Bradford talk May 2005 1

Sports scheduling – don't just give them what they ask for, give them

what they really want

Mike Wright

Department of Management Science

Lancaster University

m.wright@lancaster.ac.uk

Bradford talk May 2005 2

Devon Cricket League

• Three county-wide divisions– plus other more local ones

• Ten teams per division– promotion and relegation

• All play all home and away– once in first half of season, once in second half– so 18 matches per team– played on Saturdays through the summer

Bradford talk May 2005 3

Fixture list

Devon Cricket League 2003 Premier Division Sat 3rd May Abbotskerswell v Sidmouth Barton v Paignton North Devon v Exeter Plympton v Bovey Tracey Torquay v Sandford Sat 10th May Bovey Tracey v Abbotskerswell Exeter v Plympton Paignton v Torquay Sandford v Barton Sidmouth v North Devon Sat 17th May Abbotskerswell v Plympton

……………………………………………

Bradford talk May 2005 4

What scheduling is needed?

• Timetabling fixtures– not too hard– follow same pattern every year

• Allocating umpires– harder, varying from year to year– depends on

• number of umpires, where they live, their qualifications and experience, club affiliations, requests for days off, …

Bradford talk May 2005 5

How was it done in the past?

• League secretary– retired military man– knew the league very well

• the clubs, players, umpires etc.

– pencil and paper job– not very computer literate

• but knew enough to know he could use help

– request eventually came to my doorstep

Bradford talk May 2005 6

Original request

• Objective – minimise distance travelled• Constraints

– Some umpires can’t do top division

– Some umpires can’t do top two divisions• (depends on qualifications and experience)

– Some umpires can’t umpire specific teams• (due to affiliation, being a past player)

– Most umpires want one or more Saturdays off

– Some umpires only to be used if essential

Bradford talk May 2005 7

Initial reaction

• That’ll be easy!– But surely that can’t be all?

– Worth asking a few more questions

• Ask some extra questions– This could mean most umpires sticking just to two or

three nearby grounds

– Is that really what you want?

– Answer – well, no, I’d like to spread them around more than that

Bradford talk May 2005 8

Further questions

• … questions where my own knowledge and experience (of cricket) helped

• Do you want an umpire to have the same team in successive weeks?

• Do you want the same pair of umpires to be together two weeks running?

• Do you want the same umpire to do {x v y} and {y v x}?• Answer – oh no, we can’t have that

Bradford talk May 2005 9

Yet further questions

• Does it matter how many matches each umpire has?– Oh well yes I want the best ones to do most and the least

qualified to do least

– Depending of course on how often they’re available

• How about the balance between divisions?– I like the best ones to do mainly Premier but perhaps a

few lower down to help train the other umpires

– Middling umpires to do a mixture of perhaps one or two Premier and quite a few Division A and Division B

– Least qualified can only do Division B

Bradford talk May 2005 10

Probe a little further

• Turn the question round• Not "What isn’t OK?" (constraint-focused)

– but "what would you ideally like?" (objective-focused)

• Forget for now what may or may not be possible• What would an ideal schedule look like?

– may be hard to answer

– may not have had the luxury to think like this before

– may not have realised it was allowed!

Bradford talk May 2005 11

The ideal schedule

• Zero travel!• Specify exactly how many matches in total for

each umpire in each division• Unless forbidden, equalise as much as possible the

incidences of:– umpires with clubs– umpires with grounds– pairs of umpires

• … and where duplication is necessary, make incidences a long way apart in time

Bradford talk May 2005 12

Oh, and by the way ….

• (he's really getting the hang of this now)• I may want a specific senior umpire to be paired three times during

the season with a specific junior umpire – is that OK?– to help the junior to qualify

• Sometimes one umpire can give the other a lift– can you incorporate this?

• And can we do half a season at a time?– and take account of changes to the first half (e.g. illness causing a

change of umpire for a match) when doing the second half• And can we avoid using two top-quality umpires being together

outside the Premier Division?• And try to make sure no umpire has too many long journeys?• And of course the answer's yes

– we can do anything – well, we can try

Bradford talk May 2005 13

Data needed - where the clubs play home matches

1 Abbotskerswell 6 4 2 Barton 7 4 3 Bovey Tracey 6 5 4 Exeter 7 7 5 North Devon 2 10 6 Paignton 6 4 7 Plympton 3 3 8 Sandford 6 8 9 Sidmouth 9 6 10 Torquay 7 4 11 Alphington 7 6 12 Axminster 10 7………………………………………..

(x,y) co-ordinates on a 10 km grid. (0,0) is in South-East Cornwall.

Bradford talk May 2005 14

Data required about umpires 1 J Anning 9 7 1 ………/x…….. 5 2 1 5 2 0

2 S Bilverstone 6 3 1 ………/……… 2 3 2 3 2 0

3 G Curson 2 5 1 x..x..x../..xxxx… 4 1 1 3 1 0

4 E Daniels 2 3 1 …xx…x/..x…… 4 1 1 4 2 1

……………………………………….

43 V Gainey 3 9 2 .x.xx.x.x/…xx.xx. 0 0 3 0 1 3

44 D Howe 6 5 3 ………/……… 0 0 0 0 0 0

45 P Matten 6 8 2 ………/……… 0 3 5 0 4 4

46 G Pascoe 5 5 3 xx.xx.xxx/x.xxxxx.x 0 0 1 0 0 1

………………………………………….

Home co-ordinates, status (1 high, 3 low), availability each Saturday, target number of matches in each division, in each half of the season.

Procedure available to check for consistency.

Bradford talk May 2005 15

Further information required

• Not ump/div 3 P

• Not ump/div 2 P

• Not ump/div 3 A

• ……………………………….

• Max ump/club D Elphick Bovey Tracey 0

• Max ump/club M Glass Seaton 0

• …………………………………

• Min ump/ump B Perry J Neville 2

• Min ump/ump C Russell B Warren 3

• …………………………………

• Other types of rule also available

Bradford talk May 2005 16

Problem formulation

• Now lots of objectives• No constraints apart from the most basic

– all matches must be covered by two umpires– no umpire can do two matches at the same time

• Much more complex than it could have been– if I hadn't asked all those questions

• But now I stand a chance of exceeding expectations by miles– instead of just giving him what he asked for

Bradford talk May 2005 17

Objectives

• Travel distance– making allowance for lifts– need to decide rule for lift-giving– e.g. will give lift if adds no more than 25 miles to

umpire A's journey and umpire B's journey would have been at least 50 miles

• lots of penalty costs– some for breaking "hard" constraints– but many for breaking "soft" or "fuzzy" constraints

Bradford talk May 2005 18

Penalty costs

• Pair of umpires together more than once• Pair of umpires together more than once within X

weeks (cost depends on X)• Umpire-club pairing more than once• Umpire-club pairing more than once within X

weeks (cost depends on X)• Umpire-ground pairing more than once• Umpire-ground pairing more than once within X

weeks (cost depends on X)

Bradford talk May 2005 19

More penalty costs

• Umpire of status S having G too many matches in Division D (may depend on S, G and D)

• Umpire of status S having G too many matches in total (may depend on S and G)

• Two umpires of top status being together outside Premier Division

• Umpire having more than one long journey in the season– over 50 miles?

• Hard constraint being broken (high cost)• But hang on a moment now …

Bradford talk May 2005 20

Comparing costs

• We have to find relative weightings for all objectives• So we now need to pose awkward questions

– e.g. "how many miles of travel is equivalent to two umpires being together more than once?" etc.

• Can I ask the league secretary?– well I could but it'd flummox him– and it's not really necessary

• I can decide for myself– he's the expert on his problem, but I'm the expert on problem

formulation – a crucial part of the solution procedure– so it's vital that I really understand the context

Bradford talk May 2005 21

Solution technique

• I use a version of Simulated Annealing– quite easy to implement– gives excellent solutions within a few minutes on an

ordinary PC– much better than league secretary believed possible

• I've also tried various other techniques– it's a useful test-bed for ideas about new variations– some techniques give marginally better solutions than

others– but small effect compared with not getting the

formulation right

Bradford talk May 2005 22

Moral of the story• I could have just delivered what he asked for

– perhaps with an optimal solution– and he'd have been reasonably satisfied

• For a wholly commercial arrangement, perhaps that's what I would have done– but this customer can't pay, and isn't computer-savvy –

he doesn't know what can or can't be done– so different ethical considerations apply

• Don't just give them what they ask for – give them what they really want!– we can, and therefore we should