Guillermo Durán Rafael Epstein Gonzalo Zamorano

1. Quantitative Methods for a New Configuration of Territorial Units in a Chilean Government Agency Tender Process • Universidad de Chile • Universidad de Buenos Aires Guillermo Durán Rafael Epstein Gonzalo Zamorano Cristian Martínez former Chilean Vice-Minister of Education (Jan2008-March2010)

2. SchoolMealsProgram • Daily reaches 2 million children, from 0 to 24 years • 11,000 schools along the country (4200 Km) • Private catering firms bid on supply contracts • US$600 million a year Thelargestprocurementprocess in Chile

3. CHILE REGION 1 UT 1 UT 3 UT 2 UT 4 UT 5 REGION 2 UT 8 UT 6 UT 7 UT 9 REGION 13 UT 135 Territorial Units (TUs) CHILE: 13 regions 136 TUs UT 133 UT 134 UT 136

4. Combinatorial Auction • In 1997 a Combinatorial Auction is implemented • Milgrom P., Putting Auction Theory to Work, 2007, Cambridge University Press. • Cramton P., Shoham Y., Steinberg R. (editors), Combinatorial Auctions, 2006, The MIT Press. • Each year, 1/3 of all TUs is contracted • Bids provide services for 3 years

5. Combinatorial Auction Benefits • Cost synergies are reflected on the bids • Economies of scale • Volume discounts in purchasing inputs • Economies of density • Logistic savings when serving nearby units • US$3 billion awarded with this model • Cost reduction reported: 22%

6. A New Challenge: Bankruptcy Five firms declared bankruptcy between 2004 and 2007 leading to serious financial and social losses for the government • Bankruptcy is a big problem: • Meal service is interrupted, affecting the educational process • Restoring service in affected TUs is more expensive • Bankruptcies eliminate an actor from the market

7. Bankruptcies Causes • 1° Cause: Price War among firms • Tender system promotes competition • Companies drop their prices to eliminate competitors • After the war the prices tend to increase, higher than before • Prices Band • Try to identify the abnormal low prices • Eliminate these bids from the process

8. Bankruptcies Causes • 2° Cause: Limited liability • Aggressive bids on TUs with unknown operating conditions • When the real operation is good: • The firm starts a successful business • When the real operation is unsustainable: • The firm assumes the private costs • JUNAEB assumes the rest of the costs • Social costs, costly small auctions, less competitive market

9. Uncertainty Problem • Some TUs offer worse operating conditions • Firms don’t properly estimate its costs in these TUs • Firms offer low prices on “bad” TUs • The bidding process selects some of them • After that, they may not fulfill their contracts

10. Proposed Solution • Redesign TUs configuration • Avoid “bad conditioned”TUs • Homogenize operating conditions of TUs • Reduce the global risk of the system

11. Using OR to Reconfigure TUs

12. Chilean Geographical Division • Territorial Units • Groups of comunas • Firms bid over the whole TU • 136 TUs Comunas • The smallest administrative units • 346 comunas in Chile

13. Attractiveness Index of TU • Number of meals: magnitude of the contract • Number of schools: fixed costs of supply • Area covered (in km2): transport costs • % Inaccessible schools: geographical conditions Number of meals Number of Schools Total Area Accessibility

14. Bankruptcy: relatively “bad” TU • TUs involved in recent bankruptcies • Central Purpose: • Reconfigure the Comunas into homogeneous TUs

15. The Attractiveness Index Based on the Analytic Hierarchy Process (Saaty, 1980) total attractiveness score for TU j in region r. importance of number of meals within the set of criteria weight of TU j in region r on number of meals criterion importance of number of schools within the set of criteria weight of TU j in region r on number of schools criterion importance of size of area of TU within the set of criteria weight of TU j in region r on area criterion importance of type of access to school within the set of criteria weight of TU j in region r on accessibility criterion

16. Importance of each characteristic • aM,bS,cAr,dAc: relative importance • Pairwise comparisons made by expert advice • The final values for each criterion were: • aM: Meals 38% • bS: Schools 34% • cAr: Area 17% • dAc: Access 11%

17. Importance of each characteristic • xM,j,rxS,j,rxAR,j,rxAC, j, r • calculated by using statistical data • Example: • Region has 2 TUs • UT1 = 40,000 meals • UT2 = 60,000 meals • Then xM,1,r =40 and xM,2,r=60

18. Method 1: Local Search Heuristic • Objective: minimize the standard deviation, this is, the dispersion of TU attractiveness levels in a region • Create initial solution for every possible number of TUs • Comunas are exchanged between TUs in a Region • In each iteration, only one comuna is exchanged • The best local optimum is selected

19. Local Search Heuristic 0. Initial Solution 1. First Iteration N. After N iterations, final solution

20. Region Comunas Meals Schools Area (km ² ) Easy access Difficult access Arica 25,726 62 4,799 62 0 Camarones 54 8 3,927 7 1 Putre 248 6 5,903 6 0 General Lagos 180 9 2,244 9 0 Iquique 9,155 38 2,262 38 0 1st Region Alto Hospicio 11,387 25 573 25 0 Huara 460 12 10,475 12 0 Camiña 404 9 2,200 9 0 Colchane 252 5 4,016 5 0 Pica 799 5 8,934 5 0 Pozo Almonte 1,685 10 13,766 10 0 Total 50,350 189 59,099 188 1 Local Search Heuristic, example • Table of Characteristics: 1st Region • Lower bound fixed per UT: 15,000 • Upper bound fixed per UT: 40,000 • This region may have 2 or 3 TUs

21. Example, starting with 2 UTs Std. Dev = 5.93 Std. Dev = 1.33 Std. Dev = 0.33

22. Example, starting with 3 UTs Std. Dev = 3.37 Std. Dev = 1.67 Std. Dev = 0.88

23. The 2 TUs solution was selected 3 TUs final solution Std. Dev = 0,88 • 2 TUs final solution Std. Dev = 0,33

24. Method 2: Integer Programming • Objective: minimize the difference between the most and least attractive TU in each region • Good linearization of minimize the standard deviation • Algorithm generates all possible TUs, called clusters

25. Integer Programming Model • Formulation

26. Integer Programming Model • Formulation

27. Results Standard Deviation • Both final solutions improve standard deviation on the situation prevailing before 2007

28. Results Gap (most and least attractive TU ) • Both final solutions improve gap (max-min) on the situation prevailing before 2007

29. JUNAEB used our solution • The configuration was adopted by JUNAEB in 2007 • Since 2007, no bankruptcies have occurred • Accepted for publication in Interfaces • “Quantitative Methods for a New Configuration of Territorial Units in a Chilean Government Agency Tender Process”, Guillermo Durán, Rafael Epstein, Gonzalo Zamorano, Cristian Martínez

30. Improving Public Policies

31. Education and Opportunities

32. Efficiency and Quality

33. Quantitative Methods for a New Configuration of Territorial Units in a Chilean Government Agency Tender Process • Universidad de Chile • Universidad de Buenos Aires Guillermo Durán Rafael Epstein Gonzalo Zamorano Cristian Martínez former Chilean Vice-Minister of Education (Jan2008-March2010)