Ranking transport projects by their socioeconomic value or financial interest rate of return ?

1. Ranking transport projects by their socioeconomic value or financial interest rate of return ? Alain Bonnafous Laboratoire d’Economie des Transports Pablo Jensen Laboratoire de Physique de la Matière Condensée et des Nanostructures

2. How to optimize public subsidies ? 17 highway projects : what is the best ranking to maximize the total socio-economical Net Present Value ? Project IRRse IRR Cost (ME) Arles - Salon 74% 7,5% 283 Isle Adam - Amiens 45% 6,1% 488 Toulouse Pamiers 30% 4,1% 450 Tours - Alençon 28% 3,6% 698 Dôle - Bourg 20% 7,1% 737 Saintes - Rochefort 20% 2,3% 290 Tours - Vierzon 19% 4,1% 800 Annemasse-Thonon 18% 7,9% 378 Grenoble - Sisteron 17% 2,5% 1880 Sens - Courtenay 15% 10,1% 197 Orléans - Courtenay 13% 3,0% 470 Dijon - Dôle 12% 9,5% 213 Lyon - Balbigny 11% 1,2% 770 Ambérieu - Bourgoin 11% 1,2% 500 Rouen - Alençon 9% 1,4% 580 A88 Caen - Argentan 9% 1,2% 250 Troyes - Auxerre 4% 0,9% 1350

3. Scope :Maximize the total NVPse, taking into account a budget • constraint F / year • Budget is used to subsidize projects, to raise their IRR to 8 %

4. How to rank projects ? IRRse ? IRR ? Other ? • Does it depend on annual budget ? • Value of F determines rhythm of completion of projects • (each project draws c  of public subsidies per year during • the first 5 years). Example : for F = 150, taking IRRse ranking 1st year : Arles - Salon (sub : 38) 2nd year : Isle Adam - Amiens (sub : 230) 4th year : Toulouse Pamiers (sub : 400) • We calculate the total NVPse returned after 50 years. •  Quantify the socioeconomic value of a given ranking

5. IRRse always better than random !

6. IRR better than IRRse, for every F ! < sub >

7. Finding the optimal order • Systematic exploration : too many possibilities ! • Clever search : • Simulated annealing (1983) • Genetics (1996) • Ants (1999)

8. Example with simulated annealing : atomic cluster structure

9. Our algorithm (~ simulated annealing ) : • Start from an arbitrary initial state (random, IRR order...) • (1) Permute two randomly chosen projects, i and j • (2) Calculate the total NVPse for this new ranking. • (3) Accept the permutation if the new total NVPse > old NVPse. • (4) Otherwise, calculate p=exp((NVPse_new – NVPse_old)/T) • (5) With probability p authorize the permutation, otherwise cancel it. • (6) If the permutation is accepted, the temperature is slightlydecreased. • (7) Start over, step (1).

10. Algorithm convergence

11. Improvement / IRRse < sub >

12. Example F=50 (<F>/10) NVPse returned optimal 10973 O 10943 IRR 10312 IRRse 9097 Project Output Dijon - Dôle infinite Arles - Salon 12.53 Sens - Courtenay infinite Annemasse - Thonon 8.85 Isle Adam - Amiens 1.10 Dôle - Bourg 0.76 Toulouse Pamiers 0.69 Tours - Alençon 0.31 Tours - Vierzon 0.26 Saintes - Rochefort 0.18 Orléans - Courtenay 0.16 Ambérieu - Bourgoin 0.08 A88 Caen - Argentan 0.05 Grenoble - Sisteron 0.18 Lyon - Balbigny 0.08 Troyes - Auxerre 0.05 Rouen - Alençon 0.06 Sub 0 35 0 9 229 163 462 833 821 520 672 1478 739 3150 2276 4986 1524 Best « analytical » ranking criterion Output O : NVPse / subsidy ~ IRRse/(0.08 - IRR)

13. « Moral » : do not spend too much on (financially) bad projects, even if « good » (socioeconomically speaking), otherwise you cannot build much... • Perspectives • Repeat analysis on present highway programme (30 projects) • Full power of the method : How to optimize a programme with interdependent projects ? • Rapport Plan 2003 : « La construction d’A48 (Ambérieu-Bourgoin) interviendra dans un contexte de forte évolution du réseau routier national et autoroutier. Des aménagements programmés ou à l’étude seront soit complémentaires à l’A48, en assurant une continuité du niveau de service pour certaines relations, soit défavorables à l’A48 en favorisant les itinéraires concurrents... scénarii + ou - »