How to Divide the Costs of Urban Solid Wastes Collection among Citizens?

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1 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 Università del Piemonte Orientale vito.fragnelli@mfn.unipmn.it International Conference on Integrated Urban Solid Waste Management Scuola Superiore Sant Anna - Pisa - June 14th-15th, 2011

2 How to Divide the Costs of Urban Solid Wastes Collection among Citizens? 2 Outline The problem The model Experiments

3 How to Divide the Costs of Urban Solid Wastes Collection among Citizens? 3 The problem Decreto Ronchi (D.l. n.22, 5/2/1997) TAX cost per square meter TARIFF theoretically: cost per unit of waste cost per square meter cost per household member Game Theory COST ALLOCATION restricted to a consortium Municipalities Inhabitants

4 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 1 Alluvioni Cambiò Alzano Scrivia Arquata Scrivia Basaluzzo Belforte M.to Berzano di T ortona Borghetto Borbera C.M. Alta V al Lemme C.M. Borbera C.M. Curone Grue Capriata d Orba Carbonara Scrivia Carezzano Carpeneto Casalnoceto Cassano Spinola Cassinelle Castellar Guidobono Castellazzo Bormida Castelletto d Orba Castelnuovo Scrivia Cerreto Grue Cremolino F rancavilla Bisio F resonara Gavazzana Gavi Grondona Guazzora Isola S.Antonio Molare Municipalities Inhabitants U.S.W. (t) kg/in/y 32 Molino dei Torti Montaldeo Montaldo Bormida Novi Ligure Ovada P aderna Parodi Ligure P asturana P ontecurone P ozzolo F ormigaro P redosa Rocca Grimalda S.Agata F ossili Sale San Cristoforo Sardigliano Sarezzano Serravalle Scrivia Silvano d Orba Spineto Scrivia Stazzano T assarolo T ortona T risobbio V ignole Borbera V iguzzolo V illalvernia V illaromagnano V olpedo V olpeglino TOTAL

5 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 willingnessto-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

6 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; Novi Ligure, Cassano Spinola, Gavazzana, Pasturana, Villalvernia; 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; C.M. Curone-Grue, Alluvioni Cambiò, 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; 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; Tortona (27,220 inhabitants - 14,085 tons) and Cerreto Grue (360 inhabitants - 3 tons) are in the same group unfairness

7 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 g 1,..., g k with i=1,...,k g i = 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 g i, i = 1,..., k Maintenance cost game depending on the number of agents Account the cost for restoring the infrastructure used by an agent in g i, i = 1,..., k up to the level for agents in g j,j = i,..., k

8 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, , 101 Total number of 10, 737, , 378, , 128, 498 4, 340, , 747, , 332, 996 inhabitants 18.7% 28.6% 21.2% 7.6% 23.9% Average production of wastes (kg/in/y) T otal production 4, 563, 507 6, 961, 065 5, 457, 824 2, 170, 128 6, 873, , 026, 325 of wastes (t/y) 17.5% 26.7% 21.0% 8.4% 26.4%

9 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 G RSU 1 G RSU 2 G RSU 3 Groups < 425 > 425; < 500 > 500 Municipalities Inhabitants 74,299 39,502 56,353 three groups according to number of inhabitants G In 1 G In 2 G In 3 Groups < 5, 000 > 5, 000; < 20, 000 > 20, 000 Municipalities Inhabitants 69,643 43,270 57,241

10 How to Divide the Costs of Urban Solid Wastes Collection among Citizens? 10 The model Flows of Municipalities (54.1 % of stability) from \ to G In 1 % G In 2 % G In 3 % G RSU G RSU G RSU Flows of Inhabitants (45.4 % of stability) from \ to G In 1 % G In 2 % G In 3 % G RSU 1 32, , , G RSU 2 21, , G RSU 3 16, , , The low stability of the flows suggests to solve the infrastructure cost game according to both the criteria of grouping the agents

11 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

12 How to Divide the Costs of Urban Solid Wastes Collection among Citizens? 12 The model - The data Operating costs for the consortium ( in Italian Lire) Balance entries Building costs M aintenance costs Cost of production 6) Raw materials and consumables and goods f or 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. termination indemnities 60, 879, 782 e. other costs 10, 596, ) Depreciation and writedowns : a. depreciation of intangible assets 2, 757, 974, 328 b. depreciation of tangible assets 695, 391, 510 d. writedowns of receivables included in current assets and of liquid assets 19, 119, ) Changes in raw materials and consumables and goods for sale inventory 18,323,216 13) Other provisions 929, 241, ) Other operating costs : a. regional tax l.549/95 1, 870, 566, 600 b. local tax r.l.59/95 467, 641, 650 c. tax to M unicipalities housing the plants r.l.59/95 467, 641, 650 d. other costs 283, 526, 211 TOTAL 3,257,598,118 8,546,443,513

13 How to Divide the Costs of Urban Solid Wastes Collection among Citizens? 13 Experiments Comparison of costs using Shapley value Municipalities A 1B 2A 2B Alluvioni Cambiò 60, , , , , 672 Alzano Scrivia 70, , , , , 672 Arquata Scrivia 74, , , , , 372 Basaluzzo 71, , , , , 672 Belforte M, to 56, , , , , 672 Berzano di T ortona 42, 279 1, 101, , , , 672 Borghetto Borbera 75, , , , , 672 C.M. Alta V al Lemme 68, , , , , 372 C.M. Borbera 79, , , , , 672 C.M. Curone Grue 83, , , , , 372 Capriata d Orba 63, , , , , 672 Carbonara Scrivia 32, , , , , 672 Carezzano 61, , , , , 672 Carpeneto 52, , , , , 672 Casalnoceto 66, , , , , 672 Cassano Spinola 64, , , , , 672 Cassinelle 64, , , , , 672 Castellar Guidobono 82, , , , , 672 Castellazzo Bormida 75, , , , , 672 Castelletto d Orba 68, , , , , 672 Castelnuovo Scrivia 73, , , , , 372 Cerreto Grue 1, , , , , 672 Cremolino 64, , , , , 672 F rancavilla Bisio 71, , , , , 672 F resonara 71, , , , , 672 Gavazzana 78, 743 2, 317, 159 1, 129, , , 672 Gavi 69, , , , , 672 Grondona 69, , , , , 672 Guazzora 39, , , , , 672 Isola S.Antonio 66, , , , , 672 Molare 54, , , , , 672 Municipalities A 1B 2A 2B Molino dei T orti 48, , , , , 672 Montaldeo 39, , , , , 672 Montaldo Bormida 65, , , , , 672 Novi Ligure 62, 023 5, , , , 877 Ovada 62, , , , , 372 P aderna 66, , , , , 672 P arodi Ligure 50, , , , , 672 P asturana 62, , , , , 672 P ontecurone 81, , , , , 672 P ozzolo F ormigaro 63, , , , , 672 P redosa 87, , , , , 672 Rocca Grimalda 73, , , , , 672 S. Agata F ossili 93, , , , , 672 Sale 78, , , , , 672 San Cristoforo 62, , , , , 672 Sardigliano 81, , , , , 672 Sarezzano , , , , 672 Serravalle Scrivia 86, , , , , 372 Silvano d Orba 62, , , , , 672 Spineto Scrivia 65, , , , , 672 Stazzano 65, , , , , 672 T assarolo 83, , , , , 672 T ortona 80, , , , , 877 T risobbio 65, , , , , 672 V ignole Borbera 67, , , , , 672 V iguzzolo 63, , , , , 672 V illalvernia 81, , , , , 672 V illaromagnano 53, , , , , 672 V olpedo , , , , 672 V olpeglino 40, , , , , 672 min 571 5, , , , 672 max 93, 786 2, 317, 159 1, 129, , , 877

14 How to Divide the Costs of Urban Solid Wastes Collection among Citizens? 14 Experiments Comparison of costs using Owen value Municipalities A 1B 2A 2B Alluvioni Cambiò 60, , , , , 374 Alzano Scrivia 70, , , , , 374 Arquata Scrivia 74, , , , , 397 Basaluzzo 71, , , , , 374 Belforte M, to 56, , , , , 374 Berzano di T ortona 42, , , , , 374 Borghetto Borbera 75, , , , , 374 C.M. Alta V al Lemme 68, , , , , 397 C.M. Borbera 79, , , , , 374 C.M. Curone Grue 83, , , , , 397 Capriata d Orba 63, , , , , 374 Carbonara Scrivia 32, , , , , 374 Carezzano 61, , , , , 374 Carpeneto 52, , , , , 374 Casalnoceto 66, , , , , 374 Cassano Spinola 64, , , , , 374 Cassinelle 64, , , , , 374 Castellar Guidobono 82, , , , , 374 Castellazzo Bormida 75, , , , , 374 Castelletto d Orba 68, , , , , 374 Castelnuovo Scrivia 73, , , , , 397 Cerreto Grue 1, , , , , 374 Cremolino 64, , , , , 374 F rancavilla Bisio 71, , , , , 374 F resonara 71, , , , , 374 Gavazzana 78, 743 2, 849, , , , 374 Gavi 69, , , , , 374 Grondona 69, , , , , 374 Guazzora 39, , , , , 374 Isola S.Antonio 66, , , , , 374 Molare 54, , , , , 374 Municipalities A 1B 2A 2B Molino dei T orti 48, , , , , 374 Montaldeo 39, , , , , 374 Montaldo Bormida 65, , , , , 374 Novi Ligure 62, 023 4, , , , 631 Ovada 62, , , , , 397 P aderna 66, , , , , 374 P arodi Ligure 50, , , , , 374 P asturana 62, , , , , 374 P ontecurone 81, , , , , 374 P ozzolo F ormigaro 63, , , , , 374 P redosa 87, , , , , 374 Rocca Grimalda 73, , , , , 374 S. Agata F ossili 93, , , , , 374 Sale 78, , , , , 374 San Cristoforo 62, , , , , 374 Sardigliano 81, , , , , 374 Sarezzano , , , , 374 Serravalle Scrivia 86, , , , , 397 Silvano d Orba 62, , , , , 374 Spineto Scrivia 65, , , , , 374 Stazzano 65, , , , , 374 T assarolo 83, , , , , 374 T ortona 80, , , , , 631 T risobbio 65, , , , , 374 V ignole Borbera 67, , , , , 374 V iguzzolo 63, , , , , 374 V illalvernia 81, , , , , 374 V illaromagnano 53, , , , , 374 V olpedo , , , , 374 V olpeglino 40, , , , , 374 min 571 4, , , , 374 max 93, 786 2, 849, , , , 631

15 How to Divide the Costs of Urban Solid Wastes Collection among Citizens? 15 Experiments The best choice for some inhabitants may not acceptable for those whose payment increases Democracy vote and select a system (corrected) Consortium 1 inhabitant = 1 quota The voting procedure YES if the new cost is at least 10% less than the actual NO if the new cost is at least 10% greater than the actual Y/N otherwise

16 How to Divide the Costs of Urban Solid Wastes Collection among Citizens? 16 Experiments Results - Shapley value Game Y ES NO Y/N Result Core membership min max 1A 125, , approved NO 5, 246 2, 317, 159 1B 130, , 050 9, 702 approved NO 22, 858 1, 129, 312 2A 28, , , 460 approved (uncertain) Y ES 57, , 976 2B 63, , , 654 approved (uncertain) Y ES 57, , 877 Results - Owen value Game Y ES NO Y/N Result Core membership min max 1A 117, , , 621 approved Y ES 4, 507 2, 849, 996 1B 110, , , 518 approved NO 23, , 015 2A 63, , , 839 approved (uncertain) Y ES 52, , 903 2B 71, , , 056 approved (uncertain) Y ES 55, , 631 The Owen value is more reliable when the population of each group grows proportionally (Fragnelli-Iandolino, 2004)

17 How to Divide the Costs of Urban Solid Wastes Collection among Citizens? 17 Main References Francia C (1998) Valutazione tecnico-economica del sistema integrato di gestione dei rifiuti (in Italian), Edizioni Federambiente, Italy. Faulhaber GR (1975) Cross-Subsidization: Pricing in Public Enterprises, The American Economic Review 65 : Fragnelli V, García-Jurado I, Norde H, Patrone F, Tijs S (1999) How to Share Railway Infrastructure Costs?, in Game Practice: Contributions from Applied Game Theory (García-Jurado I, Patrone F, Tijs S eds.), Kluwer, Amsterdam, The Netherlands. Fragnelli V, Iandolino A (2004) A Cost Allocation Problem in Urban Solid Wastes Collection and Disposal, Mathematical Methods of Operations Research 59 : Gillies DB (1953) Some Theorems on N-Person Games, PhD Dissertation, Department of Mathematics, Princeton University. Littlechild SC, Thompson GF (1977) Aircraft Landing Fees: A Game Theory Approach, Bell Journal of Economics 8 : Moretti S (2004) A Model for Cooperative Inter-municipal Waste Collection Cost Evaluation towards Fair Cost Allocation, in Game Practice and the Environment (Carraro C, Fragnelli V eds.), Edward Elgar Publishing, Cheltenham, UK. Owen G (1977) Values of Games with a Priori Unions, Lecture Notes in Economic and Mathematical Systems 141 : Shapley LS (1953) A Value for n-person Games, in Contributions to the Theory of Games, Volume II (Annals of Mathematics Studies, 28) (HW Kuhn, AW Tucker eds.), Princeton University Press, Princeton, USA. Young HP (1994) Cost Allocation, in Handbook of Game Theory - Vol II (Aumann R, Hart S eds.), North Holland, Amsterdam, The Netherlands.