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

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

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 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

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 1040 406 390.38 2 Alzano Scrivia 374 170 454.55 3 Arquata Scrivia 6121 2933 479.17 4 Basaluzzo 1884 864 458.60 5 Belforte M.to 396 145 366.16 6 Berzano di T ortona 143 39 272.73 7 Borghetto Borbera 1793 877 489.12 8 C.M. Alta V al Lemme 5992 2658 443.59 9 C.M. Borbera 2556 1303 509.78 10 C.M. Curone Grue 6843 3673 536.75 11 Capriata d Orba 1839 757 411.64 12 Carbonara Scrivia 1016 214 210.63 13 Carezzano 494 197 398.79 14 Carpeneto 959 322 335.77 15 Casalnoceto 882 380 430.84 16 Cassano Spinola 2047 850 415.24 17 Cassinelle 798 333 417.29 18 Castellar Guidobono 380 202 531.58 19 Castellazzo Bormida 4254 2060 484.25 20 Castelletto d Orba 1849 818 442.40 21 Castelnuovo Scrivia 5859 2774 473.46 22 Cerreto Grue 360 3 8.33 23 Cremolino 828 342 413.04 24 F rancavilla Bisio 414 191 461.35 25 F resonara 691 319 461.65 26 Gavazzana 126 64 507.94 27 Gavi 4569 2036 445.61 28 Grondona 511 230 450.10 29 Guazzora 353 91 257.79 30 Isola S.Antonio 791 338 427.31 31 Molare 2034 719 353.49 Municipalities Inhabitants U.S.W. (t) kg/in/y 32 Molino dei Torti 804 254 315.92 33 Montaldeo 364 93 255.49 34 Montaldo Bormida 663 278 419.31 35 Novi Ligure 30021 12011 400.09 36 Ovada 12212 4937 404.27 37 P aderna 267 114 426.97 38 Parodi Ligure 745 245 328.86 39 P asturana 882 355 402.49 40 P ontecurone 4224 2218 525.09 41 P ozzolo F ormigaro 4785 1951 407.73 42 P redosa 2104 1184 562.74 43 Rocca Grimalda 1260 601 476.98 44 S.Agata F ossili 362 219 604.97 45 Sale 4363 2204 505.16 46 San Cristoforo 572 230 402.10 47 Sardigliano 460 242 526.09 48 Sarezzano 1086 4 3.68 49 Serravalle Scrivia 6243 3465 555.02 50 Silvano d Orba 1775 710 400.00 51 Spineto Scrivia 349 147 421.20 52 Stazzano 1987 843 424.26 53 T assarolo 558 300 537.63 54 T ortona 27220 14085 517.45 55 T risobbio 646 272 421.05 56 V ignole Borbera 1991 864 433.95 57 V iguzzolo 3036 1240 408.43 58 V illalvernia 914 482 527.35 59 V illaromagnano 690 238 344.93 60 V olpedo 1214 7 5.77 61 V olpeglino 161 42 260.87 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 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

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 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; 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 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

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 G RSU 1 G RSU 2 G RSU 3 Groups < 425 > 425; < 500 > 500 Municipalities 31 17 13 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 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) from \ to G In 1 % G In 2 % G In 3 % G RSU 1 29 47.5 1 1.6 1 1.6 G RSU 2 14 23.0 3 4.9 0 0.0 G RSU 3 10 16.4 2 3.3 1 1.6 Flows of Inhabitants (45.4 % of stability) from \ to G In 1 % G In 2 % G In 3 % G RSU 1 32,066 18.8 12,212 7.2 30,021 17.6 G RSU 2 21,530 12.7 17,972 10.6 0 0.0 G RSU 3 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 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, 410 10) 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, 056 11) Changes in raw materials and consumables and goods for sale inventory 18,323,216 13) Other provisions 929, 241, 200 14) 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

How to Divide the Costs of Urban Solid Wastes Collection among Citizens? 13 Experiments Comparison of costs using Shapley value Municipalities 1998 1A 1B 2A 2B Alluvioni Cambiò 60, 519 151, 433 136, 820 57, 337 57, 672 Alzano Scrivia 70, 466 491, 715 380, 463 65, 472 57, 672 Arquata Scrivia 74, 283 30, 044 45, 604 65, 472 66, 372 Basaluzzo 71, 094 97, 612 75, 527 65, 472 57, 672 Belforte M, to 56, 764 397, 704 359, 326 57, 337 57, 672 Berzano di T ortona 42, 279 1, 101, 334 995, 058 57, 337 57, 672 Borghetto Borbera 75, 826 102, 566 79, 360 65, 472 57, 672 C.M. Alta V al Lemme 68, 768 30, 691 46, 586 65, 472 66, 372 C.M. Borbera 79, 029 114, 226 55, 670 87, 976 57, 672 C.M. Curone Grue 83, 210 42, 666 40, 793 87, 976 66, 372 Capriata d Orba 63, 814 85, 639 77, 375 57, 337 57, 672 Carbonara Scrivia 32, 653 155, 011 140, 052 57, 337 57, 672 Carezzano 61, 822 318, 807 288, 043 57, 337 57, 672 Carpeneto 52, 052 164, 224 148, 377 57, 337 57, 672 Casalnoceto 66, 791 208, 505 161, 330 65, 472 57, 672 Cassano Spinola 64, 373 76, 937 69, 513 57, 337 57, 672 Cassinelle 64, 691 197, 357 178, 312 57, 337 57, 672 Castellar Guidobono 82, 408 768, 321 374, 456 87, 976 57, 672 Castellazzo Bormida 75, 071 43, 230 33, 449 65, 472 57, 672 Castelletto d Orba 68, 583 99, 460 76, 957 65, 472 57, 672 Castelnuovo Scrivia 73, 398 31, 388 47, 644 65, 472 66, 372 Cerreto Grue 1, 292 437, 474 395, 259 57, 337 57, 672 Cremolino 64, 032 190, 206 171, 852 57, 337 57, 672 F rancavilla Bisio 71, 521 444, 206 343, 704 65, 472 57, 672 F resonara 71, 567 266, 138 205, 924 65, 472 57, 672 Gavazzana 78, 743 2, 317, 159 1, 129, 312 87, 976 57, 672 Gavi 69, 081 40, 250 31, 143 65, 472 57, 672 Grondona 69, 776 359, 885 278, 460 65, 472 57, 672 Guazzora 39, 964 446, 149 403, 097 57, 337 57, 672 Isola S.Antonio 66, 243 232, 492 179, 890 65, 472 57, 672 Molare 54, 800 77, 429 69, 957 57, 337 57, 672 Municipalities 1998 1A 1B 2A 2B Molino dei T orti 48, 975 195, 884 176, 982 57, 337 57, 672 Montaldeo 39, 608 432, 667 390, 916 57, 337 57, 672 Montaldo Bormida 65, 003 237, 543 214, 620 57, 337 57, 672 Novi Ligure 62, 023 5, 246 43, 097 57, 337 85, 877 Ovada 62, 673 12, 896 22, 858 57, 337 66, 372 P aderna 66, 190 688, 769 532, 934 65, 472 57, 672 P arodi Ligure 50, 981 211, 397 190, 998 57, 337 57, 672 P asturana 62, 397 178, 561 161, 330 57, 337 57, 672 P ontecurone 81, 403 69, 120 33, 687 87, 976 57, 672 P ozzolo F ormigaro 63, 209 32, 913 29, 737 57, 337 57, 672 P redosa 87, 238 138, 765 67, 630 87, 976 57, 672 Rocca Grimalda 73, 944 145, 953 112, 931 65, 472 57, 672 S. Agata F ossili 93, 786 806, 525 393, 075 87, 976 57, 672 Sale 78, 312 66, 918 32, 614 87, 976 57, 672 San Cristoforo 62, 335 275, 333 248, 764 57, 337 57, 672 Sardigliano 81, 556 634, 700 309, 333 87, 976 57, 672 Sarezzano 571 145, 019 131, 025 57, 337 57, 672 Serravalle Scrivia 86, 042 46, 766 44, 713 87, 976 66, 372 Silvano d Orba 62, 010 88, 727 80, 165 57, 337 57, 672 Spineto Scrivia 65, 297 451, 263 407, 717 57, 337 57, 672 Stazzano 65, 770 79, 261 71, 612 57, 337 57, 672 T assarolo 83, 347 523, 229 255, 006 87, 976 57, 672 T ortona 80, 218 10, 726 47, 532 87, 976 85, 877 T risobbio 65, 274 243, 794 220, 268 57, 337 57, 672 V ignole Borbera 67, 273 92, 366 71, 468 65, 472 57, 672 V iguzzolo 63, 317 51, 874 46, 869 57, 337 57, 672 V illalvernia 81, 753 319, 433 155, 682 87, 976 57, 672 V illaromagnano 53, 472 228, 247 206, 222 57, 337 57, 672 V olpedo 894 129, 729 117, 210 57, 337 57, 672 V olpeglino 40, 441 978, 203 883, 809 57, 337 57, 672 min 571 5, 246 22, 858 57, 337 57, 672 max 93, 786 2, 317, 159 1, 129, 312 87, 976 85, 877

How to Divide the Costs of Urban Solid Wastes Collection among Citizens? 14 Experiments Comparison of costs using Owen value Municipalities 1998 1A 1B 2A 2B Alluvioni Cambiò 60, 519 130, 104 110, 373 52, 423 55, 374 Alzano Scrivia 70, 466 462, 596 306, 919 69, 112 55, 374 Arquata Scrivia 74, 283 28, 265 50, 443 69, 112 70, 397 Basaluzzo 71, 094 91, 832 60, 928 69, 112 55, 374 Belforte M, to 56, 764 341, 688 289, 868 52, 423 55, 374 Berzano di T ortona 42, 279 946, 213 802, 712 52, 423 55, 374 Borghetto Borbera 75, 826 96, 492 64, 020 69, 112 55, 374 C.M. Alta V al Lemme 68, 768 28, 874 51, 529 69, 112 70, 397 C.M. Borbera 79, 029 140, 493 44, 909 91, 903 55, 374 C.M. Curone Grue 83, 210 52, 477 45, 121 91, 903 70, 397 Capriata d Orba 63, 814 73, 577 62, 419 52, 423 55, 374 Carbonara Scrivia 32, 653 133, 178 112, 980 52, 423 55, 374 Carezzano 61, 822 273, 904 232, 364 52, 423 55, 374 Carpeneto 52, 052 141, 093 119, 695 52, 423 55, 374 Casalnoceto 66, 791 196, 157 130, 145 69, 112 55, 374 Cassano Spinola 64, 373 66, 101 56, 076 52, 423 55, 374 Cassinelle 64, 691 169, 560 143, 844 52, 423 55, 374 Castellar Guidobono 82, 408 944, 999 302, 073 91, 903 55, 374 Castellazzo Bormida 75, 071 40, 670 26, 984 69, 112 55, 374 Castelletto d Orba 68, 583 93, 570 62, 081 69, 112 55, 374 Castelnuovo Scrivia 73, 398 29, 529 52, 699 69, 112 70, 397 Cerreto Grue 1, 292 375, 857 318, 855 52, 423 55, 374 Cremolino 64, 032 163, 416 138, 633 52, 423 55, 374 F rancavilla Bisio 71, 521 417, 901 277, 265 69, 112 55, 374 F resonara 71, 567 250, 378 166, 118 69, 112 55, 374 Gavazzana 78, 743 2, 849, 996 911, 015 91, 903 55, 374 Gavi 69, 081 37, 866 25, 123 69, 112 55, 374 Grondona 69, 776 338, 573 224, 634 69, 112 55, 374 Guazzora 39, 964 383, 310 325, 178 52, 423 55, 374 Isola S.Antonio 66, 243 218, 724 145, 117 69, 112 55, 374 Molare 54, 800 66, 523 56, 435 52, 423 55, 374 Municipalities 1998 1A 1B 2A 2B Molino dei T orti 48, 975 168, 294 142, 771 52, 423 55, 374 Montaldeo 39, 608 371, 727 315, 351 52, 423 55, 374 Montaldo Bormida 65, 003 204, 085 173, 134 52, 423 55, 374 Novi Ligure 62, 023 4, 507 64, 417 52, 423 85, 631 Ovada 62, 673 11, 080 25, 283 52, 423 70, 397 P aderna 66, 190 647, 981 429, 917 69, 112 55, 374 P arodi Ligure 50, 981 181, 622 154, 078 52, 423 55, 374 P asturana 62, 397 153, 411 130, 145 52, 423 55, 374 P ontecurone 81, 403 85, 014 27, 175 91, 903 55, 374 P ozzolo F ormigaro 63, 209 28, 278 23, 989 52, 423 55, 374 P redosa 87, 238 170, 675 54, 557 91, 903 55, 374 Rocca Grimalda 73, 944 137, 310 91, 101 69, 112 55, 374 S. Agata F ossili 93, 786 991, 988 317, 094 91, 903 55, 374 Sale 78, 312 82, 306 26, 309 91, 903 55, 374 San Cristoforo 62, 335 236, 553 200, 678 52, 423 55, 374 Sardigliano 81, 556 780, 651 249, 539 91, 903 55, 374 Sarezzano 571 124, 593 105, 698 52, 423 55, 374 Serravalle Scrivia 86, 042 57, 520 49, 457 91, 903 70, 397 Silvano d Orba 62, 010 76, 230 64, 669 52, 423 55, 374 Spineto Scrivia 65, 297 387, 703 328, 905 52, 423 55, 374 Stazzano 65, 770 68, 097 57, 769 52, 423 55, 374 T assarolo 83, 347 643, 548 205, 713 91, 903 55, 374 T ortona 80, 218 13, 192 71, 045 91, 903 85, 631 T risobbio 65, 274 209, 456 177, 690 52, 423 55, 374 V ignole Borbera 67, 273 86, 896 57, 653 69, 112 55, 374 V iguzzolo 63, 317 44, 568 37, 809 52, 423 55, 374 V illalvernia 81, 753 392, 888 125, 588 91, 903 55, 374 V illaromagnano 53, 472 196, 099 166, 359 52, 423 55, 374 V olpedo 894 111, 457 94, 553 52, 423 55, 374 V olpeglino 40, 441 840, 425 712, 968 52, 423 55, 374 min 571 4, 507 23, 989 52, 423 55, 374 max 93, 786 2, 849, 996 911, 015 91, 903 85, 631

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

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, 742 44, 412 0 approved NO 5, 246 2, 317, 159 1B 130, 402 30, 050 9, 702 approved NO 22, 858 1, 129, 312 2A 28, 444 14, 250 127, 460 approved (uncertain) Y ES 57, 337 87, 976 2B 63, 274 37, 226 69, 654 approved (uncertain) Y ES 57, 672 85, 877 Results - Owen value Game Y ES NO Y/N Result Core membership min max 1A 117, 155 40, 378 12, 621 approved Y ES 4, 507 2, 849, 996 1B 110, 083 22, 553 37, 518 approved NO 23, 989 911, 015 2A 63, 974 52, 341 53, 839 approved (uncertain) Y ES 52, 423 91, 903 2B 71, 364 47, 734 51, 056 approved (uncertain) Y ES 55, 374 85, 631 The Owen value is more reliable when the population of each group grows proportionally (Fragnelli-Iandolino, 2004)

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 : 966-977. 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 : 447463. 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 : 186-204. 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 : 76-88. 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.