How to Divide the Costs of Urban Solid Wastes Collection Among Citizens? 1
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How to Divide the Costs of Urban Solid Wastes Collection among Citizens? 1 How to Divide the Costs of Urban Solid Wastes Collection among Citizens? Vito Fragnelli Dipartimento di Scienze e Tecnologie Avanzate Universit`adel Piemonte Orientale [email protected] International Conference on Integrated Urban Solid Waste Management Scuola Superiore Sant’Anna - Pisa - June 14th-15th, 2011 How to Divide the Costs of Urban Solid Wastes Collection among Citizens? 2 Outline The problem The model Experiments How to Divide the Costs of Urban Solid Wastes Collection among Citizens? 3 The problem TAX cost per square meter Decreto Ronchi (D.l. n.22, 5/2/1997) - TARIFF theoretically: cost per unit of waste cost per square meter cost per household member Game Theory COST ALLOCATION restricted to a consortium @ @ @ © @R Municipalities Inhabitants How to Divide the Costs of Urban Solid Wastes Collection among Citizens? 4 The problem The consortium Ovadese-Valle Scrivia (1998) Municipalities Inhabitants U.S.W. (t) kg/in/y Municipalities Inhabitants U.S.W. (t) kg/in/y 1 Alluvioni Cambio` 1040 406 390.38 32 Molino dei Torti 804 254 315.92 2 Alzano Scrivia 374 170 454.55 33 Montaldeo 364 93 255.49 3 Arquata Scrivia 6121 2933 479.17 34 Montaldo Bormida 663 278 419.31 4 Basaluzzo 1884 864 458.60 35 Novi Ligure 30021 12011 400.09 5 Belforte M.to 396 145 366.16 36 Ovada 12212 4937 404.27 6 Berzano di Tortona 143 39 272.73 37 Paderna 267 114 426.97 7 Borghetto Borbera 1793 877 489.12 38 Parodi Ligure 745 245 328.86 8 C.M. Alta Val Lemme 5992 2658 443.59 39 Pasturana 882 355 402.49 9 C.M. Borbera 2556 1303 509.78 40 P ontecurone 4224 2218 525.09 10 C.M. Curone − Grue 6843 3673 536.75 41 Pozzolo Formigaro 4785 1951 407.73 11 Capriata d0Orba 1839 757 411.64 42 Predosa 2104 1184 562.74 12 Carbonara Scrivia 1016 214 210.63 43 Rocca Grimalda 1260 601 476.98 13 Carezzano 494 197 398.79 44 S.Agata Fossili 362 219 604.97 14 Carpeneto 959 322 335.77 45 Sale 4363 2204 505.16 15 Casalnoceto 882 380 430.84 46 San Cristoforo 572 230 402.10 16 Cassano Spinola 2047 850 415.24 47 Sardigliano 460 242 526.09 17 Cassinelle 798 333 417.29 48 Sarezzano 1086 4 3.68 49 Serravalle Scrivia 6243 3465 555.02 18 Castellar Guidobono 380 202 531.58 0 19 Castellazzo Bormida 4254 2060 484.25 50 Silvano d Orba 1775 710 400.00 20 Castelletto d0Orba 1849 818 442.40 51 Spineto Scrivia 349 147 421.20 21 Castelnuovo Scrivia 5859 2774 473.46 52 Stazzano 1987 843 424.26 22 Cerreto Grue 360 3 8.33 53 Tassarolo 558 300 537.63 23 Cremolino 828 342 413.04 54 T ortona 27220 14085 517.45 24 Francavilla Bisio 414 191 461.35 55 Trisobbio 646 272 421.05 25 Fresonara 691 319 461.65 56 V ignole Borbera 1991 864 433.95 26 Gavazzana 126 64 507.94 57 V iguzzolo 3036 1240 408.43 27 Gavi 4569 2036 445.61 58 V illalvernia 914 482 527.35 28 Grondona 511 230 450.10 59 V illaromagnano 690 238 344.93 29 Guazzora 353 91 257.79 60 V olpedo 1214 7 5.77 30 Isola S.Antonio 791 338 427.31 61 V olpeglino 161 42 260.87 31 Molare 2034 719 353.49 TOTAL 170154 76143 How to Divide the Costs of Urban Solid Wastes Collection among Citizens? 5 The problem Cost Allocation Problem (Young, 1994) Accounting the role of each agent (municipality, inhabitant, ...), in particular the willingness- to-pay, measured as the utility of the service Game Theory is the natural habitat for these problems Fairness: make all the agents equally satisfied (or equally dissatisfied) • Cross-subsidization (Faulhaber, 1975): nobody should pay the service provided to another agent • Core (Gillies, 1953): no subgroup of agents may be better off receding from the consortium • Shapley value (1953): each agent pays his average marginal contribution w.r.t. all possible orderings • Owen value (1977): each agent pays his average marginal contribution w.r.t. a restricted set of orderings according to a priori assigned subsets of agents How to Divide the Costs of Urban Solid Wastes Collection among Citizens? 6 The model Small game Moretti (2004): game theoretic approach with a small dataset related to distances, population, waste production, not suitable for large consortia Geographical method Grouping neighboring municipalities, in order to obtain groups with similar total amount of produced wastes: 1. Tortona, Carbonara Scrivia, Cerreto Grue, Paderna, Pozzolo Formigaro, Spineto Scrivia; 16514 2. Novi Ligure, Cassano Spinola, Gavazzana, Pasturana, Villalvernia; 13762 3. Ovada, Basaluzzo, Belforte M.to, Capriata d’Orba, Carpeneto, Cassinelle, Castellazzo Bormida, Cremolino, Francavilla Bisio, Fresonara, Molare, Montaldo Bormida, Parodi Ligure, Predosa, Rocca Grimalda, San Cristoforo, Silvano d’Orba, Trisobbio; 14509 4. C.M. Curone-Grue, Alluvioni Cambi`o, Alzano Scrivia, Berzano di Tortona, Borghetto Borbera, Casalnoceto, Castellar Guidobono, Castelnuovo Scrivia, Guazzora, Isola S.Antonio, Molino dei Torti, Pontecurone, Sale, Sarezzano, Viguzzolo, Villaromagnano, Volpedo, Volpeglino; 15157 5. Serravalle Scrivia, Arquata Scrivia, Carezzano, Castelletto D’Orba, C.M. Borbera, C.M. Alta Val Lemme, Gavi, Grondona, Montaldeo, S.Agata Fossili, Sardigliano, Stazzano, Tassarolo, Vignole Borbera; 16201 Tortona (27,220 inhabitants - 14,085 tons) and Cerreto Grue (360 inhabitants - 3 tons) are in the same group → unfairness How to Divide the Costs of Urban Solid Wastes Collection among Citizens? 7 The model Infrastructure cost game (Fragnelli et al, 1999) The agents of the set N can be grouped according to different requests or needs as g1, ..., gk with ∪i=1,...,kgi = N • Building cost game (Airport Game, Littlechild - Thompson, 1977) independent from the number of agents Account the cost for building an infrastructure for agents with requests of group gi,i = 1, ..., k • Maintenance cost game depending on the number of agents Account the cost for restoring the infrastructure used by an agent in gi,i = 1, ..., k up to the level for agents in gj,j = i, ..., k How to Divide the Costs of Urban Solid Wastes Collection among Citizens? 8 The model How to group the agents? Ranges of average production of wastes for Italian municipalities referring to the inhabitants (Francia, 1998) Inhabitants > 5, 000 > 20, 000 > 60, 000 > 100, 000 Italy < 5, 000 < 20, 000 < 60, 000 < 100, 000 Number of Municipalities 5, 865 1, 769 369 56 42 8, 101 Total number of 10, 737, 664 16, 378, 976 12, 128, 498 4, 340, 256 13, 747, 602 57, 332, 996 inhabitants 18.7% 28.6% 21.2% 7.6% 23.9% Average production of wastes (kg/in/y) 425 425 450 500 500 454 T otal production 4, 563, 507 6, 961, 065 5, 457, 824 2, 170, 128 6, 873, 801 26, 026, 325 of wastes (t/y) 17.5% 26.7% 21.0% 8.4% 26.4% How to Divide the Costs of Urban Solid Wastes Collection among Citizens? 9 The model Two approaches • three groups according to average production of wastes RSU RSU RSU G1 G2 G3 Groups < 425 > 425; < 500 > 500 Municipalities 31 17 13 Inhabitants 74,299 39,502 56,353 • three groups according to number of inhabitants In In In G1 G2 G3 Groups < 5, 000 > 5, 000; < 20, 000 > 20, 000 Municipalities 53 6 2 Inhabitants 69,643 43,270 57,241 How to Divide the Costs of Urban Solid Wastes Collection among Citizens? 10 The model Flows of Municipalities (54.1 % of stability) In In In from \ to G1 % G2 % G3 % RSU G1 29 47.5 1 1.6 1 1.6 RSU G2 14 23.0 3 4.9 0 0.0 RSU G3 10 16.4 2 3.3 1 1.6 Flows of Inhabitants (45.4 % of stability) In In In from \ to G1 % G2 % G3 % RSU G1 32,066 18.8 12,212 7.2 30,021 17.6 RSU G2 21,530 12.7 17,972 10.6 0 0.0 RSU G3 16,047 9.4 13,086 7.7 27,220 16.0 The low stability of the flows suggests to solve the infrastructure cost game according to both the criteria of grouping the agents How to Divide the Costs of Urban Solid Wastes Collection among Citizens? 11 The model Two classes of games • Game 1 The agents are the municipalities • Game 2 The agents are the inhabitants Two subclasses for each class of games • Subclass A Agents are grouped according to waste production • Subclass B Agents are grouped according to number of inhabitants Finally we have to solve four games: 1A, 1B, 2A, 2B How to Divide the Costs of Urban Solid Wastes Collection among Citizens? 12 The model - The data Operating costs for the consortium (1998 - in Italian Lire) Balance entries Building costs Maintenance costs Cost of production 6) Raw materials and consumables and goods for sale 282, 549, 420 7) F or services : a. maintenance and repair expenses 399, 475, 576 b. third parties services in our plants 32, 520, 000 c. collection and transportation of U.S.W. by contract 1, 284, 328, 667 d. percolates disposal 283, 431, 840 e. environmental analysis and monitoring 60, 596, 000 f. insurance 71, 614, 313 g. other provisions 435, 680, 790 9) F or employees : a. wages and salaries 1, 049, 248, 501 b. social security costs 302, 162, 259 c. I.N.A.I.L. premiums 21, 532, 652 d.