Investigating Scheduling of Work: A Two-Stage Optimal Matching Analysis

of Workdays and Workweeks

Man Yee Kan (CTUR, University of Oxford)Laurent Lesnard (CNRS/Sciences Po)

Measuring working timeMeasuring working time

• Stylised data Vs diary data• Stylised data (LFS type) - Recalled

‘usual’ ‘normal’ weekly working hours, taking less account of atypical hours/days• Diary data – more accurate, recording

timing as well as duration of events

Workweek grid diary data Workweek grid diary data

• UK Time Use Survey (ONS, 2000-01)– June 2000 to August 2001–Couple level of data–Response rate: 45% (61% for household

questionnaires, 73% for subsequent diaries)–Workweek grid + 2 day diaries +

questionnaires

The ONS Workweek GridThe ONS Workweek Grid

Sequence analysisSequence analysis• Optimal Matching Analysis (OMA)– Measure of dissimilarity between sequences– Similarity of two sequences based on the difficulty

to transform one sequence into the other (matching)

– Three kind of operations allowed:• Insertion and deletion• Substitution

– Costs for each of these operations– Minimum cost to match two sequences = distance

ExampleA : X – Y – Y – Y

B : X – X – X – X – Y • One solution:

A : X – X – X – X – Y – Y – YB : X – X – X – X – Y

• Another one:A : X – X – X – X – Y

B : X – X – X – X – Y

ExampleA : X – Y – Y – Y

B : X – X – X – X – Y • One solution:

A : X – X – X – X – Y – Y – YB : X – X – X – X – Y

• Another one:A : X – X – X – X – Y

B : X – X – X – X – Y

3 insertions

2 deletions

1 insertion

2 substitutions

Indel Substitution

What is preserved

Events Timing

What is simplified

Timing Events

Dynamic Hamming DistanceDynamic Hamming Distance

• Only substitution operations are used to preserve the timing of events

• Interpretation of substitution cost as the degree of proximity of two states at one point in time

• Substitution costs are inversely proportional to transition frequencies

Cluster analysis of the distance matrix gives the empirical typology

Scheduling of work within the weekScheduling of work within the week

Scheduling of work hours within days

Scheduling of work days within weeks

Scheduling of work within the weekScheduling of work within the week

Scheduling of work hours within days

• 9 to 5 vs. 12 to 8• Same duration, different

scheduling• What is important here is

whether work hours are contemporaneous or not

Scheduling of work days within weeks

Scheduling of work within the weekScheduling of work within the week

Scheduling of work hours within days

• 9 to 5 vs. 12 to 8• Same duration, different

scheduling• What is important here is

whether work hours are contemporaneous or not

Scheduling of work days within weeks

• Working from Mon to Fri vs Sat to Wed

• Same number of days but totally different week

• What is crucial is whether work days are contemporaneous or not

Two-stage OMA

UK 2000 TUS

1st stage: typology of workdays1st stage: typology of workdays

TypeCluster number Name Size (%)

1 1 Standard 9 to 5 34.92 52.13

2 8 to 4 17.212 3 Long long 10.76 15.54

4long day and

evening 4.783 5 Shift morning shift 6.65 13.42

6 evening shift 3.74

7 night shift 3.034 8 Part-time part-time morning 9.66 14.33

9part-time afternoon 4.67

5 10 Short short atypical 4.56 4.56

Tempograms of the typology of workdaysTempograms of the typology of workdays

Simplified workweeks (UK)Simplified workweeks (UK)

2nd stage: Types of workweeks UK2nd stage: Types of workweeks UK

Types of workweeksTypes of workweeks

Type of workweeks UKStandard 26.1Long 20.0Shift 12.1Alternate 5.8Part- time (f week, pt days) 9.1Part- time (p week, standard days) 11.5Part- time (short week) 15.3

Summary statistics of the final typology of workweeks

Summary statistics of the final typology of workweeks

% of workweeks

Work time

No. of days off

No. of workdays

% work on Saturday

% work on Sunday

% work on weekend

%f full Saturday off

% full Sunday off

Standard 26.1 42.2 1.8 5.2 5.0 3.2 4.1 80.4 86.9

Long 20.0 52.1 1.6 5.4 14.9 10.6 12.7 53.8 68.1

Shift 12.1 37.7 1.9 5.1 12.7 11.1 11.9 56.9 63.0

Alternate 7.0 31.7 1.7 5.3 13.5 11.1 12.3 44.3 57.9

Part-time I 9.1 21.1 2.5 4.5 5.7 3.7 4.7 74.1 83.0

Part-time II

10.4 34.3 2.7 4.3 11.5 5.4 8.5 62.5 81.8

Short 15.4 21.6 4.0 3.0 10.7 8.6 9.6 64.7 70.4

SummarySummary

• Applying OMA at two stages to identify workdays and workweeks

• Costs are set according to the transitional frequencies of the events in the whole sample

• 5 types of workdays and 7 types of workweeks• Standard workdays constitute just over 50% workdays • Standard workweeks constitute about 25%

workweeks. • 3 types of part-time workweeks: standard-workday

part-time, part-workday part-time, and short workweek.

Thank you!

• For more detail, see our forthcoming paper at Journal of Royal Statistical Society Series A

• Or, at the Department of Sociology Working Paper Series:

http://www.sociology.ox.ac.uk/documents/working-papers/2009/swp09_04.pdf