Strategy of Location Incinerators in Slovak Republic Juraj Pekár Zuzana Čičková Ivan Brezina

Transkript

1 Strategy of Locatio Icierators i Slovak Republic Juraj Pekár Zuzaa Čičková Iva Brezia Departmet of Operatios Research ad Ecoometrics Faculty of Busiess Iformatics Uiversity of Ecoomics - Bratislava

2 Waste Maagemet i Slovak Republic The strategy of waste maagemet i Slovak Republic is obliged to follow curret legislatio that comprises sice 993 Waste Maagemet Program. Waste Maagemet Program for the years is a basic strategic documet that directs the evirometal policy till the year 200. Because sice Slovak Republic is a member of Europea Uio, the legislatio respects the legislatio of Europea Uio. 2

3 Icierators i Slovak Republic The basic techique of disposig of muicipal waste combustio. The umber of icierators i Slovak Republic: 40. Icierators for the domestic waste i Slovak Republic oly 2 (relatively badly structured i Bratislava ad Košice). 3

4 Strategy of buildig the icierators Two basic coceptio were developed for solvig so that problems: first coceptio is aimed for coverig the whole populatio with miimal umber of service chaels Locatio Set Coverig Problem LSCP, the aim of secod coceptio is to maximize the coverig of populatio with limited umber of service chaels Maximal Coverig Locatio Problem MCLP. 4

5 Populatio Slovak Republic (200) ihabitats 2 96 commues 38 cities ihabitats (about 56%) was livig i the cities 5

6 Goals of models shortest path whe umber of icierators is give miimal distace eeded to travel whe umber of icierators is give maximal coverig of populatio whe a certai umber of icierators ad also certai maximal distace are give 6

7 Iput data umber of cities i Slovak Republic (38), D ( x ) miimal distace matrix (elemets represet the miimal distace from city i to city j) K maximal allowable distace from the closest icierator p umber of icierators b j umber of ihabitats of j-th city A ( x ) biary elemets a (i, j =, 2,...) that represet the accessibility of icierators from the city producer of waste (the value j-th icierator is accessible from i-th city i distace K, the value 0 icierator is ot accessible i distace K) 7

8 Variables y biary variable that represets the use of the route from i-th city to j-th icierator (the value ihabitats of i-the city impart the waste to j-th collectio cetre, the value 0 that route is ot used) for i, j =, 2,..., z represets maximal distace all the icierators from all the cities producer of waste x i biary variable that represets if the icierator is ope (value ) or ot (value 0) i i-th city for i =, 2,..., y i biary variable that represets accessibility of i-th city from some of the icierators i distace K (value the city is accessible from some of the icierators i distace K, value 0 - the city is ot accessible) for i =, 2,... 8

9 Model goal fidig the miimal distace betwee icierator ad all the cities ( ) f x, y, z = z mi i= i= i= y =, j =, 2,... y x 0, i, j =, 2,... i i d y z 0, j =, 2,... { } x, y 0,, i, j =, 2,... i x = p z 0 9

10 Model 2 goal fidig miimal total distace eeded to travel whe maximal umber of icierators is give ( ) f x, y = b d y mi i= j= j i= i= y =, j =, 2,... y x 0, i, j =, 2,... i i { } x, y 0,, i, j =, 2,... i x = p 0

11 Model 3 goal to maximize the coverig of ihabitats f x, y = b y max ( ) i= i i j= a x y 0, i =, 2,... j= x j j i x j, y 0, j = p { } a 0, =, d d > K K

12 Solvig of models models were solved by GAMS model : with give parameter p = 0 model 2: with give parameter p = 0 model 3: with give parameters p = 0 ad K = 50 2

13 model : parameter p = 0 Results Dolý Kubí, Haušovce ad Topľou, Ilava, Malacky, Michalovce, Nové Zámky, Rožňava, Spišská Nová Ves, Veľký Krtíš, Zvole with maximal distace 65,5 km (Dolý Kubí Čadca) total distace ,8 km 3

14 model 2: parameter p = 0 Results Báovce ad Bebravou (Stará Turá, 56 km), Bratislava (Duajská Streda, 48,5 km), Košice (Toraľa, 98,5 km), Michalovce (Medzilaborce, 70 km), Poprad (Húšťa, 72,5 km), Prešov (Svidík, 57,5 km), Šuray (Štúrovo, 6,5), Trava (Gbely, 68,5 km), Zvole (Rimavská Sobota, 87 km), Žilia (Trsteá, 99,2 km) after each collectio ceter is give also the distat city from that the waste is trasported as well as correspodig cost (amed ito brackets). total distace ,8 km 4

15 Results model 3: parameters p = 0 ad K = 50 Bytča, Húšťa, Hurbaovo, Krupia, Partizáske, Ružomberok, Seec, Seica, Spišská Nová Ves, Vraov ad Topľou i this case 6 % of ihabitats are ot covered to 50 km distace (the maximal distace is betwee Čiera ad Tisou ad Vraov ad Topľov 86,5 km) 5

16 Results - Figure icierator, Model icierator, Model 2 icierator, Model 3 6

17 Coclusio it is possible to formulate the strategy of icierators placig that is based o fulfillmet of a give coditios coditios ca be modified for differet levels of p (maximal umber of icierators) ad K (maximal distace of the city from the closest icierator) preseted procedure ca be a base for strategy decisios about locatio of icierators i potetial localities preseted models ca be used i geeral for differet sets ad problem size 7