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O p e ra tio ns Re se a rc h T ra nsfo rme d the Sc he d uling Ma rio Gua ja rdo o f So uth Ame ric a n Wo rld NHH No rwe g ia n Sc ho o l o f E c o no mic s De pt. o f Busine ss a nd Ma na g e me nt Sc ie nc e C up Q ua lifie rs: Ce

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SLIDE 1

O p e ra tio ns Re se a rc h T ra nsfo rme d the Sc he d uling

  • f So uth Ame ric a n Wo rld

C up Q ua lifie rs:

Did it Im pro ve Fa irne ss?

Ma rio Gua ja rdo

NHH No rwe g ia n Sc ho o l o f E c o no mic s

De pt. o f Busine ss a nd Ma na g e me nt Sc ie nc e Ce ntre fo r Shipping a nd L

  • g istic s
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SLIDE 2

2

RONAL DO

Golde n Ball Be st Playe r Awar d Wor ld Cup 1998

F ORL ÁN

Golde n Ball Be st Playe r Awar d Wor ld Cup 2010

https://www.youtube.com/watch?v=X4wS2zHLt2o

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SLIDE 3

2005/ 1

1st Division

2005/ 2

U-19 Division

2007

2nd Division

2013

3r d, U-15, U-16 and U-17 Divisions

2015-2017

South Ame r ic an Wor ld Cup Qualifie r s

2015

Chile Cup

T ime line

3

Chile did no t q ua lify to 2006 Wo rld Cup Sc he dule pro po sa l fo r 2010 Wo rld Cup re je c te d by CONME BOL Chile q ua lifie d to 2010 Wo rld Cup Chile q ua lifie d to 2014 Wo rld Cup CONME BOL a g re e d ne w sc he dule b y a ra ndo m dra w… Ma thSpo rt I nte rna tio na l L e uve n, Be lg ium

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SLIDE 4

CONCACAF CONCACAF CONME BOL CONME BOL CAF CAF UE F A UE F A AF C AF C OF C OF C 6 c ontine ntal c onfe de r ations Qualific ation phase : ~200 te ams F inal phase : 32 te ams

F IF A F

  • o tb a ll Wo rld Cup

F IF A F

  • o tb a ll Wo rld Cup

4

Wor ldwide audie nc e

2014 OL : 2.1 b illio n 2014 F I F A WCup: 3.2 b illio n 2014 Supe rBo wl: 160 millio n 2014 F I F A WCup fina l: 1 b illio n

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SLIDE 5
  • 10 te a ms c o mpe te fo r 4.5 slo ts in the fina ls
  • E

ve ry te a m pla ys twic e a g a inst e ve ry o the r te a m

  • 2 ye a rs
  • 18 ro unds g ro upe d into 9 do ub le ro unds

Br azil Ur uguay Ar ge ntina Chile Ve ne zue la Colombia Bolivia Pe r u Par aguay E c uador

CONME BOL ’s South Ame r ic an Wor ld Cup Qualifie r s CONME BOL ’s South Ame r ic an Wor ld Cup Qualifie r s

5

R

  • und 1

Round 2 Round 3 Round 4

1st double r

  • und

8 – 13 Oc t

2nd double r

  • und

12 – 17 No v

…

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SLIDE 6

…

1st double r

  • und

2nd double r

  • und

Br azil Ur uguay Ar ge ntina Chile Ve ne zue la Colombia Bolivia Pe r u Par aguay E c uador

b re a k

ARGE NT INA BOL IVIA R

  • und 1

Round 2 Round 3 Round 4

Home Away Home Away Away Home Away Away

Br e aks within double r

  • unds

Br e aks within double r

  • unds

6

I nc o nve nie nt fo r the te a ms/ pla ye rs

7340 km

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SLIDE 7

…

3rd double r

  • und

Br azil Ur uguay Ar ge ntina Chile Ve ne zue la Colombia Bolivia Pe r u Par aguay E c uador

b re a k

CHIL E R

  • und 4

Round 5 Round 6 Round 7

Home Away Away Home

Br e aks within double r

  • unds

Br e aks within double r

  • unds

7

I nc o nve nie nt fo r the fa ns/ lo c a l spo nso rs

No v 2011 June 2012 Se pt 2012

Almo st a ye a r witho ut a ho me g a me

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SLIDE 8

…

1st double r

  • und

2nd double r

  • und

Br azil Ur uguay Ar ge ntina Chile Ve ne zue la Colombia Bolivia Pe r u Par aguay E c uador ARGE NT INA BOL IVIA R

  • und 1

Round 2 Round 3 Round 4

Home Away Home Away Away Home Away Away

Home vs Away star t of a double r

  • und

Home vs Away star t of a double r

  • und

8

F

  • r lo g istic a l re a so ns, sta rting a do ub le ro und with a

ho me g a me is usua lly pre fe rre d

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SLIDE 9

Ar ge ntina – Chile Ur uguay – Bolivia E c uador – Ve ne zue la Pe r u – Par aguay Colombia – Br azil Round 1 Chile – Ar ge ntina Bolivia – Ur uguay Ve ne zue la – E c uador Par aguay – Pe r u Br azil – Colombia Round 10 1st half 2nd half 1 2 3 1 2 3 9 … 9 …

T r aditional mir r

  • r

e d sc he dule (5 Wo rld Cups 1998-2014) T r aditional mir r

  • r

e d sc he dule (5 Wo rld Cups 1998-2014)

9

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SLIDE 10
  • A mirro re d sc he dule with no b re a ks in do ub le

ro unds fo r CONME BOL ’ S q ua lifie rs is infe a sib le

  • Minimum: 16
  • Old sc he dule 2002-2014: 18
  • T

ra ditio n: mirro re d ha rd to c ha ng e (sa me sc he dule use d fo r 4 la st Wo rld Cups)

Br azil Ur uguay Ar ge ntina Chile Ve ne zue la Colombia Bolivia Pe r u Par aguay E c uador

1) Could we find a mir r

  • r

e d sc he dule without br e aks within double r

  • unds?

1) Could we find a mir r

  • r

e d sc he dule without br e aks within double r

  • unds?

10

2) Could we find a sc he dule as mir

r

  • r

e d as possible without br

e aks within double r

  • unds?

2) Could we find a sc he dule as mir

r

  • r

e d as possible without br

e aks within double r

  • unds?
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SLIDE 11

Symme tr ic sc he dule s

11

  • Symme tric do ub le ro und ro b in

to urna me nt sc he dule : ma tc he s o rde re d with re spe c t to so me “struc ture ”, usua lly the se c o nd ha lf with re g a rd to the first o ne .

  • 20 o ut o f 25 E

uro pe a n le a g ue s fo llo w a symme tric sc he me

(Go o sse ns & Spie ksma 2012).

  • 15 o f the m use a mirro re d

fo rma t.

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SLIDE 12

I think the y use some kind of for mula

12

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SLIDE 13

I think the y use some kind of for mula

13

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SLIDE 14

Inte ge r pr

  • gr

amming mode l

14

De c ision var iable s De c ision var iable s

i ∈ I (set of teams), j ∈ I (i ≠ j), k ∈ K (set of rounds) i ∈ I, k ∈ KOdd = {1,3,5,…}

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SLIDE 15

Basic c onstr aints

15

  • Do ub le ro und-ro b in split in two sing le -ro und ro b in ha lve s: te a m i a nd te a m j

pla y a g a inst e a c h o the r o nc e in e a c h ha lf o f the to urna me nt

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SLIDE 16

Basic c onstr aints

16

  • Co mpa c tne ss: e ve ry te a m pla ys e xa c tly o ne g a me pe r ro und
  • Ho me -a wa y b a la nc e with o ppo ne nt: te a m i pla ys a t ho me a g a inst te a m j

e xa c tly o nc e

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SLIDE 17

Double r

  • unds c onstr

aints

17

  • Ba la nc e o f ho me -a wa y se q ue nc e s: e ve ry te a m sta rts a do ub le ro und with a

ho me g a me a t le a st 4 a nd a t mo st 5 time s

  • L
  • g ic a l re la tio nships be twe e n va ria ble s x a nd y
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SLIDE 18

T

  • p te am c onstr

aints

18

  • No te a m pla ys c o nse c utive ma tc he s a g a inst Arg e ntina a nd Bra zil.
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SLIDE 19

Obje c tive func tion

19

  • Minimize bre a ks within do uble ro unds
  • L
  • g ic a l re la tio nships
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SLIDE 20

Symme tr y: F r e nc h sc he me

20

1st half 2nd half 1 2 3 9 … … 1 3 9 2

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SLIDE 21

Symme tr y: E nglish sc he me

21

1st half 2nd half 1 2 … 9 8 2 8 1 9 …

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SLIDE 22

Symme tr y: Inve r te d sc he me

22

1st half 2nd half 1 2 … 9 8 … 1 8 9 2

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SLIDE 23

Symme tr y: bac k-to-bac k sc he me

23

1 1 2 2 8 9 8 … 9

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SLIDE 24

Symme tr y: Min-Max se par ation sc he me

24

  • E

ve ry te a m pla ys a g a inst e ve ry o the r te a m a t mo st o nc e in c c o nse c utive ro unds

  • E

ve ry te a m pla ys a g a inst e ve ry o the r te a m a t le a st o nc e in d c o nse c utive ro unds

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SLIDE 25

Imple me ntation

25

  • AMPL

/ CPL E X 12.5, I nte l Co re 2 Duo 2.26GHz ~1700 b ina ry va ria b le s ~1700 c o nstra ints

  • So lutio ns fo und q uic kly
  • Se ve ra l pro po sa ls disc usse d with the Chile a n ANF

P ma na g e rs

  • T

he y c ho se o ne o f the te mpla te sc he dule s tha t we g e ne ra te d a c c o rding to the F

r e nc h sc he me

1st half 2nd half 1 2 3 9 … … 1 3 9 2

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SLIDE 26

De c isio n: ne w sc he dule b y a ra ndo m dra w

Our sc he dule pr

  • posal

unanimously

agr e e d by the 10 CONME BOL ’s c ountr ie s 1998 2014 2002 Jan-2015 May-2015 Oc t-2017

http:/ / c o nme b o l.c o m/

Mirro re d Sa me sc he dule

| | | | | |

CONME BOL me e ting CONME BOL me e ting

Qua lifie rs fo r the 2018 Wo rld Cup Russia

Oc t-2015 |

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SLIDE 27

Ronaldo

Be st Wo rld Cup Pla ye r Awa rd 1998

F

  • r

lán

Be st Wo rld Cup Pla ye r Awa rd 2010

T E AM NAME

Shaun Botterill/Getty Images Europe (zimbio.com/) Shaun Botterill/Getty Images Europe (zimbio.com/)

T E AM NUMBE R

27

SCHE DUL E

Matchday 1 Team 1 Team 9 Team 2 Team 5 Team 4 Team 6 Team 7 Team 3 Team 8 Team 10 Matchday 2 Team 3 Team 4 Team 5 Team 7 Team 6 Team 8 Team 9 Team 2 Team 10 Team 1 Matchday 17 Team 1 Team 3 Team 2 Team 6 Team 4 Team 9 Team 7 Team 10 Team 8 Team 5 Matchday 18 Team 9 Team 1 Team 5 Team 2 Team 6 Team 4 Team 3 Team 7 Team 10 Team 8

…

1st double‐round 9th double‐round

OPE R AT IONS R E SE AR CH

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SLIDE 28

28

T e mplate sc he dule 2018 Wor ld Cup

ROUNDS

T E A M S

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SLIDE 29

29

Ne w sc he dule 2018 Wor ld Cup

…

slide-30
SLIDE 30

30

Old sc he dule 2002-2014 Wor ld Cups

…

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SLIDE 31

31

Compar ison

Bh: number of home breaks within double rounds Ba: number of away breaks within double rounds B: total number of breaks within double rounds H-A: number of double rounds started with a home game A-H: number of double rounds started with an away game

… Did it Im pro ve Fa irne ss?

Ba la nc e = Fa irne ss?

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SLIDE 32

32

A sc he dule is g-r

anking- balanc e d, if a fte r e a c h

ro und, the diffe re nc e b e twe e n the numb e r o f ho me g a me s pla ye d b y a ny two te a ms up till the n is a t mo st g (Go o sse ns

& Spie ksma , 2012).

g=1

T he minimum po ssible . Old sc he dule

g=3

E xample : S tanding s afte r 6 ro unds

… Did it Im pro ve Fa irne ss?

Ba la nc e = Fa irne ss?

F air r anking afte r e ac h r

  • und
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SLIDE 33

33

  • Perhaps the most

most even and exciting even and exciting tournament ever tournament ever seen in this competition.

“T HI S I S T HE MOS T E VE N QUAL I F I CAT I ON I N A L ONG WHI L E ”

Ge r ar do Mar tino Coac h

“T HI S QUAL I F I CAT I ON T OURNAME NT WI L L BE VE RY I NT E NS E UNT I L T HE L AS T ROUNDS ”

Juan Pizzi Coac h

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SLIDE 34

34

Right before the last match of the 2018 tournament, only Brazil was already qualified to the World Cup finals while 6 other teams were still fighting for the 3.5 qualification berths that remained available.

Qualifie r situation right be for e the last matc h Standings r ight be for e the last matc h

… Did it Im pro ve Fa irne ss?

C ha nc e s till the e nd = Fa irne ss?

(unc e r tainty)

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SLIDE 35

35

Some var iation me asur e s F inal standings

… Did it Im pro ve Fa irne ss?

T ig htne ss = Fa irne ss?

…

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SLIDE 36

36

http://851.cl http://301060.com.ar

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SLIDE 37

37

… Did it Im pro ve Fa irne ss?

I’ d like to think the sc he d ule p ro vid e d the o p p o rtunitie s fo r a ll te a m s to q ua lify o nly b y the ir fo o tb a ll m e rits

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SLIDE 38

Conc luding r e mar ks

38

  • Sc he duling fa irne ss = no t c re a te (a nd, mo re o ve r, e limina te ) o ppo rtunitie s fo r

te a ms to pe rfo rm b e tte r b e c a use o f the sc he dule inste a d o f the ir o wn me rits

Ho w to de sig n rule s that do no t favo r c e rtain c o mpe tito rs? Ho w to de sig n a sc he dule o f play that a prio ri o ffe rs similar c hanc e s to e ac h partic ipant? Ho w to re c o nc ile vario us (o fte n c o nflic ting ) re que sts e xpre sse d by the stake ho lde rs?

✓ Ba la nc e

✓ Unc e rta inty ✓ Tig htne ss

✓ A g re e m e nt

in p ra c tic e

… Did it Im pro ve Fa irne ss?

un

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SLIDE 39

39

G o o d luc k!

Sp a rta k Sta d ium