Optimal planning of selective waste collection

Transcription

1 Sustanable Development and Plannng V 78 Optmal plannng of selectve aste collecton S. Racu, D. Costescu, E. Roşca & M. Popa Unversty Poltehnca of Bucharest, Romana Abstract The paper presents an optmsaton method for selectve aste collecton servces n unversty campuses n Bucharest. Based on geographc nformaton system (GIS) procedures and algorthms, an optmsaton method for selectve aste collecton servces s developed. The area of Bucharest Cty, the road netork, the locaton of the selectve aste collecton ponts n the man unversty campuses and the locaton of the collecton staton are organzed n GIS format. Complex geodatabase structures that allo solvng the large scale selectve aste collecton problem are desgned. The routng soluton that mnmses the total travel tme s determned takng nto consderaton the local road netork propertes and the locaton of the collecton staton for each category of aste (glass, paper and plastc). The methodology s appled for the man Unversty Campuses n Bucharest. The map th the routng soluton, the requred number of vehcles and the schedule for each category of aste and for each vehcle are obtaned. The developed method provdes nformatonal and technologcal support for publc authortes and selectve aste collecton operators. Keyords: selectve aste collecton, optmsaton, vehcle routng, schedulng, geographc nformaton system. Introducton The problem presented n ths paper s from a study carred out for the selectve aste collecton management system n unversty campuses n Bucharest. Wth over students, Bucharest s the greatest natonal unversty centre of Romana. There are over mportant unverstes th academc, admnstratve and resdental actvtes organzed n campuses spread out n dfferent areas of the cty. The campuses have dfferent organzaton systems, accordng th the structure, locaton, tradton and evoluton of each unversty. Due to the large WIT Transactons on Ecology and the Envronment, Vol 0, 20 WIT Press.tpress.com, ISSN (on-lne) do:0.249/sdp06

2 786 Sustanable Development and Plannng V number of the student and employees n all these campuses, selectve aste management s essental for mnmzng the mpact on the envronment. Snce 2006 the muncpal authorty n partnershp th aste collecton cooperatves and assocatons has been developng a selectve aste collecton management system. For the perod February July 2006 a plot project as appled for selectve collecton of paper, glass and paper n the area of Unversty Poltehnca of Bucharest. In that stage ere collected about kg recyclable astes, from hch 2000 kg paper, 7000 kg plastc and 3000 kg glass. Snce then the system has been developed n other campuses. Fgure shos the ncreasng volume of selectve aste collected n unversty campuses tonnes Paper Fgure : 2008 Plastc Glass Volume of selectve aste collected n unversty campuses. In order to ncrease the effcency and effectveness of the selectve collecton system, optmsaton methods are necessary for servces plannng. In ths paper e descrbe methods for vehcle routng and collecton servce schedulng. Examples for campuses located n one of the sx admnstratve sectors of the Bucharest are gven. 2 Selectve collecton model overve The optmsaton of selectve collecton servces mples solvng transport routng and schedulng problems. The objectves of these to combnatoral problems consst of mnmsng the total haulage tme, the fleet sze, the transport costs or an aggregated functon of the above mentoned. The problem s defned on a graph G ( J, D), here J K L ; K k, k2,..., k N s the vertex set ncludng the collecton aste centres or arehouses for paper, plastc and glass and L l, l2,..., lm s the vertex set ncludng the selectve collecton ponts here blue contaners for paper, yello contaner for plastc and green contaner for glass are located. The arc set s WIT Transactons on Ecology and the Envronment, Vol 0, 20 WIT Press.tpress.com, ISSN (on-lne)

3 Sustanable Development and Plannng V defned as 787 D (k, l j ) k K, l j L (l, l j ) l, l j L, j. Each arc has assocated a non-negatve value t j representng travel tme. Each selectve collecton pont l has assocated a non-negatve value t p representng the aste contaner pckng tme. Three contaners (for selectve paper, plastc and glass aste) th the capacty Vsel 3 m 3 are located n each collecton pont. On a sngle route, a vehcle can collect three contaners for the same category of aste (Fgure 2). Dfferent contaner fllng ntenstes are regstered for each type of aste. Therefore each selectve collecton pont has assocated a set of pckng perods T,2,3, here = for paper contaner, =2 for I plastc contaner and =3 for glass contaner. l k l2 l3 k2 l4 l l6 unloaded trp loaded trp Fgure 2: Examples of vehcle trp. The Vehcle Routng Problem (VRP) nvolves fndng a set of routes, startng and endng at one collecton centre, hch servces a set of selectve collecton ponts. The objectve functon s to mnmse the total travel tme. Let Z,2,..., Z max denote the set of trps that satsfy all the collectng demands for all categores of aste. The routng phase can be mathematcally expressed as: 3 N M M M Mnmze z z zj t j zj t j () z Z j j subject to 3 z Z z Z max WIT Transactons on Ecology and the Envronment, Vol 0, 20 WIT Press.tpress.com, ISSN (on-lne) (2)

4 788 Sustanable Development and Plannng V 3 N N z Z zj z max T z Z T j N (3),,2,3 mn T max T (4),,2,3, j,2,..., M () here z : decson varable; z f the trp z s planned for the aste ; z 0 otherse. : decson varable; z : 0 otherse. decson varable; z f zj : otherse. decson varable; zj f the centre k collect category of aste; the trp z starts from centre k and z 0 f the trp z serve the pont lj and zj 0 otherse. The objectve functon () measures the total travel tme of the system. Equaton (2) expresses the trp allocaton on aste category collecton. Relaton (3) s a constrant related to the type of the collecton centres. The restrctons (4) and () express the demand satsfacton restrctons. When for each collecton pont, a tme nterval I mn, max for pckng operaton s settled accordng th the locaton n the campus (facultes and admnstratve buldngs area or student resdental area), the problem turns nto a Vehcle Routng Problem th Tme Wndos (VRPTW). Bodn [] presented an overve of VRPTW optmsaton methods. In the case of selectve aste collecton presented n ths paper, a geographc nformaton system (GIS) model s developed for solvng VRPTW. Allocaton and routng procedure avalable n ArcGIS Netork Analyst Extenson are used. The secton 4 provdes a descrpton of the logcal structure desgned for the GIS model. In order to solve the VRPTW, e have to schedule the collectng trps accordng th the perodcally demands. The problem deals th fndng the subsets of collecton ponts, hch have to be served at the same tme. The next secton presents an algorthm for selectng and orderng the sets of selectve collecton contaners, hch are to be processed on a task. The algorthm s appled for each aste category and for the gven set of pckng perods. WIT Transactons on Ecology and the Envronment, Vol 0, 20 WIT Press.tpress.com, ISSN (on-lne)

5 Sustanable Development and Plannng V 789 Vehcle routng problem s solved for each aste collecton centre and for each set of contaners obtaned as soluton n schedulng algorthm. Fnally, the detaled vehcle schedules are calculated, th respect to the tme ndo constrants. 3 Collecton plannng algorthm Dfferent determnstc schedulng methods are developed for practcal applcaton (Martelo et al. [2]). The problem of schedulng contaners pckng operaton needs a pecular approach. As mentoned before, the sets of pckng are gven for contaner locaton l L and for each category of perods T selectve aste,2,3. The frst step conssts n dentfyng the subsets of collecton ponts th smultaneous demands for a selectve aste category (Fgure 3). We descrbe belo the algorthm bult for solvng ths ssue. T T2 T3 l T T T3 T2 T22 T23 l2... lm T 2 TM TM2 TM3 TM TM TM2 TM3 λ2 λ Fgure 3: tme Gantt chart of pckng perods. We consder the follong parameters:, 2,..., M here,2,3 s the tme hen n the locaton l the contaner for the aste The vector of collectng tmes and have to be collect. The due date parameters j representng the tmes hen collecton operaton has to be processed for the aste. The set of tasks j ncludng all locaton lk hch have to be served at the tme j. The set of schedulng perod T,,2,3. max WIT Transactons on Ecology and the Envronment, Vol 0, 20 WIT Press.tpress.com, ISSN (on-lne)

6 790 Sustanable Development and Plannng V The algorthm for solvng the contaner allocaton on collecton tasks follos the next steps:. Parameter ntalzaton.. Assgn the gven perod to any collecton tme,2,..., M..2. Assgn for the frst teraton j and j mn j M T, and j..3. Assgn the maxmum perod to the schedulng perod Tmax max T. M 2. Iteraton 2.. For all,2,..., M, f T then j j l, and go to step Calculate the parameters for the next teraton mn j 3. M. Untl T j max go to step 2.. If j j, Tmax j then go to step 3. Savng the soluton 3.. Export the sets of task j n a table format, hch ll be used as nput data n the GIS model. 4 Vehcle routng model Based on geographc nformaton system (GIS) procedures, a model for solvng the vehcle routng problem s developed. The model s appled for dentfyng the routes startng and endng at one collecton centre and servng the set of selectve collecton contaners. The routng soluton that mnmses the total travel tme s determned takng nto consderaton the local road netork propertes and the locaton of the collecton contaners for each category of aste (glass, paper and plastc). Before the routng model could be constructed, preparng geospatal databases s necessary. The datasets used n the GIS model nclude: Area of admnstratve sectors of Bucharest Cty; Road netork; Area of unversty campuses; Locaton of the selectve aste collecton centres; Locaton of the selectve aste collecton contaners n the unversty campuses. The map representaton of the geospatal datasets s shon n fgure 4. WIT Transactons on Ecology and the Envronment, Vol 0, 20 WIT Press.tpress.com, ISSN (on-lne)

7 Sustanable Development and Plannng V Legend Unversty campuses Collectng contaner Collecton Centre Fgure 4: Personal Geodatabase Map of the model features. Feature Data Set Selectve Collecton Sets Feature Class Collecton aste centres Paper Contaner Selectve Collecton System Plastc Contaner Glass Contaner Feature Data Set Bucharest Road Netork Feature Class Streets Netork Dataset Street Netork Fgure : Elements n netork datasets creaton. WIT Transactons on Ecology and the Envronment, Vol 0, 20 WIT Press.tpress.com, ISSN (on-lne) 79

8 792 Sustanable Development and Plannng V In order to create a netork dataset and solvng the large scale selectve aste collecton problem s necessary to organse all the datasets n an ntegrated geodatabase structure (Fgure ). A netork dataset s created based on the road netork geospatal database. Connectvty rules are appled and tme and dstance attrbutes are used as evaluators n the netork dataset. Wth all the geospatal data dgtzed and necessary attrbutes added, the vehcle routng model can be bult. The ArcToolBox ArcGIS softare s used for creatng the model shon n Fgure 6. Procedure Make Route Layer s appled for the street netork dataset. The selectve collecton contaners are located on the route layer and Netork Analyst procedure s used for solvng the vehcle routng problem. CollectonNetork Model StreetNetork Make Route Layer Route Add Locaton Netork Analyst PaperContaner Solve PaperContaner RouteLayer Fgure 6: Flo chart of the vehcle routng GIS model. The model has to be successvely appled for each set of selectve aste contaners (paper, plastc and glass) and for all sets of task j establshed n the I prevous step. Case study The model descrbed before has been appled to optmse the selectve aste collecton system n unversty campuses located n the Sxth Admnstratve Sector of Bucharest. Fgure 4 shos the locaton of the selectve aste contaners and collectng arehouses. The prevous presented algorthm has been used n order to plannng the collecton servces. A collectng tasks selecton s presented n Table. The routng problem has been solved successvely for each task th the developed GIS model. The route layer resulted for the frst task s shon n Fgure 7. WIT Transactons on Ecology and the Envronment, Vol 0, 20 WIT Press.tpress.com, ISSN (on-lne)

9 Sustanable Development and Plannng V Table : Collectng servces. OBJECTID CollectonPont W_Id Perod Allocaton Task Automatca #00 2 Rectorat #00 3 Mecanca 0 #003 4 Transportur 20 #006 IntrareVasleMlea 0 #003 6 P22 #00 7 Blocur_U #00 8 R 0 #003 9 Belvedere #00 0 R3 4 #00 ComplexLeu 0 #003 2 CantnaLeu #00 3 Grozavest 0 #003 4 Grozavest2 0 #003 ANEFS 2 Wahrehouse #03 # Drept 2 Wahrehouse #03 # CamneConstruct 7 Wahrehouse #03 #0302 Fgure 7: Route layers. WIT Transactons on Ecology and the Envronment, Vol 0, 20 WIT Press.tpress.com, ISSN (on-lne) 793

10 794 Sustanable Development and Plannng V Each collectng pont needs 2 mnutes for loadng/unloadng the contaner. The total travel tme along all routes s calculated based on each arc travel tme from the netork dataset. Detaled schedule table are obtaned for each collectng vehcle. 6 Concluson Selectve aste collectng n unversty campuses s mportant for mnmzng the mpact on the envronment. The collecton servces have to be organsed n campuses th restrcted access and n traffc congested urban areas. In order to reduce the total costs, the vehcle fuel consumpton and pollutant emsson, effcent methods for plannng the recyclable aste collectng trps are necessary. GIS tools and procedure are useful for optmal plannng of selectve aste collecton. The GIS model presented n ths paper solves the routng problem. Addtonal programmng algorthm s necessary for plannng the collecton servces. The developed methods provde nformatonal and technologcal support for publc authortes and selectve aste collecton operators. Decson makers can also use the model to explore tradeoffs beteen plannng alternatves and dentfy the optmal soluton. The proposed model could be easly adapted for other practcal specal cases. Acknoledgement The paper has been supported by the research contract 920 Cvc Educaton for Selectve Waste Collecton n Unversty Campuses ECOSED, fundng by UEFISCDI/PNCDI-II. References [] Bodn, L.D., Tenty Years of Routng and Schedulng, Operatons Research, 38, pp. 7-79, 990. [2] Martelo, S., Laporte, G., Mnoux, M., Rbero, C. (eds). Survey n combnatoral optmzaton, Volume 3 of Annals of Dscrete Mathematcs, North-Holland, Amsterdam, 987. [3] ECOROM, ECOROM Annual Report, Bucurest, Romana, 20. [4] ESRI, ArcGIS9. Netork Analyst, Redlands, USA, 200. WIT Transactons on Ecology and the Envronment, Vol 0, 20 WIT Press.tpress.com, ISSN (on-lne)