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Quantitative Methods for a New Configuration of Territorial Units in a Chilean Government Agency Tender Process Guillermo Durán Rafael Epstein Gonzalo.

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Presentation on theme: "Quantitative Methods for a New Configuration of Territorial Units in a Chilean Government Agency Tender Process Guillermo Durán Rafael Epstein Gonzalo."— Presentation transcript:

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

2  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 The largest procurement process in Chile School Meals Program

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

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

13  Number of meals: magnitude of the contract  Number of schools: fixed costs of supply  Area covered (in km 2 ): transport costs  % Inaccessible schools: geographical conditions Attractiveness Index of TU Number of Schools Total Area Accessibility Number of meals

14 Attractiveness Category Territorial Units (TU Codes)Total TUs Below Average 101, 1004, 1007, 1005, 1010, 302, 609, 803, 805, 1101 10 Average102, 301, 6053 Above Average606, 607, 13213 Bankruptcy: relatively “bad” TU  TUs involved in recent bankruptcies  Central Purpose: Reconfigure the Comunas into homogeneous TUs

15 Based on the Analytic Hierarchy Process (Saaty, 1980) The Attractiveness Index 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  a M, b S, c Ar, d Ac : relative importance  Pairwise comparisons made by expert advice  The final values for each criterion were: a M :Meals 38% b S :Schools 34% c Ar :Area 17% d Ac :Access 11%

17 Importance of each characteristic  x M,j,r x S,j,r x AR,j,r x AC, j, r calculated by using statistical data  Example: Region has 2 TUs UT1 = 40,000 meals UT2 = 60,000 meals Then x M,1,r =40 and x M,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 Local Search Heuristic, example Lower bound fixed per UT: 15,000 Upper bound fixed per UT: 40,000 This region may have 2 or 3 TUs  Table of Characteristics: 1 st Region

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

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

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

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 Region Standard DeviationImprovement OriginalHeuristicModelO v/s HO v/s M I5,930,330,2994%95% II0,18 0% III0,740,19 75% IV5,941,810,8869%85% V1,470,680,9953%33% VI3,270,470,1686%95% VII4,050,410,5390%87% VIII2,440,600,8775%64% IX3,900,400,0390%99% X1,040,840,8819%15%  Both final solutions improve standard deviation on the situation prevailing before 2007

28 Results Gap (most and least attractive TU ) Region Differences (max - min)Improvement OriginalHeuristicModelO v/s HO v/s M I12,700,550,0496%100% II0,20 0% III2,551,02 60% IV46,493,361,5892%97% V12,624,821,2662%88% VI40,842,580,3794%99% VII63,481,140,1798% VIII72,862,872,4996% IX47,091,370,1397%100% X3,812,512,2534%41%  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 Covers 2 million students in 11,000 schools School meal program, scholarships, health programs, housing US$1,000 million annual budget Highly respected government institution. Singled out by the UN as exemplary model for school meal programs JUNAEB

32 Efficiency and Quality

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


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