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 ntre fo r Shipping a nd L o g istic s Did it Im pro ve Fa irne ss?
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 2
T ime line 2005/ 1 2005/ 2 2007 2013 2015 2015-2017 1st Division U-19 Division 2nd 3r d, U-15, U-16 and Chile Cup South Ame r ic an Wor ld Division U-17 Divisions Cup Qualifie r s Chile did no t q ua lify Ma thSpo rt I nte rna tio na l to 2006 Wo rld Cup L e uve n, Be lg ium 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 3 ra ndo m dra w…
F F IF IF A F A F o o tb a ll Wo rld Cup o o tb a ll Wo rld Cup UE UE F F A A Wor ldwide audie nc e CONCACAF CONCACAF 2014 OL : 2.1 b illio n AF AF C C 2014 F I F A WCup: 3.2 b illio n 2014 Supe rBo wl: 160 millio n CAF CAF 2014 F I F A WCup fina l: 1 b illio n CONME CONME BOL BOL OF OF C C 6 c ontine ntal c onfe de r ations Qualific ation phase : ~200 te ams F inal phase : 32 te ams 4
Ve ne zue la Colombia CONME CONME BOL BOL ’s South Ame r ’s South Ame r ic an ic an E c uador Wor Wor ld Cup Qualifie r ld Cup Qualifie r s s Br azil Pe r u Bolivia • 10 te a ms c o mpe te fo r 4.5 slo ts in the fina ls Par aguay • 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 Chile Ar ge ntina Ur uguay • 18 ro unds g ro upe d into 9 do ub le ro unds R ound 1 Round 2 Round 3 Round 4 … 1 st double r 2 nd double r ound ound 8 – 13 Oc t 12 – 17 No v 5
Ve ne zue la Colombia Br Br e aks within double r e aks within double r ounds ounds E c uador 7340 km Br azil Pe r u Bolivia R ound 1 Round 2 Round 3 Round 4 Home Away Home Away Par aguay ARGE NT INA … Away Home Away Away BOL IVIA Chile Ar ge ntina Ur uguay b re a k 1 st double r 2 nd double r ound ound I nc o nve nie nt fo r the te a ms/ pla ye rs 6
Ve ne zue la Colombia Br Br e aks within double r e aks within double r ounds ounds E c uador Br azil Pe r u Bolivia R ound 4 Round 5 Round 6 Round 7 Home Away Away Home Par aguay CHIL E … b re a k Chile Ar ge ntina Ur uguay 3 rd double r ound Se pt 2012 No v 2011 June 2012 Almo st a ye a r witho ut a ho me g a me I nc o nve nie nt fo r the fa ns/ lo c a l spo nso rs 7
Ve ne zue la Colombia Home vs Away star Home vs Away star t of a t of a E c uador double r double r ound ound Br azil Pe r u Bolivia R ound 1 Round 2 Round 3 Round 4 Home Away Home Away Par aguay ARGE NT INA … Away Home Away Away BOL IVIA Chile Ar ge ntina Ur uguay 1 st double r 2 nd double r ound ound F o 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 8
T T r r aditional mir aditional mir r r or or e d sc he dule (5 Wo rld Cups 1998-2014) e d sc he dule (5 Wo rld Cups 1998-2014) 1 st half 2 nd half 1 2 3 … 9 1 2 3 … 9 Round 1 Round 10 Ar ge ntina – Chile Chile – Ar ge ntina Ur uguay – Bolivia Bolivia – Ur uguay E c uador – Ve ne zue la Ve ne zue la – E c uador Pe r u – Par aguay Par aguay – Pe r u Colombia – Br azil Br azil – Colombia 9
Ve ne zue la Colombia 1) Could we find a mir 1) Could we find a mir r r or or e d sc he dule e d sc he dule E c uador without br without br e aks within double r e aks within double r ounds? ounds? Br azil Pe r u • A mirro re d sc he dule with no b re a ks in do ub le Bolivia ro unds fo r CONME BOL ’ S q ua lifie rs is infe a sib le Par aguay • Minimum: 16 • Old sc he dule 2002-2014: 18 Chile Ar ge ntina Ur uguay • 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) 2) Could we find a sc he dule as mir 2) Could we find a sc he dule as mir r r or or e d as e d as possible without br possible without br e aks within double r e aks within double r ounds? ounds? 10
Symme tr ic sc he dule s • 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. 11
12 mula I think the y use some kind of for
13 mula I think the y use some kind of for
Inte ge r pr ogr amming mode l De c ision var De c ision var iable s iable s i ∈ I (set of teams) , j ∈ I ( i ≠ j ), k ∈ K (set of rounds) i ∈ I, k ∈ K Odd = {1,3,5,…} 14
Basic c onstr aints 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 15
Basic c onstr aints 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 • 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 16
Double r ounds c onstr aints • 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 o g ic a l re la tio nships be twe e n va ria ble s x a nd y • L 17
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. aints op te am c onstr T •
19 Minimize bre a ks within do uble ro unds Obje c tive func tion o g ic a l re la tio nships L • •
20 1 9 2 nd half … 3 2 e nc h sc he me 9 … 1 st half 3 r y: F 2 Symme tr 1
21 8 … 2 nd half 2 1 9 nglish sc he me 9 8 1 st half … y: E 2 Symme tr 1
22 1 2 2 nd half … 8 9 te d sc he me 9 8 y: Inve r 1 st half … 2 Symme tr 1
23 9 9 8 y: bac k-to-bac k sc he me 8 … 2 2 1 Symme tr 1
Symme tr y: Min-Max se par ation sc he me 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 • E 24
Imple me ntation • 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 1 st half 2 nd half 3 9 1 2 3 … 9 2 … 1 25
CONME CONME BOL BOL me e ting me e ting http:/ / c o nme b o l.c o m/ Mirro re d Our sc he dule pr oposal De c isio n : ne w unanimously sc he dule b y a ra ndo m dra w Qua lifie rs fo r the 2018 agr e e d by the 10 Wo rld Cup Russia CONME BOL ’s c ountr ie s Sa me sc he dule | | | | | | | 1998 2002 2014 Jan-2015 May-2015 Oc t-2015 Oc t-2017
T E AM NAME T E AM NUMBE R SCHE DUL E Matchday 1 Matchday 2 Matchday 17 Matchday 18 Team 1 Team 9 Team 3 Team 4 Team 1 Team 3 Team 9 Team 1 Team 2 Team 5 Team 5 Team 7 Team 2 Team 6 Team 5 Team 2 Team 4 Team 6 Team 6 Team 8 … Team 4 Team 9 Team 6 Team 4 Team 7 Team 3 Team 9 Team 2 Team 7 Team 10 Team 3 Team 7 Team 8 Team 10 Team 10 Team 1 Team 8 Team 5 Team 10 Team 8 Shaun Botterill/Getty Images Europe (zimbio.com/) Shaun Botterill/Getty Images Europe (zimbio.com/) 1 st double ‐ round 9 th double ‐ round Ronaldo F or lán Be st Wo rld Cup Be st Wo rld Cup Pla ye r Awa rd 1998 Pla ye r Awa rd 2010 OPE R AT IONS R E SE AR CH 27
T e mplate sc he dule 2018 Wor ld Cup ROUNDS T E A M S 28
… 29 ld Cup Ne w sc he dule 2018 Wor
Old sc he dule 2002-2014 Wor ld Cups … 30
… Did it Im pro ve Fa irne ss? Ba la nc e = Fa irne ss? Compar ison B h : number of home breaks within double rounds B a : 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 31
… 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 ound A sc he dule is g-r anking- E xample : S tanding s afte r 6 ro unds 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 32
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