Scheduling the Italian Football League

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Scheduling the Italian

Football LeagueF. Della Croce, D. Oliveri

David Moh


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Overview

Introduction

Problem Description

Requirements

Approach

Solution

Phase 1

Phase 2 Phase 3

Example

Result

Real Data

Conclusion


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Overview

Introduction

Problem Description

Requirements

Approach

Solution

Result


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Introduction

Problem Description

Scheduling the Italian Major Football League tournament calendar ( Serie A )

Set N of n teams

All in different towns

Scheduling a double round robin tournament

Team plays twice one home and one away

Travel distance is not an issue

A team much have a break between two consecutive home or away matches

Matches can be played simultaneously

2 TV company airing the home matches live

Create a schedule with minimal breaks while keeping a balanced TV coverage


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Introduction

Requirements

Each city is represented by max of two football team

Each city has one stadium, so for city with two football team need to have

complementary home/away schedules

Each team plays 2 times with another team, one home and one away

Best teams in the previous year (seeded teams) cannot occur in the first andlast weeks of the calendar

City with two football team that are playing against each other cannot occurin the first and last weeks of the calendar

Home matches of teams are divided equally over the 2 TV


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Introduction

Approach

ILP based approach

Pattern

String of symbols: A= away and H=home

Problem solved in 3 phases

Create feasible pattern sets

Create feasible timetable from the pattern sets

Create final calendar from the timetable


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Overview

Introduction

Solution

Phase 1

Phase 2

Phase 3

Example

Result


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Solution

Phase 1

Only patterns with no more than 4 breaks are allowed

Only pattern set composed of complementary patterns pairs

, {0, 1} 1, if pattern i is assigned to TV k

0, otherwise

number of breaks of pattern I Total number of teams assigned to TV k (home)

, {0, 1} 1, if pattern i plays at home on weekj

0, if pattern i plays at away on weekj

C The set of complementary patterns pairs


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Solution

Phase 1


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Solution

Phase 1


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Solution

Phase 1


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Solution

Phase 1

P1, P2, P3, P4, P5, P6 chosen

P2, P3, P5, P6 assigned to TV1

P1, P4, assigned to TV2


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Solution

Phase 2

,, {0, 1} 1, if pattern i is matched to patternj in week t

0, otherwise

, The set of patterns playing home in week t

where pattern i plays away


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Solution

Phase 2


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Solution

Phase 2

P1, P2, P3, P4, P5, P6 chosen from phase 1


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Solution

Phase 3

, {0, 1} 1, if pattern i is matched to teamj

0, otherwise

, Cost coefficient of pattern i for teamj

Set pattern assigned in phase 1 to TV k

Set teams assigned to TV k

C Set of complementary patterns pairs D Set of team pairs belonging to the same city

Set of pattern i that cannot be matched to a seeded team

Set of pattern i that cannot be matched to a team

T Set of seeded teams


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Solution

Phase 3


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Solution

Example

We have 6 teams: A, B, C, D, E, F

A, B, C, D belongs to TV 1 and E, F to TV 2

Seeded teams A, E

Same city teams A, B

= 1

P2, P3, P5, P6 assigned to B, A, C, D respectively

P1, P4 assigned to F, E respectively


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Solution

Example

P2, P3, P5, P6 assigned to B, A, C, D respectively

P1, P4 assigned to F, E respectively


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Solution

Example

A, B, C, D belongs to TV 1 and E, F to TV 2

Seeded teams A, E

Same city teams A, B

= 1


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Overview

Introduction

Solution

Result

Real Data

Conclusion


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Result

Real data

Real data from year 2001-2002, 2002-2003, 2003-2004

18 teams

All data had 4 seeded teams

Same town team

2001-2002 & 2002-2003 3 pair of teams

2003-2004 2 pair of teams

Minimum number of breaks: 48


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Result

Real data

For each year 5 calendars were made


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Result

Conclusion

ILP approach works for double round robin calendar

Requirements

Improvement of the calendar

Scheduling the Italian Football League

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