become 2.87 times the p re sen t d ur ing th e 22 yea rs fr om 1 978 through to 2000 , k7 [?he
adjustmen t coe f fi c i e nt of est imated p a pe r sh i pme nt from t he manufacturer] i s calcu l ated as fol l ows , i. e .
(k )264 /P4 = 2.87, 7
k7 = 1. 00802 The f o l lowing clssumptions are se t out i n t he simu l ation o f t hree c as es . Ca se I (1) Th'2 upper l i Mit o f che r ec0ver,' rat e e f was~e pape r (S)2 i s 50 %, i. e.
S::: 50(%).
(2) The actual p a pe r e xp, Ht rati o (k ) i s l kep t at the p re sen t l e vel , i.e .
0 . 0 2 4.
(3) The actual waste pape r p ric e (g4) changes in the fo llowing f o ~~ different wa ys .
---------------- .----2 S [r ecove r y r at e of waste p a pe r ] is d8 f i ned by the ratio of (z4 /zS)X 100 .
Waste Paper Recycling System in Japan 3 Letting the time origin (t =0) be J a nuary, 1978, (No.l) g4 is constant after 1 9 79. i.e. (No.2) g4
is import e d wh e n the i nv e ntor y - s al e s rati o (= Y4/z6) b e comes l e ss than 0 .1 5 [month)
g4 = 14.13 + 0.05887t
(No.3) g4 becomes 2 times during 10 years. i.e.
g4 = 14.13 + O.ll77t
(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 pape r for paper Production (g5) increases by 0.008% per a nnum. 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. i.e.
(NO.2)
a = 0
(No. 7)
a = 2. 5
(No.8)
a = 5. 0
( No . 9 )
a = 7. 5
g4 = 14.13 becomes 2 times d:.lr ing 20 years.
i.e.
i. e.
275
g
6
= 0 .731 + 4.333 x 10-4 t
Case n (1) The net paper export ratio (k ): l kl = 0 . 0 2 4 (2) The actual waste paper price (g4): g4 becomes 2 times during 20 years. (3) The waste paper recovery rate (S) c hang es in th e following ranges: (No.2) S ~ 50 (%) (1978-2000) (No.5)
S ~ 50 (%) S 5 55 (%)
(1978 - 1 984) , (1985 - 2000) ,
(NO.6)
S 5 50(%) S 5 55 (%)
(1978 - 1 984) , (1985 - 1990) ,
and it increases by 5 % for 1 0 ye ars after 1990.
In Cas e I, the e ff e ct of th e wa s t e paper p ri c e trend on the waste paper supply trend which is anticipated to incr e as e according to the ra p~ dly rising demand for paper under the assump tion that the uppe r limit o f th e r e c o very rate is fixed at 50 %, is made cl e ar . In Case n , th e effect on t he wast e p a p er supp ly trend of changing the upper limit of th e wast e pap er recovery rate is analys e d. In Cas e nr, wheth e r or not waste paper import will be e ffective a s a measure for making up for th e shortage of the waste pape r supp ly which is antici p at e d to occur in the futur e is e xamine d.
RESULT AND DISCUSSION
4- 1 Confipmation of t he model by compa pi s on with the pea l data The comparison of the calculated zl [Amount of paper production), z6 [Amount of waste pape r purchased by the manufacturer] an d Y5 [Inver:-. tory of waste p a p er 1n the ma nu facturer) wl t n the actual data is shown in Fig . 4 . From th e se results of the simulation, it is safe ly con -
].6r---------------------------------------------------------~
1.4
0.6
Case nr (1) The net paper eXFo rt ratio (k ) : l
0.2
kl = 0. 0 ~4
(2) The actual waste p aper p ri ~e (g ): 9 bec omes 4 2 times juring 20 years . (3) The upper limit on ;:he '.va st.e pape r r ec cJVe r y rat e (S) i s kept at 50 %. i.e.
o
1968
Fig. 4 Comparison
S::: 50
(4) As for the import policy of waste p aper, the following cases are considered. That is, a % of the estimated purchasing amount of waste paper in the manufacturer 3 The unit of time
t
1970
is measured in months
1972
Year
1974
1976
1978
of calculated values and real data
cluded that the model d e v e lope d her e is confident.
4- 2 The calcu lated values of' trre "XlY'-!.::li:;&es the pea l data of '.Jn i cn ': ~ . , :r ;: _ ;, ;;:~;] ;an-:; An advantage of utilizing this kind of mathe matical model i s that it is possibl e to estimate the variabl.' s th e real data of which are
T. Takamatsu e t al.
276
not available, by using the calculated values from the model. As an example, the es timated values o~ z (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~der] are shown in Fig.5. z4 and Y3 represent the same tendency
1(10 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 t h 'J recovery rate by consolidating the structure of the waste paper collection system; (iii) To compensate for the domestic shortage of h:as te papt..:r by importing it from abroad.
1.8 In order Lo evaluate the availabili t"· of such neasures
o
1968
1970
1972
1974 Year
in thier changes. Since z has the first order time lag with respeci to z3 (Amount of paper consumed by households], y shows a larger increasing tendency when ~ompared to z . (See Eqs. (3) and (8) in Appendix 1] Both z4 and y increased yearly up to 1973 along w~th the 3 rapid incrase of z . After the oil crisis of 1973, however, th~y once dec r " a sp d and then became almost unchanged. At present, they have shown a gradually increasing tendency. Until 1975, z_ also shows the same , :0 trend as z4 Slnce the recovery rate of waste paper remalned almost unchanged, and consequently z9 increased annually. After 1976, z has been increasing and, therefore, z is 5 . 1 y decreaslng. ' constant or s l'l<:int r,o uy"; l ', 9speaking, Y4 is almost constant, though it shows small monthly perturbations. This tendency is probably attributed to the fact that recovery traders have very limited stock yards. On the other hand, the total stock of waste paper at the manufacturer is increasing annually compensating for the insufficient stock capability at the recovery traders.
4-3
FOY'ecastin:; of the futw>e tj't?Y!.d
As for the anticipated rapid rise in the demand for waste pap er as a raw material according to the increase in the deman G for paper in the future, an apprehension is ofte n expressed as to whether or not it is actually p~ssible to supply the amount of waste paper to meet demand. In such a situation, the
and to assess the environmental impacts which would result from the execution of these measures, it is indispensable to quantitatively forecast the future demand for the ",ast e paper by using such a dynamic model as developed here and to carefully examine the forecasted results. In this section, the results of 1976 1978 the many simulations used to forecast the future trend of waste paper utilization at the manufacturer are s>-'o'""n and changes of the amount of waste paper collected, the dome: stic inventory of waste l:-'a per and the amount of waste paper disposed of as refuse are estimated assuming that these three measures are implemented in the future. In Fig.6 the simulation results of Case I where only the price of waste pap er is steadily increased by limiting the recovery rate within 50% are shown. From this figure, it is clear what will happe n in tc.e suppl y of and the demand for waste l 'd per, and how the amount of waste i"a per disposed of as refuse will change. This figure s h ows that th e supply of waste i a p e r cannot catch up with its demand, and the time will come sooner or later when the d omestic inve ntory of waste paper bec o mes zero, no matter how hig h the price of waste paper would be increased. The ~ ~ ount of waste paper disposed of as refuse increases more and more. Fig.7 show ~ the simulation results of Case TI where the recovery rate is increased by consolidating the structure of the collection system. In this case , it is clarified that the shortage in the supply of waste p aper would not occur until 200 0, if the upper limit of the recovery rate ~ould q r adua ll v increase up to 60 %. The increase ratio of the amount of waste paper disposed of as refuse is also s mall compared to that Case I.
277
Waste Paper Recycling System 1n Japan Fig.8 sh,..,,'s the r esults of Case nr whe r e the was t e p aper is imp o r t ed from abroad i n o rder to compensate f or th e domestic shortage. As shown in th i s figure, t he import of waste pape r can delay the time when the shortage of t he supply will s tart to occu r, but it r esu lt s i n large fluctuati ons in the inventory of waste p a pe r. Mo r eove r, th e amount o f was t e pape r disposed of as r e fu se is ve r y large as i n Case I, which r es ult s i n some env ironmen tal po llutio n prob l e 'Tls. From these viewpoin t s it i s not good to d epen d on the import of was t e pape r in or der t o p r even t sho rtage in the supp l y of waste pape r. Judging from t he r es ult s mentioned above , it can be easily unde r stood that the most e ffective and desir able countermeasure t o ove rcome the antici p ated sho rt age of was t e pape r s upp l y i n t he futur e is t o inc r ease the r ecove r y rat e of waste pape r up to 60% by consolidat i ng t he co ll ec tion system .
x106 ton 2.0 1.8 1.6 1.4 1.2 1.0
o
1978
'85
'80
'90
'95
Year
2000
Fig. 6 Forecasting of Y4' z6' and z9 in case I
x10 6 ton 2.0 1 .8
z6(No.6)
h0
IV\
1.6 1.4 __
1.2
~,
5
)
'9(No.5)
1.0
0.6
2xY4 \(NO .2)
0.4
\
\ \
\
0.2 01978
(No. 5)
/'<'
0.8
\
'80
'85
'90
Year
'95
2000
Fig. 7 Forecasting of Y , z6' and z9 in case II 4
CONCLUSION I n this r eport , t he waste p a pe r r ecyc li ng system is taken up as a concrete example of a resource r ecycling sys t em . A dynamic mode l ,vas developed and , based on this mode l, the q uantitative assessmen t o f several measures for p r even ti ng the anticipated sho rta ge o f the supp l y of waste pape r i n the futur e i s per f o rmed , The bas ic structure of t he model developed is b a sed on th e mate r ia l b alan ce sho~TI in Fig.l. By taking into account many con trolli ng and
i n flu encing fa cto rs and adding trrrr to th e bas i c mode l as in f o rmatio n flows, the who l e mode l structu r e was g radua ll y devel o, 'ed , and finally obtained as shown in Fig.2. The fundamen tal structure which is obtained by r ea rranging the model equations according to t he direction of the information flo ws , is shov.'J1 in Fig. 3. As is c lear fr Gm t h is fi g ure, the p r ocedur e for the simulation calculation p r oceeds from the exogenous variables r elated to economic factors t o t~8 opposite dir ect ion of the material flo w. The p rameters i nc lud ed in the model ar e
T. Takamatsu et al.
278 es timat ed fr om the real data , and the conf i dence of th e mode l is confirmed by compa ri ng the ca l cu l ated values fr om the model with th e r e al dat ~ ranging o v e r 1 0 ye~r ~ , (Fig . 4 . ) The mode l is first utiliz ed for pre dicting th e change of state variables th e r ea l data of which a r e not avail a b l e. (Fig. 5) Then , it i s used to quan titative l y assess thr ee measures for p r event ing th~ an ti cipated shortage of t he s upply of waste p a pe r in t he fu ture .
>110 6 ton 2.0 1.8 1.6 1.4 1.2 1.0
0.6
____
'
I
.~ \/\VJ.:iIAtV/~:· ,
\ ,
0.4
\ \
2XY 4 (NO.2\
0.2
\'V1\
;\\:\ ,1\
V , , !' ii: V\ \
:i ,I
'-'\
\
~No.7l
(NO.8~
r,
\ ' ,
/ V
~
i
°197~8~1-8~0~~~~'~85~~~'~ \ ~19~0"~~~'~9~5~~~·2~000
Year Fig. 8 Forecasting of Y4' z6, and z9 in case III
Fr om the r es ult s of th e s imulatio n (Fig. 6-8 ), i t was c larifi ed that the i ncrease i n the r ecovery ra te of Case IT i s the most desirable among these thr ee meas ur es. Th e sys t em a pp roach based on th e quanti ta ti vc mode l as shown in t his p aper , cou ld be ve r y he l pfu l in e valuating and as sess ing many dif f e r ent !:,e asur e s intorduced to r eso lve i ssues not only in was te pape r rec yc lin g s ys tems, b u t also i n many o th er larg e , comp l e x, r e sources recyc li ng systems .
APPENDIX 1 MATHEMATI CAL MODEL (a) Equations r e late d t o Yi
(i=1 -5 )
dY (t) l - - - = z l (t) - z2 (t) dt
(1)
d Y2 (t) - - - = z2 (t) - z3(t) - z l O (t) dt
(2 )
dY3( t) ACKN ,.lh"LEDGEMENT
dt
z3(t) - z4 (t)
(3)
z5 (t) - z6(t)
(4)
dY4 (t)
The authors wi s h to acknowledg e Mr. M. Arakawa for hi s va l uab l e assistance.
dt dY5(t )
~ = z6(t)
REFERENCES OECD Repo rt (1976) . " Prospects a nd Policies for I,aste Pape r Recyc li ng in th e Pulp and o f Paper Indu st r y ". Glass e r y , C . R., an~ V. K. Gupta (1 965 ). A li p ea r programming analysi s of paper recy cl ing. Stud i es i n Managemen t Science and Systems Vo l. 2. No rt h - Hol l and. Chap .1 3 , pp . 273 - 292 . Clif ford , J . S ., M. A. Laughton , T . S . McRobe rt s and P . V. Slee (1 978 ) . LP model li ng i n the p a pe r i ndustry as an a i d t o r ecyc li ng dec isions . Con se rvat i on & Recycling , ~ 9 7-1 09 . Turner , R.K., R. Grace , and D. I' . Pearce (1 978). The economics of was te : . p er r ecyc li ng . Resource Conse r va t ion , Soc ial and Economi c Dimensio ns of Recyc ling, Langama n Group Limited , London , Chap .16, pp . 296343 .
(b)
- z7 (t)
Equation relat ed t o z.
~
(5)
(i=l - l O)
zl (t)
P11 z7 (t) + P 12 z 8(t)
z2 (t )
k Z (t) 7 31
x (t) + zlO(t) 9
(6 ) (7)
1
whe r e Z has the first orde r time lag . h 31 w ~t r espect to z3 ' i. e .
dZ P14
z3(t) =
31 dt
1 12
(t) + z31 (t) = z3(t) 1
x 17 (T)1 00 P2(t)
(8 )
(9 ) Z4(t '{ P9 + P 1 0 X 20 (t) } - k x (t) (10) 6 6 x
16
(t) - x3 (t) + (1-k )x (t) 6 6
(11) (12)
Waste Paper Recyc lin g System ln Japan X13 (t)x
lS
(t)
(13) (14) (15 )
(c) Equations related to x.
(i= 1 -23)
1,00 5 i-I . 6Li= 1 (6) 27 (t-l) 1
tc27 (t-l) + SX (t-l)} l
(T)gS (t)+x
22
(T)g6 (t) } (29)
XIS (t)
x
(t)
-6l rl=. £-)65 i -I 2 7 (t-i)
(T)
x
16 17
XlS(T) x
where k (t) has the first order time lag S3 wlth r espec t to kS(t).
21
_l_{l - P 11x (t)} 14 P12
x
(16)
(T) [x
17
l
xl (t)
1
x
24 (t) - 2 5 (t)
279
x
19 20
21 k
l-~
(T) + x
1
22
(30)
xl (t)
(32)
(7)
(33)
x 17 (T)
(t)
1 1 16 1 00 g4(t)
(t)
~ x
1
g3
19
(3 1 )
(34) (35)
(t)
i. e . x (17) 2 x YS(t) - x
2
(IS)
(t)
x
lI ~
(~)i-12 (t-i)
6 "-=1 6
21 22 23
(t)
P3 g 1 (t) + P4 g 2 (t)
+ Ps
(36 )
(t)
P6 g1 (t) + P 7 g (t) 2
+ PS
(37)
(t)
x
17
(t) + xlS(t)
(3S)
6
AFPENDIX 2 l {2 (t-l) + Sx (t -l )} 6 6 4 Xs (t)
(19) MEANING OF EACH EQUATION (2 0 )1
where k (t) has the first order time lag 43 wlth respec t to k (t) 4 i. e . (20) 2 (21) 1 ,00 5 i -I ~i=1(6) 23(~ -i ) l{2 (t-l) + SX (t -l) } 6 3 7
x (t)
(22) (23) 1
i3
(24)
x (t) = Y2(t) - x S(t) 9 1 ,00 5 i-I x l O (t) = 6 Li= 1 (6) 2
i 11
2
(t - i)
2 { (t -l ) + Sxl O (t-l) } 2
(t)
(25) (26) 1
where k (t) has the first order time lag 23 with r espect to k (t) . 2 i. e . dk T ~ + k = k2 (26) 2 2 dt 23 Yl (t) -
1
x
11
(t)
(27)
1
100 P I (t)~23(T) - x 12 (t) (2S)
(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 outp ut. For examp l e , the time derivative of y [the inventory of paper at t he manufacture~ ] is equal to the difference between 21 [l'.mount of paper production at the manufacturer ] and 22 [Amount of paper shipment from the manufac turer]. Here, y. is an unknown va ri able the value of which h~s to be calculated from t he observed or es timat ed values of the mate rial fl ow 2. (t) (j=l- 7,1 0) J
(b) Equation of 2i
where k (t) has the first order time lag with re~~ect to k (t), 3 i. e . dk33 T--+k =k (23) 2 3 dt 33 3
x
(a) Equation of Yi
(i=l-lO)
Eq. (6): 2
[Amount of pape r p roduction a t th e is equal to the sum of the two values which are calculated by multiplying each yield factor Pl l and P 12 by 27 [Amount of waste pape r consumption aE th e manufacturer] and 2S [Amount of pu l p consumption at the manufacturer] , res pect ively.
manufactu~er]
Eq. (7): 22 [Amount of pape r shipment from the manufacturer ] is concurrently equal to the amount 0 f pape r pu rc hased by the ·.,; holesa l er. The wholesaler seems to for ecast his pur chasing amount by analysing t he past trend of the amount of pape r p urchased by cons\.l:" cr. He re it is assumed that t he es timat ed value of 2 , 2 , can be obtained from the diffe r . ·n tia13equ~~ion ~hich has the first order time lag ·,:ith res pect to 2 . (The time constant p is assumed to be months . ) The es timate~4value 231 is modi fi ed by multip~in~ b! a f actor k used to compens ~ te for the inade 7 quacy in this es timation. The actua l amount of p aper pu rchased by th e wholesaler (2 ) is 2 given by subtructing the variation of Ehe pape r stock at t l: c wholesdl,T (x ), due to 9
1
T. Takamatsu c: ~
280
th e invento r y adjustment , from the modified estimated value of z3 (k z ) and adding the 7 31 amount of net paper e xpo rt (ZlO)' Eq. (8): The amount of pape r puchased by con sumer (z3) is equa l to the value which is obtained by mul ti pl ~.' i "S t'i'c seasonal ind ex of pape r consumption (p ) by the average p a pe r consumption per montfi which is calculated by d i viding the annual i,ape r d e mand in the domestic ma rk u t(x ) by 12. 17 Eq. (9): The pape r p urchased by t he consumer is d i sposed of with a certain time l ag with respect to the purchas ing time. This time lag is assumed to :,' the first order '-"icos" tim" c;on,; tilllt to is on c mont!~. 13 Eq . (1 0 ): Zs [Amount of waste pa:, e r coll ec ted by the recovery trad e r] is a ~s" med to be determined by adding the term r elevan t to the inven tory adjustment to the p roduct of z [Amount of paper discbarged from househoids] and (P9+ P 1 0 x 0 ) [Estimated r ecovery rat e] . Where est~mated recovery rat e is p resumed to be a linea r fun ction of x [Auxiliary varia ble on t he waste pape r prfge] . The capabili ty of the inventory adjustment of the r ecov ery trader seems to be insufficient. Th e r e fo r e , as a coefficient to express its weak ness in adjustment aLility, k [Coefficient of inven tory adjustment in re80very trader] is introduced, and this coefficient is multiplied to x6 [Variation of the inv0 ntory of waste paper at the recovery trader]. Eq. (11): z6 [Amount of waste paper purchased by the ma: :ufacturer] is determined by sub tracting x [Variation of invento r y of waste pape r at t~e manufacturer] from x [Estimat ' 16 ea, pue:: h as~ng amount of waste pape r by the manufacturer] and adding th e supplementary amount of waste p aper which is kept in stock to compensate for t he weakness in the inven tory adjustment ability of the recovery trader . Eqs . (12) (13): z7 and z [amounts of utiliza tion of waste paper an~ virgin p ulp, re spec tiv e l y ] is determined by multi p l ying ?3 C!1 utilizatio n ratio (x ) or (x ) ~y x ["la"", d mont',l ... ' [:% ,0, r i ro~~ction]~3 Eq . (14): Zg [Amount of ',vaste p ape r disposed of as r e fus e] is the amount of uncollected ... r l~'7lo~n L 0 f i.· a: ,·-: r -ii sc:::a r q·.:c :: r ,; ;n !lOUS'~' h~ldl . Eq. (1 5) : Since z [:'lonthly n e t p aper expor t] , 10 ~s v e r y small compared to the pape r production, zlO is assumed to be constant t hought out a yea r and to be (1/12) xx [~!::. ual p a18 per expo rt]. (c) Equations of Xi
(i =1 - 23)
Equations relevant to (x ,x ,x ), (x ,x ,x ), 2 6 (x7 , x8'x~) and (XI O,Xll,k1 2) ail hav~ t~e same matnemat~cal st ructur e , and they are utilized to calculate the va riations of the inventories .
a. l .
Eq. (16) - (27): Va riab l es x. (i=1 -3) , x, (j=4 -6 ) are relevant to the invenEories of wJste pa per at the manufacturer and at the recovery trad e r s , resoectively. x (k=7-9) and x (e=1 0- 1 2) ar~ also r e leva~t to the inve~tories of p a pe r at t he wholesale r and manufacturer, r espective l y. The average monthly utilization of paper or waste pape r (x., i=1,4,7,lO) is calculated by smoothing the Bast r eco rd in such a way that th e older t he data is , the smaller is the coeffici e nt weighed ~y us ing an exponential type of wighting function. The standard value of each inventory of paper or waste paper (X i ' i=L , ~;, 8 , 11) is expressed by th e p r oduc t of tne average utilization of p ape r o r waste paper and the average inventorysales ratio of pape r or waste paper (k ,k , S 4 k3 , k ) . 2 Iffien the average inventory-sales ratio changes, it s change does not directly cause the varia tion of the standard level of the inventory, but its influenc e 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 was t e p aper (x" i=3,6,9,12) is tae difference between the acEual inventory (Yi' i=S,4,21) and i ts standard level. Eq . (28): The planned month l y paper p roduction (x ) is given by sub tracting the var iation of 13 , ' t h e lnventory due to t h e lnventory a d'Justment f e om the p roduct of the average planned month ly :' a p( r p roduction (x /12) and the seasonal 23 ind e x of paper productlon (Pl)' Eventually, this value becomes equal to che amount of paper p roduction at the manufacturer (zl) ' Eq~(29) :
The utilization ratio of waste paper for pape r and board (x 4) is obtained by di vidi ng t', e. "urn of t", l' ewo products by th e annual demand for all kinds of paper. The first prod uct is obtained by multiplying the annual demand for pape r by the uti lization rati o of waste pape r for paper production (gsL and the second is the annual de:-:,a nd for board multiplied by the uti li zation ratio of waste pape r for board p roduction (g6) ' Eq . (3 0 ): The utilization ratio of virg i n pulp for p a p er and board (x 5) is obtained from Eqs. (6), (12), (13) and ehe condition that zl=x 13 · Eq . (31): Estimated amount of p urchased waste paper by the manufacturer (x ) is obtained by lp soomthing the pas t value of cne amount of co: ~ sum p tion of waste pape r z7 (t - i) with an exponential type we ighting factor. Conse quently, this value is equal to the average value of t ",-- waste pape r consumption at the manufacturer (x l)' El{ . (32) : .7,nt,ual domestic consumption of paper and board (x ) is the sum of the annual 17
Waste Paper Recycling System In Japan domestic consump tion of pape r (x ) . 22
(x
2l
) and board
Eq. (33): Annual paper export (x lis the net balance defined by the differen~~ be tween the amount of export and that of import. This value i s calculated from Eq. (3S) by using the net paper export ratio kl (=x /x ). lS 23 Eq. (34): The price index of was te paper (x ) 19 is the ratio of t h0 waste paper p rice trena (g ) with respect to th e p ric e in 1 970. (The av~rage price of waste pape r is ~16) Eq. (35): An auxil iary variable of the pr i c:e of waste pape r (x ) is defined by a ratio of the 20 price index of wast e paper (x 9) and the wholesale p ric e index trend (g ). lThis variable 3 means the actual trend of the price index of paper. Eqs. (36) (37): Domestic demands of pape r and boa rd are both approximated by a linear function of the actual gross national expend iture (g ) and the actual priva te plan t and equipme~t inves tment (g2)' Eq. (3S): The p lann ed annual pape r p roduction (x ) is the sum of the annual paper demand 23 (x ) and the annual paper export (x )' 17 lS APPEND IX 3
3-1 Exogenous variables Exogenous variables Table A Given Data are set up as given conditions. The Year actual gross na5.749 1.0218 , 1968 tional expenditure 6.365 1.2378 : 1969 trend (g ) and the 7.061 1.4195 1970 actual p~ivate 7.583 1. 4835 . 1971 plant and equip8.274 1.5670 j 1972 ment investment 9.087 1.8566 , 1973 tr end (g2) are 1974 8.973 1.6545 ' given by the value 9.197 1.4399 1975 per annum, and 9.740 1.4893 : 1976 th eir values are 10.248 , 1.52941 1977 given in Table A. Here "actual" means (1013 yen/year) that the pr ic e increase from 197 0 has been taken into account in the values. The whol f'! sale p ri ce index trend (g3) and the waste paper price index (g4) are g~ven as monthly values. The price of corrugated card board, which is the most utilized amon g all of the kinds of waste pape r, is taken as a r epresentat ive value of the waste pape r p ric e . The utilization ratio of waste paper for p a pe r and board (x ) calcu lated from the utiliza4 tion rati o or waste paper for p a per (g5) and t he one for board (g ), is gradually increasing up to 36-42% ove~ a pe riod of 10 yea rs, for the j?c riod of which the simulation calculation in perfo r med.
3-2 Para'!1etel's
281
[a] ~he seasonal index of pape r production (P l) and the s easonal index Table B Values of PI and P 2 of pape r con(1976-1977) sumption (P2) P2 PI 1Month are given by the monthly 1 90.8 90.5 values. The 2 92.2 94.5 values of P l 3 100.8 105.4 and p from 4 99.9 99.1 196 5 1 973 5 100.8 101.0 are constant. 6 101.5 101.0 Taking into 7 102.0 99.8 consideration 8 98.2 100.4 the influence 104.4 9 103.3 of the oil 102.3 10 . 104.8 crisis in 1 97~, 102.2 103.5 different 12 : 101.4 100.2 values are used, for 19 74 and 1 975. After1975, the constant values are us ed again, as shown in Table B.
to
I
LlL :
[bl p. (i=3-S) are regression coefficients. The r ~g ress ~on analysis is perfo rmed in order to correlate g and g with th~ real data of the domestic c5nsumptfons of paper and board. By using the r eg ression coefficient obtained, annual demands for pape r and for board are e stimated. The regression coefficients are obtained as follows; P3=566,OS, P4 =1415,2, P5=575.S5, RL=~.9922 P6 = 253,76, P7=2469.2S, PS=409.92, R =0.9S16 Based on these values, x. (i=17,lS,21,23) are es timated as shown in TaBle C.
Table C Comparison of the Estimated Values and the Real Data Year
Estimated x 17
1968 1969 1970 1971 1972 1973 1974 1975 1976 1977
9668 11012 12289 12965 13856 15648 14769 14119 14756 15328 (10
Real data of!, x 17 9957 11310 12973 12907 13638 15975 15646 13600 15394 15702 3
ton)
[cl P9 ' 9 : The coefficient in relation to 1 es timaged recovery rate (SI) and the auxiliary variable on the p rice of waste paper (x ) given by 20 SI (t) = P9 + PIOx 20
t~e
are obtained by the regress ion analysis o f t he annual real data. The relationship between the price of waste : ~ aper and the estimated recovery rate is very complex due to the influences of the o i l crisis of 1974 , the active c~mpaign for energy and resourc e saving since t hen , and the movement to collect waste pape r previously brought from many places to one central p lace as opposed to house by house
282
T. Takamatsu
collection. The r eg r ess i on ca l c ulation was ther e for e pe rfo~ med inde;,e nden tl y in th e foll ow ing t wo pe riods. (i) Jan.1968-Dec.1974 (ii) Jan . 1 975 -Dec .1 977 [d] P ll' P 1 2: The amount of consumption o f waste p aper and p ulp is r epr ese nted by a li n ea r function of the amount o f p roduction of p aper and board . ~he yie ld rat e i s calcul at ed from the real data ranging over 1 0 yea rs . The ave rag e valu es o f p and p a r e obtained as foll ows , 11 12 0 . 9029,
P12 = 0 . 9792
[e ] P13' P14: The time cons tants of P13 and are flxed as P 14 P 13 = 1, P 14 = 2 When P 13=P 14' z3 (t)=z (t) i s obtained from the compar l son o r EQs.i7)2 and (9 ). [f] T . (i=5,4 , 3,2): Tb" variables are all time ~onstants. They are set as T = T. l
=
3
[g] k : By taking the ave rage o f t he p ast 1 0 l ye ars, kl is obtained as kl
0 . 024
[h] k . (i=2,3,4,5): By taking into account the oI l crisis i n 1 97 4, each i nven tory-sal es ratio i s obtained as the follo wing t wo dif f e r e nt va l ues before Feb . 1 9 74 and after March 1974 by calculating t he average va l u es i n each period. pe riod
k2
k3
k4
k5
~an.1 968 -Fab.1 9 74
k . 0 . 47 0 . 34 0 .25 0 . 67 lO ~ar.1 97 4-Dec .1 9 77 kif 0 . 8 0 . 44 0 . 3 0 . 98 The actual inventory - sales ratio (k. ) is p r esumed to have t he first o rde r tiffi~ lag wi th r espec t to the step change of k . .
et a l . NOMENCLATURE A\VPCM
Average Va lu e o f Waste Paper Con sump tion at the manufacturer S~'I?IM Standard Leve l of Waste Paper Inventory at the Manufact-,urcr VIWPM Variati on of I nven tory of Waste pape r at t he Manufacturer AWPPM Average Value of Ivaste Paper purchased at the Manufacturer SWPIR Standard Leve l of Waste Paper Invento r y VIWPR Va riation of I nven tor y of Waste Paper at t he Recove r y Trader APSW Average Va lue of Paper Shipment fro m the Wholesaler SPIW Standa rd Leve l o f Paper Inventory at the Who l es al e r VIPW Variation of Inven tory of Paper at t he Wholesaler APSM Average Va lue of Paper Shipment x lO from th e Manufacturer x SPIM Standard Leve l of Paper Inventory 11 at the Manufacturer x VIPM Variation of Inven tory of Paper at 12 t he Manufacturer Planned Month l y Pape r Production at the Manufac tur e r x URWPPB Utilization Rat i o of Ivaste Paper 14 for Pape r and Board Production x UR\'PP Ut ilizati on Ratio of Vi r g in Pulp 15 for Paper and Board Production EPWPM Estimated Purchas i ng Amount of x 16 Waste Paper at the Man ufacture r x APDD Annual Paper Demand in the Domestic 17 Market APE Annual Paper Ex po rt PIWP Pric e Ind ex of Waste Paper AVl;-IPP Auxiliary variab l e on Waste Pape r Price x ADCP Annual Do mes ti c Consumption o f 21 Paper x ADCB Annual Domestic Consumpt i o n of 22 Board x PAP PM Planned Annua l Paper Production at 23 the i1anu fa ctur e r
l
i. e . k i3
k. + (k - k. )(l-exp( -~) lO If l O T.
}
IPM
is 1 for Mar. 1974.
IPW
[i] k : This i s the c o e ffi cient o f
invrntory k =1 means t ha t t he inventory adjustment i~ pe r I n the s i mu lati on , it is f ormed comp l ete l y. assumed t ha t k =0 . 7 . 6
PSH IWPR
[j] k7: During t he 1 0 y e ars fr om 1 968 to 1 977, th e pape r p roduction i nc r ease d about 1.6 times. By taking into a::count the time constant of th e delay (p ) , k is obtained from th e relations h i p (k7)li20/P~4=1.6 as follows,
PPM
where t
adjus~ment in t he r ecove r y trader.
k7 = 1.11786 whe r e P 14=2 .
Inventory of Pape r at t he ~anufacturer
l
I WP:-1
PSM PCH PDH WPCRI \VPP~l
WPGl
Inven t o r y o f Paper at the Wholesalers Pape r Stock in Househo ld s I nven t o r y of \"as t e Pap er at the Recove r y Trader I nvento r y of Waste Pape r at t he Manu fa ctu r e r Amount of Pape r Pr oduct ion 'a t t he Manufactu r e r Amount of Paper Shipmen t from t he :-lanufa c tur er Amount of Pape r Cons umed by House ho ld s Amount of Paper Di scha r ged from Ho us eho l ds Amoun t of Waste Pape r Co llected by Recovery Traders Amount of \vaste Pa p er Purc h ased by Manufact ur e r Amount of Was t e Paper Consump tion at t he M~nufactu r e r
Waste Paper Recycling System in Japan z
8
z9
VPCM WPDR
zlO NPE gl g2
AGNE APEI
g3 g4 gs
WPI AWPP URWPP
g6
URI-lPB
k kl 2
NPER I SRPM
k3 k
4
ks k6 k
7
Amount of Virgin Pulp Consumpt ion at the Manufacturer Amount of Waste Paper Disposed of as Refuse Amount of Net Paper Export Actual Gross Nat ional Expenditure Actual Private Plant and Equivment Inves tment Hholesal p. Price Ind ex Actual Haste Paper Price Utilization Ratio of Haste Paper for Paper Production Utilization Ratio of Waste Paper for Board Production
Net Paper Export Ratio Invento ry-sal es Ratio of Paper at t he Manu factur e r ISRPH Inven tor y - sales Ratio of Paper at the Wholesaler ISRWPR Inv ento ry-sales Ratio of Waste Paper at the Recovery Trad e r I SRWPM Inventory-sales Ratio of vJaste Paper at th e Manufacturer Coefficient of Inventory AdjustCIAR ment at the Recovery Traders ACPSM Adjustment Coef fici ent of Paper Shipment from the Manufacturer
Pl SIPP Seasonal Ind ex of Paper Production P2 S IPC Seasonal Ind ex of Paper Consumption p . (i=3 - 10) Regression Coe ff icients l Pll YFWP Yielc Factor of Waste Paper p YFUP yield Factor of Virgin Pulp plij=13,14) Time Constants J
RR
S
T . (i= 2-S)
Recovery Rate Time Constants
l
t 'r
month year
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 Ch emical Engineen'n g, Kob e University, Kobe, japan
Abstract. The aim of this paper is to mak e c l ea r the p rosi,e cts and po licies for waste paper r ecyc ling and utilization in Japan . The was t e p a pe r r ecy cling sys t em is composed of wany p roc e sses rel evan t to the p roducti on , dis tribution and cor6umption of pape r and boa~d, and the gene rati o n , recovery and dis posal of wa ste p a pe r. A dy namic model of the national leve l i s devel oped fi:- ;; ': Sf) as to <;i::lU lat c> th e behaviour of th e who le system and to c l arify the real i ssue in this system. Then , the dynamic simul a ti on on th e futur e trend of waste pape r r ecycling and uti l ization i s carri e d o ut and at t he same time th e po l icy that will be th e most p romising in order t o p romot e t he was t e p a pe r r ecyc ling is made clear . The quantitative assessmen t of several p ra c t i ca l measu r es for th e r e conci l iation of t he p ro b lem of futur e waste p a pe r supp l y and requir e men t is pe r formed . As a r es ult , i t i s conc l u ." ed that th e most effective and desirab l e counte rmeasur e for overcoming t he antici pa t e d sho r tag e of waste p a pe r supply in the futur e i s to increase the r ecove ry rat e of waste p a pe r up to 60% by revisin g and consolidating the co ll ec tion sec tor . Ke ywords .
Waste pape r r e cyc l ing; mode l ling ; system anal ys i s ; s i mulation
INTRODUCTION
th e was t e p a pe r r eco v e ry and uti l ization , and at t he same time to made clear wh at po licy wi l l be most p romi si ng in order t o p romote waste pape r r ecycljng,
In r e cent ye ars , the .recycle utilization of r esources has been of g r e at impor tanc e as an effective measure for the solution of energy , re s ources and env i ronmental po llution p rob lems . Within t h is conte xt , the recover y and utilization of wa ste p a pe r l h ave tended to increase in developed countries. Many s tudi es h ave been pub l ished wh ic h h a ve tried to e x p l ain why th e recove ry of was t e p a pe r a nd its util i zation have inc r e as ed and why and by how much it is expected to increase i n t he futur e . (OECD r eport , 1 976 ; Glassery and Gup ta , 1 9 7. 5 ; Cliff o rd and Co - wo rkers , 1 9 78; Tunne r , Grace and Pearce , 1 978 ) The ai m o f th e r ese arch r epo rt e d he r e i s to mak e clea r th e p rospects and p o l icies for waste pape r recyc l ing system in Japan . For this p~ rpose , a dynamic model of the national level in Jap an is first d eve loped . This includes a ll t he p rocesses rel evant to th e p roduction, distribution and consumption of p a pe r a nd board , and th e generation , r eco v e r y and dis posal of waste p a pe r . By using the d e v eloped mode l, the real issue i n t he p romotion of waste paper rec yc ling and utilization i s clar i fi e d . By changing t he assumptions a bo ut po l ic y developme nt wh ic h mayo r way no t be realized, many s imulation calculations are pe rformed to f o recast the future tr e nds of
A rough materia l balance in t he p rocess es of the pape r p rodu ction , distribution, wast e p a pe r r ecove ry and disposal in Jap an is shown in Fig. 1 . The p aper and p ul p industry in
DO"7estic CO>lsu",;,ticm
( 16 . 3)
r.
I~ ."Iefuse (9.4)
c-o-n-s-u-m-e...Jrc.-,~
(6.9)
(0.5)
- ---,-J
IWho1e-s~l ;;
(6 . 9) ( 0 . 3)
I
YManufacturer fJ A A
:':,, ~:: (9 . 1) Fig. 1
1 Throug hout t .n ~. s p a pe r , t h e t e rm waste p a pe r a l so inc l udes was t e b oard . 271
-.J
L ?-.A l::
I '";:; cY'tec!.
0. 3) Paper f l ow in Japan (mil l ion ton; 1 978)
272 Jap an has grown very rapidly along ',:i th eco nomic deve l opment since th e 1 9 6 0 ' s . The ac tual product io n 0 ' pape r and boa rd exc, ",c, ' c 16 mi llion tons , in 1978. The'actual production of pu l p is about 1 0 I ~. i l l i o n tons , and the an nual consumption of pape r and board pe r cap ita is 141. 6 kg. Almost al l pa p er and boa rd p ro duced is domestically consumed. About 40 % of t he amount consummed is r ecovered . Of th e r emain ing unrecovered 60% , about 1 0% i s stored or utilized as a p ermanent stock such as books i n libraries and b uild i ng p a p e r i n construction etc. About 30 % i s us e d for some s p ecial t ype of pape r and board such as pa r affin coated pape r for wate r- p roofi ng etc . which is not suitab l e f o r recycled use and t hus even tual l y becomes refuse . About 20 % is also dis posed of as refuse , even thou ';" it is still r eusab l e . Recovered was t e p a p e r is a valuab l e raw mate rial f or the pape r and boa rd i ndustry and is comp l e t ely utili z ed f o r domestic de mand . The im; 'orta ;-,c C' o f r eco v ered was t e paper as a raw mate ri a l is g r owing due to the sour ing pr i ces of both v irgin p ul p and imported pulp wood . (44 % of the t otal nec e ssary p ul p wood came fr om i mports , i n 19 79) .
can b e simp ly e xp r e ss e d as s ho·.,·!"! i n Fig . 3 . From this figur e , it j~ easil~' und e rstood ~O~ and from what variab l e s the ~ajor state v~ria bles ar e d e t e ~in e d . As for t he state varia bl e s Yl [ Inventory of r a r er at t he ~a n uf ac tu r e r 1 ' Y2 [Inve ntor y of pal)e r at t :-- e ·..:".o l e sa le r ] , Y4 ! I nv e ntor y of wast e pape r at t ~e r e covery trad e r 1 and 1" , [Inve :: ', 'c ' of ·. :a s t e p aper at t'1e manufact~r~r] in the d iff e r e :'tial equations of t he mod e l, the f o 11 0· . :ing relation commonly holds; [Chang e of inven tory ] [Estinat e d s:l l e s a::lount] + [De sira b le month - end inve ntory ] - [Pr e s e n t inve ntory] - [Actual s .l e s amount] where for y and y_, the additio ~a l t e r ::l r e lated to th e inv~ ntory adju s tne nt must b e adde d to the ri ght h and side of t h e eq uation . Th e diff e rential e quation wit h r e s pect to y 3 [Pape r stock in hous e ho l d s ] s hows that t h e time d e rivat i v e of th e p a pe r s tock in con sumers is equa l to t he d'.ff e r e nc e of z [Amount o f pa pe r consumrne d b~' l: o useholJs] and z4 [Amount of p a pe r disc h arged fro n h ous e holds] . The diff e r e ntial equati o ns of z4 shows that z h as a time l a g of t he first . 4 o r der w1th res pect to z3 '
MODEL STRUCTURE The sta rting po int of the anal y sis he r e i s the s i mp l e mate rial flow mode l, Fig.l . The r e covery o f waste paper is strongly influenced by business trend s . Therefore , it i s first nec essary to e xamine the month l y changes of both t he economic factors re l ating to waste pap er recovery - (that i s , the price of waste p a pe r , gross national expend iture , private investmen t in plant and equipment , e t c . ) , and the quanti:·..::tive factors of paper , board and waste pape r - (that i s , amo u nt of produc ti on , utiliz at i on rat e , recovery rat e and amount of stocks e t c . ) In order to build a mathematical model of such a l arge scale system as the wast e p a , n r r _, cling system at the natio nal level , it is nec essary t o analyse the information available at present so as t o mak e the r e lationshi p amo ng the variab l es c l ear. Then, a t e ntat i ve mod e l is bui lt, and it is examin e d as to wheth e r or not t h e model out p ut s can sufficiently e xp lain the behaviour of the real data . If agre e ment between t c',,-, model o utp uts and the r eal data can not b e o b tained, the tentative mod e l is revised by c h anging the numbe r and the i-.i:,d of state va r iab l"~s ,",O::i- to d e cre as e the discre l) anc y between the mod e l out p uts a nd th e r e al data . By repe ating the p rocedure exp lain e d above , t he most updat e d mod e l for the -."aste p < ce r r e cycling syste m in Jap an is o b tai ne d , as s h own in Fig . 2. The d e tailed math e matical exp r ess ion of t h is model is given in App e ndix 1, and t he ~ean in g of each equation is e xplained i n App endix 2.
From this contracte d mathemati c al model s hown in Fi g . 3 , th e values of e ac h s tat e varia b l e can b e consecutivel y de t e rni ne d by pe rfoming the calculation according to t he step s di · r ecte d by the arrows in th e fi g ur e .
SPi ULATI ON Bas e d on t: ,,· d y namic mod e l d e v e lope d in t he previous sect i on , t o,. calculation for t l~ e simulat i on is p e rformed for th e p eriod of th e p ast ten years (from 1968 t h roug h to 1977). The calculate d valu e s fro m t he ~o d e l ar e comIt i s p are d to the availab le r e al d at a . la t e r s h o~n t h at t hey agr ee qu i te ~ e ll wit h e ac h oth e r. Judging from t h i s good a g r eeme nt , it may safely b G s aid that th e ca lculat e d valu e s o f the state varia bl .s t h e r e al da t~ of wh ic h ar e ~ o t ava ila b l e cou l d be a fairl y go od es tiMati on o f t ;-: e :::,a s t. r o f L -:esc: varia l:: l e s . ,"l"
7h e valu e s of t he ~a r a~ e t e r s a ~~ e xt e rnal i np uts (e xogenous vari ab l e s) US Gd in th e sinulation calculati o:, ar e sh o~ ~ i ~ ~ rpe njix 3. T~~e
ove r
for e casti~ g o ~ fro~
~ ~~e
~utu~ c
~ r ese~ t ~ ~
t:1e
; 'e rf o r:-1 e d b":-' c a rri:)~
O 'Jt
to
tr end
ra~ g i ~g
~:SC ~ . ~ .
is
t:-.e s i:-:-::.ll ation f o r
t:-. e s e v e ral cas es '..::~e r e t:~ e a ssu::'l: tior,s o~ t~ e futur e e sti ~ ati o ~ o f ~ a ~~' e c o~ o~ic and s oc ial factors ar e c~ a n g e j . The annual ir,c r -2a s es i;: - :- e x ogc :10'J.S va r i a bl es gl fActual g r o s s nationa l e X P G~ditur e ] ~~ ~ 9, [~ct',Jal ; r~vat e ?la~t anj e ~ui9~ e ~t ir.\;!2 sE::1e :lt] :J!:-
j a sed o n By e l im i nating auxiliar y state variabl e s Xi (i =1 - 23) in the math e matical e xp r e ssion of t h e model , the' at ",<'!'la ti ca l structure of t'1 e model
:
t~1 e
e sti~at e d as
ar.:l ua l
0 c o ~o:-:-:i =
S:-.O",-::--. i1. -:a ;:' l e 1 , g r o ~t~
rat e
f o r e cast ed jy :' :-.12 Ja ;:~ ar. e s ·~ go \"e r :1:-l-2 :-.t :s. :1j
e conon ists.
t: ':e
Waste Pa per Recyclin g System·in Japan
--"
/ SIPP PJ
)
Fig. 2 Waste paper recv_ c 1·~ng model I.A .A . - T
273
T. Takama t s u e t al .
274
exte.nal variables g. (T) (i=1,2) 1
~ZlO=[kl/(l-kl)fl(gl,gZ) Z4=(Z3(t)-Z4)/PIZ
~
Y3- Z 3(t)-Z4(t)
~Z3 PZf1(gl,gZ)/lOO
YZ=a Z (t)+b Z (t)-z3(t)-yZ
where a Z (t)=k 7 z 31 (t), b Z (t)=k 33 F 1 (z3)'
zZ=aZ(t)+bZ(t)-YZ(t)
+[kl/(l-kl))fl(gl,gZ)~ r l z -a (t)+b (t)-y (t) 1 1 1 1
where a,(:)'[p",(g"g,)/100)/(l-k,), and b
1
(t)-k Z3 F (zZ) 1
y
~Zg=zl(t)f3(gl,gZ,gS,g6)
Z9=z4(t)-zS(t) 1
and z31=(z3(t)-z31)/P14
Yl = a1(t)+b1(t)-zZ(t)-Y 1
~
z7=zl(t)f Z (gl, g Z,gS,g6)
zS=a 4 (t)+k (b (t)-Y4(t)) 6 4
(j=3,4,S,6)
g j (t)
4 =a 4 ( t)+b 4 (t)-z6(t)- Y4+(1-k 6 ) ( Y4- b 4(t)) YS=aS(t)+bS(t)-z 7 (t)- YS+(1-k 6 )( Y4 - b4(t))
~
where a s (t)=F 1 (z7)' b S (t)=k S3 F 1 (z7) a 4 (t)=z4(t)f 4 (g3,g4)
z6=a S (t)+b
(t)-YS(t) S +(1-k ) ( Y4(t)-b (t)) 6 4
and b
4
(t)=k
F (z6) 43 1
I
where fl(gl,gZ)=~P3+P6)gl+(P4+P7)gZ+(PS+Pg))/lZ, fz(gl, g Z, g S,g6) = [gS(P3g1+P4gZ+PS)+ g 6(P6g1+P7gZ+Pg))/lZf
1
,
f 3 (gl, g Z, g S,g6)=(1-P 11 f 1 )/PIZ' f4 (g3 ,g4)=P9+ (PI0/100) (g4/gS) /16, "" i-I Fl ( Zj ) = i h (S/6) Zj (t-i)/6 Fig. 3 Compu t i n g p r oced ure f o r th e equ3 t ion s of th e mod e l Tab l e The va l ues be t wee n Es t ima t ed Val u es 19 79 and 1989 are es of gl an d g 2 timat e d by taking into account the ye a r l y g2 gl Ye a r change in business tr e nds. The va l ues 1.708 10 .81 19 78 after 1990 a r e esti 1.911 11 .84 19 80 mat ed under the as 2.134 13.03 19 82 sumption tha t the eco 2.40 2 14.54 19 84 nomic growth rat e is 2.6 20 15 . 84 19 86 constant . 3.00 2 17.78 19 88 3 . 38 6 19.5 8 1990 As fo r the parameters, 3 .7 33 21. 38 1992 (1) p and P2 [Sea4.115 2 3. 35 199 4 1 sonal ind i ces of pape r 4.5 37 25.50 1996 p roduction and p a pe r 5.00 2 2 7 . 84 1998 consumption,respec 30.41 I 5 . 515 2000 tive ly ] a r e f i xe d as 13 p = p = 100 . Sea (10 y en/ yea r) 1 2 b at ~" on ~ s not tak sonal pertur e n '~nto account. (2 ) p . (i= 3- l 4) [Reg r ess ion coef fi cients ], kj (j~2 -S ) [ I nventor y - sa les ratios ], k [Coeff i cient of inventory adjustmen t a~ th e recove r y trad e r] are a ss umed to be the same as in 19 77 . (3) Since the pape r p r odu c ti on is estimat ed to become 2.87 times the p re sen t d ur ing th e 22 yea rs fr om 1 978 through to 2000 , k7 [?he
adjustmen t coe f fi c i e nt of est imated p a pe r sh i pme nt from t he manufacturer] i s calcu l ated as fol l ows , i. e .
(k )264 /P4 = 2.87, 7
k7 = 1. 00802 The f o l lowing clssumptions are se t out i n t he simu l ation o f t hree c as es . Ca se I (1) Th'2 upper l i Mit o f che r ec0ver,' rat e e f was~e pape r (S)2 i s 50 %, i. e.
S::: 50(%).
(2) The actual p a pe r e xp, Ht rati o (k ) i s l kep t at the p re sen t l e vel , i.e .
0 . 0 2 4.
(3) The actual waste pape r p ric e (g4) changes in the fo llowing f o ~~ different wa ys .
---------------- .----2 S [r ecove r y r at e of waste p a pe r ] is d8 f i ned by the ratio of (z4 /zS)X 100 .
Waste Paper Recycling System in Japan 3 Letting the time origin (t =0) be J a nuary, 1978, (No.l) g4 is constant after 1 9 79. i.e. (No.2) g4
is import e d wh e n the i nv e ntor y - s al e s rati o (= Y4/z6) b e comes l e ss than 0 .1 5 [month)
g4 = 14.13 + 0.05887t
(No.3) g4 becomes 2 times during 10 years. i.e.
g4 = 14.13 + O.ll77t
(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 pape r for paper Production (g5) increases by 0.008% per a nnum. 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. i.e.
(NO.2)
a = 0
(No. 7)
a = 2. 5
(No.8)
a = 5. 0
( No . 9 )
a = 7. 5
g4 = 14.13 becomes 2 times d:.lr ing 20 years.
i.e.
i. e.
275
g
6
= 0 .731 + 4.333 x 10-4 t
Case n (1) The net paper export ratio (k ): l kl = 0 . 0 2 4 (2) The actual waste paper price (g4): g4 becomes 2 times during 20 years. (3) The waste paper recovery rate (S) c hang es in th e following ranges: (No.2) S ~ 50 (%) (1978-2000) (No.5)
S ~ 50 (%) S 5 55 (%)
(1978 - 1 984) , (1985 - 2000) ,
(NO.6)
S 5 50(%) S 5 55 (%)
(1978 - 1 984) , (1985 - 1990) ,
and it increases by 5 % for 1 0 ye ars after 1990.
In Cas e I, the e ff e ct of th e wa s t e paper p ri c e trend on the waste paper supply trend which is anticipated to incr e as e according to the ra p~ dly rising demand for paper under the assump tion that the uppe r limit o f th e r e c o very rate is fixed at 50 %, is made cl e ar . In Case n , th e effect on t he wast e p a p er supp ly trend of changing the upper limit of th e wast e pap er recovery rate is analys e d. In Cas e nr, wheth e r or not waste paper import will be e ffective a s a measure for making up for th e shortage of the waste pape r supp ly which is antici p at e d to occur in the futur e is e xamine d.
RESULT AND DISCUSSION
4- 1 Confipmation of t he model by compa pi s on with the pea l data The comparison of the calculated zl [Amount of paper production), z6 [Amount of waste pape r purchased by the manufacturer] an d Y5 [Inver:-. tory of waste p a p er 1n the ma nu facturer) wl t n the actual data is shown in Fig . 4 . From th e se results of the simulation, it is safe ly con -
].6r---------------------------------------------------------~
1.4
0.6
Case nr (1) The net paper eXFo rt ratio (k ) : l
0.2
kl = 0. 0 ~4
(2) The actual waste p aper p ri ~e (g ): 9 bec omes 4 2 times juring 20 years . (3) The upper limit on ;:he '.va st.e pape r r ec cJVe r y rat e (S) i s kept at 50 %. i.e.
o
1968
Fig. 4 Comparison
S::: 50
(4) As for the import policy of waste p aper, the following cases are considered. That is, a % of the estimated purchasing amount of waste paper in the manufacturer 3 The unit of time
t
1970
is measured in months
1972
Year
1974
1976
1978
of calculated values and real data
cluded that the model d e v e lope d her e is confident.
4- 2 The calcu lated values of' trre "XlY'-!.::li:;&es the pea l data of '.Jn i cn ': ~ . , :r ;: _ ;, ;;:~;] ;an-:; An advantage of utilizing this kind of mathe matical model i s that it is possibl e to estimate the variabl.' s th e real data of which are
T. Takamatsu e t al.
276
not available, by using the calculated values from the model. As an example, the es timated values o~ z (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~der] are shown in Fig.5. z4 and Y3 represent the same tendency
1(10 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 t h 'J recovery rate by consolidating the structure of the waste paper collection system; (iii) To compensate for the domestic shortage of h:as te papt..:r by importing it from abroad.
1.8 In order Lo evaluate the availabili t"· of such neasures
o
1968
1970
1972
1974 Year
in thier changes. Since z has the first order time lag with respeci to z3 (Amount of paper consumed by households], y shows a larger increasing tendency when ~ompared to z . (See Eqs. (3) and (8) in Appendix 1] Both z4 and y increased yearly up to 1973 along w~th the 3 rapid incrase of z . After the oil crisis of 1973, however, th~y once dec r " a sp d and then became almost unchanged. At present, they have shown a gradually increasing tendency. Until 1975, z_ also shows the same , :0 trend as z4 Slnce the recovery rate of waste paper remalned almost unchanged, and consequently z9 increased annually. After 1976, z has been increasing and, therefore, z is 5 . 1 y decreaslng. ' constant or s l'l<:int r,o uy"; l ', 9speaking, Y4 is almost constant, though it shows small monthly perturbations. This tendency is probably attributed to the fact that recovery traders have very limited stock yards. On the other hand, the total stock of waste paper at the manufacturer is increasing annually compensating for the insufficient stock capability at the recovery traders.
4-3
FOY'ecastin:; of the futw>e tj't?Y!.d
As for the anticipated rapid rise in the demand for waste pap er as a raw material according to the increase in the deman G for paper in the future, an apprehension is ofte n expressed as to whether or not it is actually p~ssible to supply the amount of waste paper to meet demand. In such a situation, the
and to assess the environmental impacts which would result from the execution of these measures, it is indispensable to quantitatively forecast the future demand for the ",ast e paper by using such a dynamic model as developed here and to carefully examine the forecasted results. In this section, the results of 1976 1978 the many simulations used to forecast the future trend of waste paper utilization at the manufacturer are s>-'o'""n and changes of the amount of waste paper collected, the dome: stic inventory of waste l:-'a per and the amount of waste paper disposed of as refuse are estimated assuming that these three measures are implemented in the future. In Fig.6 the simulation results of Case I where only the price of waste pap er is steadily increased by limiting the recovery rate within 50% are shown. From this figure, it is clear what will happe n in tc.e suppl y of and the demand for waste l 'd per, and how the amount of waste i"a per disposed of as refuse will change. This figure s h ows that th e supply of waste i a p e r cannot catch up with its demand, and the time will come sooner or later when the d omestic inve ntory of waste paper bec o mes zero, no matter how hig h the price of waste paper would be increased. The ~ ~ ount of waste paper disposed of as refuse increases more and more. Fig.7 show ~ the simulation results of Case TI where the recovery rate is increased by consolidating the structure of the collection system. In this case , it is clarified that the shortage in the supply of waste p aper would not occur until 200 0, if the upper limit of the recovery rate ~ould q r adua ll v increase up to 60 %. The increase ratio of the amount of waste paper disposed of as refuse is also s mall compared to that Case I.
277
Waste Paper Recycling System 1n Japan Fig.8 sh,..,,'s the r esults of Case nr whe r e the was t e p aper is imp o r t ed from abroad i n o rder to compensate f or th e domestic shortage. As shown in th i s figure, t he import of waste pape r can delay the time when the shortage of t he supply will s tart to occu r, but it r esu lt s i n large fluctuati ons in the inventory of waste p a pe r. Mo r eove r, th e amount o f was t e pape r disposed of as r e fu se is ve r y large as i n Case I, which r es ult s i n some env ironmen tal po llutio n prob l e 'Tls. From these viewpoin t s it i s not good to d epen d on the import of was t e pape r in or der t o p r even t sho rtage in the supp l y of waste pape r. Judging from t he r es ult s mentioned above , it can be easily unde r stood that the most e ffective and desir able countermeasure t o ove rcome the antici p ated sho rt age of was t e pape r s upp l y i n t he futur e is t o inc r ease the r ecove r y rat e of waste pape r up to 60% by consolidat i ng t he co ll ec tion system .
x106 ton 2.0 1.8 1.6 1.4 1.2 1.0
o
1978
'85
'80
'90
'95
Year
2000
Fig. 6 Forecasting of Y4' z6' and z9 in case I
x10 6 ton 2.0 1 .8
z6(No.6)
h0
IV\
1.6 1.4 __
1.2
~,
5
)
'9(No.5)
1.0
0.6
2xY4 \(NO .2)
0.4
\
\ \
\
0.2 01978
(No. 5)
/'<'
0.8
\
'80
'85
'90
Year
'95
2000
Fig. 7 Forecasting of Y , z6' and z9 in case II 4
CONCLUSION I n this r eport , t he waste p a pe r r ecyc li ng system is taken up as a concrete example of a resource r ecycling sys t em . A dynamic mode l ,vas developed and , based on this mode l, the q uantitative assessmen t o f several measures for p r even ti ng the anticipated sho rta ge o f the supp l y of waste pape r i n the futur e i s per f o rmed , The bas ic structure of t he model developed is b a sed on th e mate r ia l b alan ce sho~TI in Fig.l. By taking into account many con trolli ng and
i n flu encing fa cto rs and adding trrrr to th e bas i c mode l as in f o rmatio n flows, the who l e mode l structu r e was g radua ll y devel o, 'ed , and finally obtained as shown in Fig.2. The fundamen tal structure which is obtained by r ea rranging the model equations according to t he direction of the information flo ws , is shov.'J1 in Fig. 3. As is c lear fr Gm t h is fi g ure, the p r ocedur e for the simulation calculation p r oceeds from the exogenous variables r elated to economic factors t o t~8 opposite dir ect ion of the material flo w. The p rameters i nc lud ed in the model ar e
T. Takamatsu et al.
278 es timat ed fr om the real data , and the conf i dence of th e mode l is confirmed by compa ri ng the ca l cu l ated values fr om the model with th e r e al dat ~ ranging o v e r 1 0 ye~r ~ , (Fig . 4 . ) The mode l is first utiliz ed for pre dicting th e change of state variables th e r ea l data of which a r e not avail a b l e. (Fig. 5) Then , it i s used to quan titative l y assess thr ee measures for p r event ing th~ an ti cipated shortage of t he s upply of waste p a pe r in t he fu ture .
>110 6 ton 2.0 1.8 1.6 1.4 1.2 1.0
0.6
____
'
I
.~ \/\VJ.:iIAtV/~:· ,
\ ,
0.4
\ \
2XY 4 (NO.2\
0.2
\'V1\
;\\:\ ,1\
V , , !' ii: V\ \
:i ,I
'-'\
\
~No.7l
(NO.8~
r,
\ ' ,
/ V
~
i
°197~8~1-8~0~~~~'~85~~~'~ \ ~19~0"~~~'~9~5~~~·2~000
Year Fig. 8 Forecasting of Y4' z6, and z9 in case III
Fr om the r es ult s of th e s imulatio n (Fig. 6-8 ), i t was c larifi ed that the i ncrease i n the r ecovery ra te of Case IT i s the most desirable among these thr ee meas ur es. Th e sys t em a pp roach based on th e quanti ta ti vc mode l as shown in t his p aper , cou ld be ve r y he l pfu l in e valuating and as sess ing many dif f e r ent !:,e asur e s intorduced to r eso lve i ssues not only in was te pape r rec yc lin g s ys tems, b u t also i n many o th er larg e , comp l e x, r e sources recyc li ng systems .
APPENDIX 1 MATHEMATI CAL MODEL (a) Equations r e late d t o Yi
(i=1 -5 )
dY (t) l - - - = z l (t) - z2 (t) dt
(1)
d Y2 (t) - - - = z2 (t) - z3(t) - z l O (t) dt
(2 )
dY3( t) ACKN ,.lh"LEDGEMENT
dt
z3(t) - z4 (t)
(3)
z5 (t) - z6(t)
(4)
dY4 (t)
The authors wi s h to acknowledg e Mr. M. Arakawa for hi s va l uab l e assistance.
dt dY5(t )
~ = z6(t)
REFERENCES OECD Repo rt (1976) . " Prospects a nd Policies for I,aste Pape r Recyc li ng in th e Pulp and o f Paper Indu st r y ". Glass e r y , C . R., an~ V. K. Gupta (1 965 ). A li p ea r programming analysi s of paper recy cl ing. Stud i es i n Managemen t Science and Systems Vo l. 2. No rt h - Hol l and. Chap .1 3 , pp . 273 - 292 . Clif ford , J . S ., M. A. Laughton , T . S . McRobe rt s and P . V. Slee (1 978 ) . LP model li ng i n the p a pe r i ndustry as an a i d t o r ecyc li ng dec isions . Con se rvat i on & Recycling , ~ 9 7-1 09 . Turner , R.K., R. Grace , and D. I' . Pearce (1 978). The economics of was te : . p er r ecyc li ng . Resource Conse r va t ion , Soc ial and Economi c Dimensio ns of Recyc ling, Langama n Group Limited , London , Chap .16, pp . 296343 .
(b)
- z7 (t)
Equation relat ed t o z.
~
(5)
(i=l - l O)
zl (t)
P11 z7 (t) + P 12 z 8(t)
z2 (t )
k Z (t) 7 31
x (t) + zlO(t) 9
(6 ) (7)
1
whe r e Z has the first orde r time lag . h 31 w ~t r espect to z3 ' i. e .
dZ P14
z3(t) =
31 dt
1 12
(t) + z31 (t) = z3(t) 1
x 17 (T)1 00 P2(t)
(8 )
(9 ) Z4(t '{ P9 + P 1 0 X 20 (t) } - k x (t) (10) 6 6 x
16
(t) - x3 (t) + (1-k )x (t) 6 6
(11) (12)
Waste Paper Recyc lin g System ln Japan X13 (t)x
lS
(t)
(13) (14) (15 )
(c) Equations related to x.
(i= 1 -23)
1,00 5 i-I . 6Li= 1 (6) 27 (t-l) 1
tc27 (t-l) + SX (t-l)} l
(T)gS (t)+x
22
(T)g6 (t) } (29)
XIS (t)
x
(t)
-6l rl=. £-)65 i -I 2 7 (t-i)
(T)
x
16 17
XlS(T) x
where k (t) has the first order time lag S3 wlth r espec t to kS(t).
21
_l_{l - P 11x (t)} 14 P12
x
(16)
(T) [x
17
l
xl (t)
1
x
24 (t) - 2 5 (t)
279
x
19 20
21 k
l-~
(T) + x
1
22
(30)
xl (t)
(32)
(7)
(33)
x 17 (T)
(t)
1 1 16 1 00 g4(t)
(t)
~ x
1
g3
19
(3 1 )
(34) (35)
(t)
i. e . x (17) 2 x YS(t) - x
2
(IS)
(t)
x
lI ~
(~)i-12 (t-i)
6 "-=1 6
21 22 23
(t)
P3 g 1 (t) + P4 g 2 (t)
+ Ps
(36 )
(t)
P6 g1 (t) + P 7 g (t) 2
+ PS
(37)
(t)
x
17
(t) + xlS(t)
(3S)
6
AFPENDIX 2 l {2 (t-l) + Sx (t -l )} 6 6 4 Xs (t)
(19) MEANING OF EACH EQUATION (2 0 )1
where k (t) has the first order time lag 43 wlth respec t to k (t) 4 i. e . (20) 2 (21) 1 ,00 5 i -I ~i=1(6) 23(~ -i ) l{2 (t-l) + SX (t -l) } 6 3 7
x (t)
(22) (23) 1
i3
(24)
x (t) = Y2(t) - x S(t) 9 1 ,00 5 i-I x l O (t) = 6 Li= 1 (6) 2
i 11
2
(t - i)
2 { (t -l ) + Sxl O (t-l) } 2
(t)
(25) (26) 1
where k (t) has the first order time lag 23 with r espect to k (t) . 2 i. e . dk T ~ + k = k2 (26) 2 2 dt 23 Yl (t) -
1
x
11
(t)
(27)
1
100 P I (t)~23(T) - x 12 (t) (2S)
(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 outp ut. For examp l e , the time derivative of y [the inventory of paper at t he manufacture~ ] is equal to the difference between 21 [l'.mount of paper production at the manufacturer ] and 22 [Amount of paper shipment from the manufac turer]. Here, y. is an unknown va ri able the value of which h~s to be calculated from t he observed or es timat ed values of the mate rial fl ow 2. (t) (j=l- 7,1 0) J
(b) Equation of 2i
where k (t) has the first order time lag with re~~ect to k (t), 3 i. e . dk33 T--+k =k (23) 2 3 dt 33 3
x
(a) Equation of Yi
(i=l-lO)
Eq. (6): 2
[Amount of pape r p roduction a t th e is equal to the sum of the two values which are calculated by multiplying each yield factor Pl l and P 12 by 27 [Amount of waste pape r consumption aE th e manufacturer] and 2S [Amount of pu l p consumption at the manufacturer] , res pect ively.
manufactu~er]
Eq. (7): 22 [Amount of pape r shipment from the manufacturer ] is concurrently equal to the amount 0 f pape r pu rc hased by the ·.,; holesa l er. The wholesaler seems to for ecast his pur chasing amount by analysing t he past trend of the amount of pape r p urchased by cons\.l:" cr. He re it is assumed that t he es timat ed value of 2 , 2 , can be obtained from the diffe r . ·n tia13equ~~ion ~hich has the first order time lag ·,:ith res pect to 2 . (The time constant p is assumed to be months . ) The es timate~4value 231 is modi fi ed by multip~in~ b! a f actor k used to compens ~ te for the inade 7 quacy in this es timation. The actua l amount of p aper pu rchased by th e wholesaler (2 ) is 2 given by subtructing the variation of Ehe pape r stock at t l: c wholesdl,T (x ), due to 9
1
T. Takamatsu c: ~
280
th e invento r y adjustment , from the modified estimated value of z3 (k z ) and adding the 7 31 amount of net paper e xpo rt (ZlO)' Eq. (8): The amount of pape r puchased by con sumer (z3) is equa l to the value which is obtained by mul ti pl ~.' i "S t'i'c seasonal ind ex of pape r consumption (p ) by the average p a pe r consumption per montfi which is calculated by d i viding the annual i,ape r d e mand in the domestic ma rk u t(x ) by 12. 17 Eq. (9): The pape r p urchased by t he consumer is d i sposed of with a certain time l ag with respect to the purchas ing time. This time lag is assumed to :,' the first order '-"icos" tim" c;on,; tilllt to is on c mont!~. 13 Eq . (1 0 ): Zs [Amount of waste pa:, e r coll ec ted by the recovery trad e r] is a ~s" med to be determined by adding the term r elevan t to the inven tory adjustment to the p roduct of z [Amount of paper discbarged from househoids] and (P9+ P 1 0 x 0 ) [Estimated r ecovery rat e] . Where est~mated recovery rat e is p resumed to be a linea r fun ction of x [Auxiliary varia ble on t he waste pape r prfge] . The capabili ty of the inventory adjustment of the r ecov ery trader seems to be insufficient. Th e r e fo r e , as a coefficient to express its weak ness in adjustment aLility, k [Coefficient of inven tory adjustment in re80very trader] is introduced, and this coefficient is multiplied to x6 [Variation of the inv0 ntory of waste paper at the recovery trader]. Eq. (11): z6 [Amount of waste paper purchased by the ma: :ufacturer] is determined by sub tracting x [Variation of invento r y of waste pape r at t~e manufacturer] from x [Estimat ' 16 ea, pue:: h as~ng amount of waste pape r by the manufacturer] and adding th e supplementary amount of waste p aper which is kept in stock to compensate for t he weakness in the inven tory adjustment ability of the recovery trader . Eqs . (12) (13): z7 and z [amounts of utiliza tion of waste paper an~ virgin p ulp, re spec tiv e l y ] is determined by multi p l ying ?3 C!1 utilizatio n ratio (x ) or (x ) ~y x ["la"", d mont',l ... ' [:% ,0, r i ro~~ction]~3 Eq . (14): Zg [Amount of ',vaste p ape r disposed of as r e fus e] is the amount of uncollected ... r l~'7lo~n L 0 f i.· a: ,·-: r -ii sc:::a r q·.:c :: r ,; ;n !lOUS'~' h~ldl . Eq. (1 5) : Since z [:'lonthly n e t p aper expor t] , 10 ~s v e r y small compared to the pape r production, zlO is assumed to be constant t hought out a yea r and to be (1/12) xx [~!::. ual p a18 per expo rt]. (c) Equations of Xi
(i =1 - 23)
Equations relevant to (x ,x ,x ), (x ,x ,x ), 2 6 (x7 , x8'x~) and (XI O,Xll,k1 2) ail hav~ t~e same matnemat~cal st ructur e , and they are utilized to calculate the va riations of the inventories .
a. l .
Eq. (16) - (27): Va riab l es x. (i=1 -3) , x, (j=4 -6 ) are relevant to the invenEories of wJste pa per at the manufacturer and at the recovery trad e r s , resoectively. x (k=7-9) and x (e=1 0- 1 2) ar~ also r e leva~t to the inve~tories of p a pe r at t he wholesale r and manufacturer, r espective l y. The average monthly utilization of paper or waste pape r (x., i=1,4,7,lO) is calculated by smoothing the Bast r eco rd in such a way that th e older t he data is , the smaller is the coeffici e nt weighed ~y us ing an exponential type of wighting function. The standard value of each inventory of paper or waste paper (X i ' i=L , ~;, 8 , 11) is expressed by th e p r oduc t of tne average utilization of p ape r o r waste paper and the average inventorysales ratio of pape r or waste paper (k ,k , S 4 k3 , k ) . 2 Iffien the average inventory-sales ratio changes, it s change does not directly cause the varia tion of the standard level of the inventory, but its influenc e 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 was t e p aper (x" i=3,6,9,12) is tae difference between the acEual inventory (Yi' i=S,4,21) and i ts standard level. Eq . (28): The planned month l y paper p roduction (x ) is given by sub tracting the var iation of 13 , ' t h e lnventory due to t h e lnventory a d'Justment f e om the p roduct of the average planned month ly :' a p( r p roduction (x /12) and the seasonal 23 ind e x of paper productlon (Pl)' Eventually, this value becomes equal to che amount of paper p roduction at the manufacturer (zl) ' Eq~(29) :
The utilization ratio of waste paper for pape r and board (x 4) is obtained by di vidi ng t', e. "urn of t", l' ewo products by th e annual demand for all kinds of paper. The first prod uct is obtained by multiplying the annual demand for pape r by the uti lization rati o of waste pape r for paper production (gsL and the second is the annual de:-:,a nd for board multiplied by the uti li zation ratio of waste pape r for board p roduction (g6) ' Eq . (3 0 ): The utilization ratio of virg i n pulp for p a p er and board (x 5) is obtained from Eqs. (6), (12), (13) and ehe condition that zl=x 13 · Eq . (31): Estimated amount of p urchased waste paper by the manufacturer (x ) is obtained by lp soomthing the pas t value of cne amount of co: ~ sum p tion of waste pape r z7 (t - i) with an exponential type we ighting factor. Conse quently, this value is equal to the average value of t ",-- waste pape r consumption at the manufacturer (x l)' El{ . (32) : .7,nt,ual domestic consumption of paper and board (x ) is the sum of the annual 17
Waste Paper Recycling System In Japan domestic consump tion of pape r (x ) . 22
(x
2l
) and board
Eq. (33): Annual paper export (x lis the net balance defined by the differen~~ be tween the amount of export and that of import. This value i s calculated from Eq. (3S) by using the net paper export ratio kl (=x /x ). lS 23 Eq. (34): The price index of was te paper (x ) 19 is the ratio of t h0 waste paper p rice trena (g ) with respect to th e p ric e in 1 970. (The av~rage price of waste pape r is ~16) Eq. (35): An auxil iary variable of the pr i c:e of waste pape r (x ) is defined by a ratio of the 20 price index of wast e paper (x 9) and the wholesale p ric e index trend (g ). lThis variable 3 means the actual trend of the price index of paper. Eqs. (36) (37): Domestic demands of pape r and boa rd are both approximated by a linear function of the actual gross national expend iture (g ) and the actual priva te plan t and equipme~t inves tment (g2)' Eq. (3S): The p lann ed annual pape r p roduction (x ) is the sum of the annual paper demand 23 (x ) and the annual paper export (x )' 17 lS APPEND IX 3
3-1 Exogenous variables Exogenous variables Table A Given Data are set up as given conditions. The Year actual gross na5.749 1.0218 , 1968 tional expenditure 6.365 1.2378 : 1969 trend (g ) and the 7.061 1.4195 1970 actual p~ivate 7.583 1. 4835 . 1971 plant and equip8.274 1.5670 j 1972 ment investment 9.087 1.8566 , 1973 tr end (g2) are 1974 8.973 1.6545 ' given by the value 9.197 1.4399 1975 per annum, and 9.740 1.4893 : 1976 th eir values are 10.248 , 1.52941 1977 given in Table A. Here "actual" means (1013 yen/year) that the pr ic e increase from 197 0 has been taken into account in the values. The whol f'! sale p ri ce index trend (g3) and the waste paper price index (g4) are g~ven as monthly values. The price of corrugated card board, which is the most utilized amon g all of the kinds of waste pape r, is taken as a r epresentat ive value of the waste pape r p ric e . The utilization ratio of waste paper for p a pe r and board (x ) calcu lated from the utiliza4 tion rati o or waste paper for p a per (g5) and t he one for board (g ), is gradually increasing up to 36-42% ove~ a pe riod of 10 yea rs, for the j?c riod of which the simulation calculation in perfo r med.
3-2 Para'!1etel's
281
[a] ~he seasonal index of pape r production (P l) and the s easonal index Table B Values of PI and P 2 of pape r con(1976-1977) sumption (P2) P2 PI 1Month are given by the monthly 1 90.8 90.5 values. The 2 92.2 94.5 values of P l 3 100.8 105.4 and p from 4 99.9 99.1 196 5 1 973 5 100.8 101.0 are constant. 6 101.5 101.0 Taking into 7 102.0 99.8 consideration 8 98.2 100.4 the influence 104.4 9 103.3 of the oil 102.3 10 . 104.8 crisis in 1 97~, 102.2 103.5 different 12 : 101.4 100.2 values are used, for 19 74 and 1 975. After1975, the constant values are us ed again, as shown in Table B.
to
I
LlL :
[bl p. (i=3-S) are regression coefficients. The r ~g ress ~on analysis is perfo rmed in order to correlate g and g with th~ real data of the domestic c5nsumptfons of paper and board. By using the r eg ression coefficient obtained, annual demands for pape r and for board are e stimated. The regression coefficients are obtained as follows; P3=566,OS, P4 =1415,2, P5=575.S5, RL=~.9922 P6 = 253,76, P7=2469.2S, PS=409.92, R =0.9S16 Based on these values, x. (i=17,lS,21,23) are es timated as shown in TaBle C.
Table C Comparison of the Estimated Values and the Real Data Year
Estimated x 17
1968 1969 1970 1971 1972 1973 1974 1975 1976 1977
9668 11012 12289 12965 13856 15648 14769 14119 14756 15328 (10
Real data of!, x 17 9957 11310 12973 12907 13638 15975 15646 13600 15394 15702 3
ton)
[cl P9 ' 9 : The coefficient in relation to 1 es timaged recovery rate (SI) and the auxiliary variable on the p rice of waste paper (x ) given by 20 SI (t) = P9 + PIOx 20
t~e
are obtained by the regress ion analysis o f t he annual real data. The relationship between the price of waste : ~ aper and the estimated recovery rate is very complex due to the influences of the o i l crisis of 1974 , the active c~mpaign for energy and resourc e saving since t hen , and the movement to collect waste pape r previously brought from many places to one central p lace as opposed to house by house
282
T. Takamatsu
collection. The r eg r ess i on ca l c ulation was ther e for e pe rfo~ med inde;,e nden tl y in th e foll ow ing t wo pe riods. (i) Jan.1968-Dec.1974 (ii) Jan . 1 975 -Dec .1 977 [d] P ll' P 1 2: The amount of consumption o f waste p aper and p ulp is r epr ese nted by a li n ea r function of the amount o f p roduction of p aper and board . ~he yie ld rat e i s calcul at ed from the real data ranging over 1 0 yea rs . The ave rag e valu es o f p and p a r e obtained as foll ows , 11 12 0 . 9029,
P12 = 0 . 9792
[e ] P13' P14: The time cons tants of P13 and are flxed as P 14 P 13 = 1, P 14 = 2 When P 13=P 14' z3 (t)=z (t) i s obtained from the compar l son o r EQs.i7)2 and (9 ). [f] T . (i=5,4 , 3,2): Tb" variables are all time ~onstants. They are set as T = T. l
=
3
[g] k : By taking the ave rage o f t he p ast 1 0 l ye ars, kl is obtained as kl
0 . 024
[h] k . (i=2,3,4,5): By taking into account the oI l crisis i n 1 97 4, each i nven tory-sal es ratio i s obtained as the follo wing t wo dif f e r e nt va l ues before Feb . 1 9 74 and after March 1974 by calculating t he average va l u es i n each period. pe riod
k2
k3
k4
k5
~an.1 968 -Fab.1 9 74
k . 0 . 47 0 . 34 0 .25 0 . 67 lO ~ar.1 97 4-Dec .1 9 77 kif 0 . 8 0 . 44 0 . 3 0 . 98 The actual inventory - sales ratio (k. ) is p r esumed to have t he first o rde r tiffi~ lag wi th r espec t to the step change of k . .
et a l . NOMENCLATURE A\VPCM
Average Va lu e o f Waste Paper Con sump tion at the manufacturer S~'I?IM Standard Leve l of Waste Paper Inventory at the Manufact-,urcr VIWPM Variati on of I nven tory of Waste pape r at t he Manufacturer AWPPM Average Value of Ivaste Paper purchased at the Manufacturer SWPIR Standard Leve l of Waste Paper Invento r y VIWPR Va riation of I nven tor y of Waste Paper at t he Recove r y Trader APSW Average Va lue of Paper Shipment fro m the Wholesaler SPIW Standa rd Leve l o f Paper Inventory at the Who l es al e r VIPW Variation of Inven tory of Paper at t he Wholesaler APSM Average Va lue of Paper Shipment x lO from th e Manufacturer x SPIM Standard Leve l of Paper Inventory 11 at the Manufacturer x VIPM Variation of Inven tory of Paper at 12 t he Manufacturer Planned Month l y Pape r Production at the Manufac tur e r x URWPPB Utilization Rat i o of Ivaste Paper 14 for Pape r and Board Production x UR\'PP Ut ilizati on Ratio of Vi r g in Pulp 15 for Paper and Board Production EPWPM Estimated Purchas i ng Amount of x 16 Waste Paper at the Man ufacture r x APDD Annual Paper Demand in the Domestic 17 Market APE Annual Paper Ex po rt PIWP Pric e Ind ex of Waste Paper AVl;-IPP Auxiliary variab l e on Waste Pape r Price x ADCP Annual Do mes ti c Consumption o f 21 Paper x ADCB Annual Domestic Consumpt i o n of 22 Board x PAP PM Planned Annua l Paper Production at 23 the i1anu fa ctur e r
l
i. e . k i3
k. + (k - k. )(l-exp( -~) lO If l O T.
}
IPM
is 1 for Mar. 1974.
IPW
[i] k : This i s the c o e ffi cient o f
invrntory k =1 means t ha t t he inventory adjustment i~ pe r I n the s i mu lati on , it is f ormed comp l ete l y. assumed t ha t k =0 . 7 . 6
PSH IWPR
[j] k7: During t he 1 0 y e ars fr om 1 968 to 1 977, th e pape r p roduction i nc r ease d about 1.6 times. By taking into a::count the time constant of th e delay (p ) , k is obtained from th e relations h i p (k7)li20/P~4=1.6 as follows,
PPM
where t
adjus~ment in t he r ecove r y trader.
k7 = 1.11786 whe r e P 14=2 .
Inventory of Pape r at t he ~anufacturer
l
I WP:-1
PSM PCH PDH WPCRI \VPP~l
WPGl
Inven t o r y o f Paper at the Wholesalers Pape r Stock in Househo ld s I nven t o r y of \"as t e Pap er at the Recove r y Trader I nvento r y of Waste Pape r at t he Manu fa ctu r e r Amount of Pape r Pr oduct ion 'a t t he Manufactu r e r Amount of Paper Shipmen t from t he :-lanufa c tur er Amount of Pape r Cons umed by House ho ld s Amount of Paper Di scha r ged from Ho us eho l ds Amoun t of Waste Pape r Co llected by Recovery Traders Amount of \vaste Pa p er Purc h ased by Manufact ur e r Amount of Was t e Paper Consump tion at t he M~nufactu r e r
Waste Paper Recycling System in Japan z
8
z9
VPCM WPDR
zlO NPE gl g2
AGNE APEI
g3 g4 gs
WPI AWPP URWPP
g6
URI-lPB
k kl 2
NPER I SRPM
k3 k
4
ks k6 k
7
Amount of Virgin Pulp Consumpt ion at the Manufacturer Amount of Waste Paper Disposed of as Refuse Amount of Net Paper Export Actual Gross Nat ional Expenditure Actual Private Plant and Equivment Inves tment Hholesal p. Price Ind ex Actual Haste Paper Price Utilization Ratio of Haste Paper for Paper Production Utilization Ratio of Waste Paper for Board Production
Net Paper Export Ratio Invento ry-sal es Ratio of Paper at t he Manu factur e r ISRPH Inven tor y - sales Ratio of Paper at the Wholesaler ISRWPR Inv ento ry-sales Ratio of Waste Paper at the Recovery Trad e r I SRWPM Inventory-sales Ratio of vJaste Paper at th e Manufacturer Coefficient of Inventory AdjustCIAR ment at the Recovery Traders ACPSM Adjustment Coef fici ent of Paper Shipment from the Manufacturer
Pl SIPP Seasonal Ind ex of Paper Production P2 S IPC Seasonal Ind ex of Paper Consumption p . (i=3 - 10) Regression Coe ff icients l Pll YFWP Yielc Factor of Waste Paper p YFUP yield Factor of Virgin Pulp plij=13,14) Time Constants J
RR
S
T . (i= 2-S)
Recovery Rate Time Constants
l
t 'r
month year
283