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Isse date 1996 Resorce Type Jornal Article / 学術雑誌論文 Resorce Version pblisher

1 Kobe University Repository : Kernel Title A logistics model for post-consmer waste recycling Athor(s) Ishikawa, Masanob Citation 日本包装学会誌, 5(2): Isse date 1996 Resorce Type Jornal Article / 学術雑誌論文 Resorce Version pblisher URL Create Date:

2 ]. Pack. Sci. Technol. Vol. 5 No. 2 (1996) A Logistics Model for Post-Consmer Waste Recycling Masanob ISHIKAWA* In this paper, we propose a logistics model for post-consmer packaging waste recycling (Grid City Model). This model can predict the transport distance and the nmber of trcks needed to collect post-consmer packaging waste for recycling. The parameters needed are poplation, area, waste discard nit, nmber of collection stations, size of a collection trck, freqency of collection. Tradeoff relation between the service level of waste collection and environmental load or the nmber of trcks is explicitly described in the Grid City Model. Both the nit transport distance (D/W) and the nmber of collection trcks per a nit waste (M/W) are described as a sm of the "density effect" and the "scale effect": the 4'density effect depends on the effective capacity of the collection trck (q) and independent of the waste discard nit () nor the collection, freqency (0; the "scale effect" depends on both and f and independent of q. Both D/W and M/W of sorted collection of PET bottle is mch larger than those of the hosehold waste in a typical case. Keywords: Recycling, Sorted collection, Logistics, Transportation, Model. Post-consmer waste, Introdction This paper describes the essence of or model of logistics for post consmer waste packaging (Grid City Model). The model was developed by the athor for a joint project sponsored by Japan Consmers' Co-operative Union and Environmental Agency (Anonymos, 1995), and condcted by the Nomra Research Institte Ltd. (NRI). The objectives of the stdy were to examine qantitatively the effect of characteristics of a region; e.g. poplation density, waste discard nit t on the environmental load of recycling, to compare the inventory of different recycling system; material recycling, thermal recycling, and chemical recycling. The recycling was a key problem from the early stage of LCA stdy (e.g. MRI, 1974; MRI, 1975). Among LCA stdies of recycling of postconsmer waste (hereafter referred to as PCW), transportation process has been always an irksome process: becase the environmental load of transportation in the recycling is sspected to be large and the transportation process in a recycling * Tokyo University of Fisheries, Department of Food Science and Technology, Konan, Minato-k, Tokyo, 108 Japan -119-

3 A Logistics Model for Post-Consmer Waste Recycling of PCW was sally described by a simple scenario sch as an assmption of the transportation distance; this means that reslts directly depend on the assmption. In the present paper, the athor attempts to give a clear and transparent strctre to the collection and transportation process for a LCA stdy. The present paper can be divided into two parts. In the first part, we explain the key concepts of the model, and show the explicit expression. In C.i.-:'ii parameters for a city I Social parameters Area per a recycle center (A) Tortosity factor() Poplation per a recycle center (P) Waste generation per a recycle center (W) y var:lal:lles I ;p / /// Effective capacity of a trck (q) Transport distance CD) Nmber of collection stations (N) Freqency of collection (f) v Nmber of collection trcks (M) Transport distance per a nit waste (D/W) Nmber of collection trcks per a nit waste CMIW) I alranl1eters ofcollection cdrc)(!l.:lctl.vlt;v Loss time per a station (t L ). Data: P, A, W, N, f, F, t D, D, M Fig. 1 A schematic diagram of "Grid City Model" the second part, we show how we determined the parameters based on data from 30 mnicipalities in Japan and compare the observed data and the model predictions. Model A schematic diagram of the Grid City Model is depicted in Figre 1. In this figre, each open block are parameters or variables, and arrows indi

4 ]. Pack. Sci. Technol. Vol. 5 No. 2 (1996) cate casal relationships. In the largest gray block, we collected the otpt variables; D t M, D/W, M/W. The parameters which characterize the city are in the top of the right colmn; A, S, P,W. This grop of parameters shold be given for a certain city, however, an average vale of Sfor 30 mnicipalities in Japan is given in this paper and the average vale can be sbstitted to it. The parameter in the top of the left colmn is Pi: the apparent density of the i-th waste in the collection trcks which was calclated from data on composition of hosehold waste (Kyoto-shi Seisokyok, 1994). In the bottom of the left colmn t policy variables are shown; q, N, f. We consider these variables are policy variables for improvement. We groped the parameters which relate to the collection prodctivity in the bottom of the right colmn; v p, tl' k. It may be interesting to trace the arrows start from parameters of collection prodctivity, one will find that there is no casal path between transport distance and these parameters. Althogh everyone will agree that collection prodctivity shold be a major factor in the economy of collection system, this means that the environmental load of transport is independent from the collection prodctivity. This can be nderstood if we see the waste material flow from the Lagrangean point of view; when we 0 bserve the transport distance riding on a certain waste discarded at a certain point, the distance shold depend on only state variables sch as geometric parameters. Let s consider a city which has a reglar grid type configration (Figre 2). In this city, a collection trck starts from the recycling center which locates in the center of the sqare area drives to the collection area. In the collection area, the trck collects the waste at collection stations ntil its Collection area t? Collection station < i=l i=2 L i=1 > Fig.2 The geometry of collection stations, collection canter, and grid -121-

5 A Logistics Model for Post-Consmer Waste Recycling maximm capacity: it means that a collection area is dependent on the capacity of the trck. After filling its load space, the trck retrns to the recycling center. The collection trck repeats this collection trip several times a day. The distance of a collection trip is expressed as: In eqation (1), sperscript G denotes grid city model, sbscripts 1 and 2 denote driving distance in the collection area, and the distance between recycling center and the collection area, respectively. The average vale of d can be obtained as: Similarly, the average vale of d is: (1) (2) d?:m ff (3) In eqation (3), m denotes the nmber of collection stations which can be served in a trip, A denotes area per a collection center, N denotes the nmber of collection stations per a collection center. When we consider a macro balance of waste discarded and the waste collected a year, m can be expressed by q, N, f, and Was: f q N m=--w- (4) Since A is eqal to L 2, the average transport distance of a trip is described as: do =(1 + J-).JA (5) In the above eqation, f denotes freqency of collection service. It is evident that the actal distance will differ from this vale becase the actal road configration is not a reglar grid. We introdce a factor which correct this effect (: tortosity factor). D(J = DO is given as: _ D i - (W. ) q/ + /;.../N;..[A; (6) In eqation (6), D denotes total driving distance of collection trcks of a recycling center per year, sperscript 0 denotes the observed vale. Since the total nmber of the collection trips a year is given by WIq, tortosity factor of the i-th city (7) Therefore, if we have an average vale of the tortosity factor, we can estimate the total transport distance D from the eqation below. Let s introdce poplation (P) instead of W sing the waste discard nit (). W= p When we sbstitte eqation (9) into (8) and divide it by W, we get: (8) (9) D _.(JA + L. rn, fa) (10) W- q V]JVP From this eqation, the transport distance per a nit mass of waste is a decreasing fnction of poplation density (PIA), when the ratio of the nmber of collection stations and poplation (NIP) is kept constant. l'his eqation can be interpreted as showing a qantitative trade-off relationship between the environmental load and -122-

6 ]. Pack. Sci. Technol. Vol. 5 No. 2 (1996) the service level of waste collection: when f or N increase, the service level will increase bt the environmental load will increase. Althogh the nmber of trcks (M) is independent of environmental load, it is important for the economy of the system. Let s consider what determines M. The time necessary for a collection trip (t1) is defined as the sm of the driving time, loss time (t L ), and the loading time. Assming that the velocity is constant (v P ), a certain amont of loss time is necessary per a collection station, and the loading time is proportional to the amont of the waste, we have an expression of t T as below T ;r. q N f q t =V;-+W-.tL+I (11) From mass balance, the average nmber of collection trips of a collection trck per a operation day (n) is given as: n= M F q (12) Since the prodct of nand t T is f, M can be given as below from rearrangement of the prodct. 1 {w. ( f.q) w} M =-D' _. 1+ _ IN..[jf+ j N t L +- F t q v p W k (13) Dividing eqation (13) by (9) followed by sbstittion of (9) yields: M = _1.{..[jf + f. rn. la + f ILN +l} W F t D vp q vp' V p V PP k (14) This eqation shows that the nmber of collection trcks per a nit mass of waste is a decreasing fnction of poplation density when N/P is constant. As is expected, the increase in consmer's convenience: increase in f or N, reslts in increase in M/W which can be interpreted as a sbstitte variable of nit collection cost. Identification of parameters Model parameters:, vp, t L, and k are determined by the data of 30 mnicipalities in Japan. The poplation of the cities vary from thirty thosand p to three million: 3 cities over one million, 6 cities over five hndred thosand, 12 cities over two hndred thosand, 7 cities over fifty thosand, and remaining two cities are between twenty thosand and fifty thosand. The tortosity factor of a certain city was calclated from eqation (6), and a simple average of the tortosity factor was calclated. The parameters which represent collection prodctivity: v p, t L, and k are determined by a mltiple regression analysis. In order to reflect the actal condition, the model was slightly modified for analysis. Since the nmber of trips per a working day (n) shold be an integer, n' is defined as: (15) where Ceiling(x) denotes the minimm integer which is not smaller than x. The nmber of stations collected in a collection trip (m) is expressed by n f as: (16) The actal driving distance of a trip (do) can be calclated from the observed data as -123-

7 A Logistics Model for Post-Consmer Waste Recycling below. (17) We define the effective capacity of the collection trck as: I W; qj =M(F(n/ Sbstittion of eqations (16), (17). and (18) into (11) and rearrangement yields: where and x,=df Reslts y;=m'j _ W j Zj- M,..F..n', In eqation (19), parameters sch as a,. yare identified from regression analysis from the observed data set (fr, Xi' Yi' z). Table 1 Reslts of mltiple regression analysis Vale t vale a (s/m) r2 = ** 1% significance b (sistation) ** g (s/kg) ** (18) Table 2 Velocity, Loss time, and Loading rate (19) (20) (21) The average tortosity factor was 1.52 (l>n_l=o. 703). The reslts of mltiple regression analysis are listed in Table 1. The t-vale of Pand y were large enogh to clear 1% significance. The parameters calclated from the these parameters are given in Table 2. Althogh the t-vale of ex was low, the Velocity (v) Loss time (tj Loading rate (k) 31.5 km/h 12.1 s/station kg/s vale of v p which is derived from ex, does not contradict or intitive expectation. In Table 3, we tablated the reslts of or actal observation of collection process. The observed vale of the loading rate coincided with the observation. The observed vale of velocity were somewhat smaller than the reslt of or analysis. However, considering the low t-vale of the parameter, we are satisfied that the reslt was only 50% larger than the observed vales. Matsi also observed the actal collection activity in Vji city (Matsi, 1994). He obtained the loss time, the loading time, the driving velocity between the collection center and the collection area as well as the driving velocity in the collection area. The loss time of or reslts (12.1s/station) are extremely in good agreement with the average vale (10 s/station) reported by Matsi (1994). The driving velocity of or reslts (31.5km/hor) is arond 50% larger than those reported by Matsi for drive between the collection center and the collection area, and arond 2.5 times as mch as the velocity reported for the drive in the collection area. The correlation between the observed data and the predicted from eqation (8) is depicted in Fig

8 }. Pack. Sci. Technol. Vol. 5 No. 2 (1996) Table 3 Observed vale of velocity and loading rate City Poplation Area (km 2 ) Velocity (km/h) Loading rate (kg/s) Waste Collection Transport A 73, bottle/can B 213, bottle C 213, can re 3. Considering the simplicity of the model, the agreement is excellent. The predicted nmber of trcks are correlated with the actal data in Figre 4. The nmber of collection trcks was also in good agreement with the observation. Application 1\ E+06 (1) E "" Q) 2.00E+06 rfj ;0 \-0 o 1.00E+06 c:: cd b.. c; O.OOE+OO "3 O.OOE+OO U I'"..o Actal transport distance/km year- 1 Fig. 3 Correlation between the actal distance and the calclated distance 1.50E+02 rfj OOE+02 \-0 Q). a ::i c:: "0 Q) 5.00E+Ol :; ca O.OOE+OO., Fig. 4 Correlation between the actal nmber and the calclated nmber of trcks i.,.:. O.OOE+OO 1.00E E+Ol 2.00E E+02 Actal nmber of trcks 3.00E E+02 In order to examine the environmental and economic effects of selective collection of PCW, let s calclate the actal cases and see what this model tells. We take p two cases; sorted collection of PET bottles and mixed collection of hosehold waste. Since PET bottles are one of the most blky pew, the environmental and economic effects of sorted collection of PCW are expected to be most evident when compared to mixed collection of hosehold waste. The vales of parameters we assmed are given in Table 4. The nit transport distance (D/W) and the nmber of collection trcks per a waste (M/W) are drawn as fnctions of the nmber of collection stations (N) for different collection freqency (f) in Figres 5,6,7, and 8. Unit transport distance As is expected, D/W increased with increase of both Nand f (Figres 5 and 6). However, D/W of PET bottle was larger than that of hose-hold waste for 10 to 100 times depending on both N and f

9 A Logistics Model for Post-Consmer Waste Recycling Table 4 The parameters we sed for calclation of Figres 5, 6, 7 and 8 Parameter Poplation Area Nmber of the recycling center Waste discard nit Hosehold waste PET bottle Effective capacity of a collection trck Hosehold waste PET bottle Tortosity factor Working days of the recycling center Working hors of the recycling center Vale 3,230, km kg/day/capita kg/day/capita 1,400kg/trck 110 kg/trck day/year 8 hors/day Ib(l E "' ccq E E+03 """ o 0 00 C 1::... 'a 1.00E E+02 PET 1.00E E+04 Nmber of collection stations / E+05 f= year 1.OOE+06 Fig. 5 Unit transport distance of sorted collection of PET bottle 1.00E+02r Ib() E Hosehold Waste "' Q) c=.s 1.00E+01 Nmber of collection stations I - Fig. 6 Unit transport distance of mixed collection of hosehold waste -126-

10 ]. Pack. Sei. Teehnol. Vol. 5 No. 2 (1996) Nmber of collection trcks The reslts of calclation are given in Figres 7 and 8. Qalitatively, the reslts resemble to those of nit transport distance. M/W of PET bottle is mch larger than that of the hosehold waste for 5 to 500 times depending on both Nand f. Discssion Tortosity factor In or stdy, the average tortosity factor was 1.52 (n-l=o. 703). One of the reason why the average tortosity factor was larger than nity may \0 1.00E 03 (l) >. UJ ::s ob '" 1.00E 04 UJ ::s.b = 1.00E-05 o (l) PET 1=365 year a e ::s Z 1.00E E E E E+05 Nmber of collection stations / E+06 Fig. 7 Nmber of collection trcks per nit waste in the case of sorted collection of PET bottle ' E-05 >. UJ E... U'J 1.00E-06 ::s 1:: c 3 Hosehold Waste (5 '0 l.ooe-o?... Q).0 E=' Z 1.00E E E E E+06 Nmber of collection stations / - Fig. 8 Nmber of collection trcks per nit waste in the case of mixed collection of hosehold waste -127-

11 ]. Pack. Sci. Technol. Vol. 5 No. 2 (1996) be that the location of recycling center (waste treatment center) is likely to be in the peripheral area; which will case less collection efficiency than that of the grid city model. Model performance From comparison of the model prediction and the actal data, we can conclde that, in average, the Grid City Model can predict the transport distance and the nmber of collection trcks. However, we shold be carefl to apply this model to a specific city, in sch a case, we mst acceptsomewhat large error shown in Figre 3 or 4. However, even in sch a case, the Grid City Model has advantage over simple scenario approach becase the Grid City Model can give the vale of error of the prediction. Unit transport distance D/W of PET bottle was larger than that of hosehold waste for 10 to 100 times depending on both Nand f. This indicates that the environmental merit of recycling wold be somewhat disconted by the increase of transportation. The difference between PET and hosehold waste is explained by two reasons; one is the difference of effective density (hereafter we refer this effect as "density effect") and the other is the difference of waste discard nit (hereafter we refer this effect as "scale effect"). The D/W is expressed as the sm of a constant term and a Nl/ 2 term. It is evident that the effective density affect only the first constantterm, therefor this term describes the "density effect". The fact that the "density effect" appear only in the transport between the recycling center and the collection area, and not in the transport in the collection area looks to be pecliar. This is becase that the total transport distance in the collection area can be described only by the total waste discarded: nder a give collection freqency, one can calclate the nmber of collection stations that shold be collected in a day, this means that the waste discarded in these stations in a day shold be collected in a day no matter how blky the waste might be, and this reqires that the collection trck shold visit all the collection stations in the area. Therefor the transport distance in the collection area is determined from only location of the collection stations. Similarly, the waste discard nit () only affect the second term in eqation (9). The reason why we call this as "scale effect" is that this term expresses the scale merit of collection. Consider the extreme case that the amont of waste discarded in one collection station is eqal to the effective capacity of the collection trck, it is evident that the transport distance in the collection area shold be minimal vale of nll. The balance of these two effects depends on cases. In general, if the waste discard nit () is large or the collection freqency (t) is small, D/W wold be mostly determined by the "density effect", and D/W wold be almost independent of the nmber of the collection stations (N) nor the collection freqency (f); this is the case of hosehold waste collection (Figre 6). On the contrary, if the waste discard nit () is small or the collection freqency (t) is large, the "scale effect" wold dominate in eqation (10), and D/W wold increase with the increase of N and f; this is the case of sorted collection of PET -128-

12 A Logistics Model for Post-Consmer Waste Recycling bottle (Figre 5). Please note that the asymptotic vales in Figres 5 and 6 are determined by the "density effect". Nmber of collection trcks M/W of PET bottle is mch larger than that of the hosehold waste for 5 to 500 times depending on both Nand f. This means that the sorted collection of PET bottle reqires mch larger cost than the conventional hosehold waste collection. It is evident that the increase in cost cold be redced by a simltaneos collection of several selected wastes; since this increases the waste discard nit (). The difference between PET and hosehold waste can be similarly explained by the "density effect" and the "scale effect". The "density effect" of M/W is defined by the first term of the eqation (14), and the "scale effect" of M/W is defined by the sm of the terms except the first terms in the eqation (14). In the case of M/W, since the "scale effect" incldes a term proportional to N, M/W increases mch faster with increase of N compared with the case of D/W (Figre 7). between the service level of waste collection and the nmber of collection trcks are explicitly described in the Grid City Model. Both the nit transport distance (D/W) and the nmber of collection trcks per a nit waste (M/W) are described as a sm of the "density effect" and the "scale effect": the "density effecf' depends on the effective capacity of the collection trck, and independent of the waste discard nit () nor the collection freqency (0; the "scale effect" depends on both the waste discard nit () and the collection freqency (f), and independent of the effective capacity of the collection trck. Both D/W and M/W of sorted collection of PET bottle is mch larger than those of the hosehold waste in a typical case. Acknowledgment The athor wold like to thank Mr. Kanamori and Mr. Motokawa for observation of the actal collection. Part of the present work was financially spported by Japan Consmer's Co-operative Union and Environmental Agency. Conclsions A model (Grid City Model) was developed, which can predict the transport distance and the nmber of collection trcks from data sch as poplation, area, tortosity factor, waste discharge nit, nmber of collection stations, size of a collection trck, and freqency of collection. Trade-off relation between the service level of waste collection and environmental load, and References 1) Anonymos: 'Hoso haikibts no risaikr ni kannsr teiryotekibnnseki (A Qantitative analysis of the post consmer packaging waste re cycle)'; Working Grop and Nomra Research Institte, Ltd.; Tokyo (In Japanese) 2) Kyoto-shi Seiso-kyok (Cleaning Brea of Kyoto): 'Gomi Saisosei Chosa Hokoksho (Report on detailed composition of waste) '; Kyoto-shi Seiso kyok; Kyoto ) Shoichiro Matsi: 'Chtoshi ni oker gomi no -129-

13 ]. Pack. Sci. Technol. Vol. 5 No. 2 (1996) haishts oyobi shsh no gennjyo ni kannsr kennky (A research on the present stats of the waste discard and collection in medim size city) '; Gradate thesis of Department of Hygiene Engineering, Faclty of Engineering, Kyoto University, ) MRI: 'Resorce and Environmental Profile Analysis of Nine Beer Container Alternatives': MRI Report MRI Project No. 3794D; ) MRI: 'Resorce and Environmental Profile Analysis of 10 Beer Container Systems': MRI Report MRI Project No D; 1975 (Received 1 November 1995) (Accepted 25 Janary 1996) *)(i, *n'?,tjtfjn.q'21m_c7) I) -+)-.{ 7 }vc7)tc7)m-t7tjv (Grid City 9i, AD, fffifl, _4tmt.ijltiL, Aj--:/3 /fi, 1&, 1&mMl-C:o mo)-tt-t:' A* cjj±jlfjj, JBlijiO)raO)l' 1/- '*7 ij{:' o):f:r)li'j:. -:> LBjl'2x-5 nt:o Wt_ O)MiZii ti (D/W) c_ O)m_-Er (M/W) i!;1.lcm':bt1 ::. ctj{t!t:.o S!,;t, l&1flo)fffluo)'i, mmj!'i, _Jjjl1f1Ulc, IN mblt-c* <!:ij< nt: o!it!t 1tJJr- A,:S\""( PET rf{ JvO)Jjj]IJJNmO) D/W c M/W ';I:, c b':1i!*_o)tmjnm'jtllimtj"*tj'-:>to * *** (=r 108 timt&ii1 i4-5-7) Model) mt o :'O)-cr}lI':n'!, _i _c_jffij731.ij-c:o tj){7 j

A buyer seller game model for selection and negotiation of purchasing bids: Extensions and new models

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