Personnel rostering - Local and global constraint consistency - - PowerPoint PPT Presentation

▶
personnel rostering local and global constraint
SMART_READER_LITE
LIVE PREVIEW

Personnel rostering - Local and global constraint consistency - - PowerPoint PPT Presentation

Jan 30, 2024 94 likes •723 views

Personnel rostering - Local and global constraint consistency Pieter Smet, Fabio Salassa , Greet Vanden Berghe KU Leuven, Polytecnico di Torino April 1, 2016 Greet Vanden Berghe - Personnel rostering 1/24 Personnel rostering Days

slide-1
SLIDE 1

Personnel rostering - Local and global constraint consistency

Pieter Smet, Fabio Salassa∗, Greet Vanden Berghe KU Leuven, ∗Polytecnico di Torino April 1, 2016

Greet Vanden Berghe - Personnel rostering 1/24

slide-2
SLIDE 2

Personnel rostering

Employee 1 Employee 2 Employee 3 Employee 4 Employee 5 Number of E shifts Number of L shifts Number of N shifts Days worked Greet Vanden Berghe - Personnel rostering 2/24

slide-3
SLIDE 3

Personnel rostering

E E E E Employee 1 L L E E Employee 2 N N N L Employee 3 E N N N N Employee 4 L L L L Employee 5 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Number of E shifts Number of L shifts Number of N shifts Days worked 4 4 4 5 4 Greet Vanden Berghe - Personnel rostering 2/24

slide-4
SLIDE 4

Personnel rostering

E E E E Employee 1 L L E E Employee 2 N N N L Employee 3 E N N N N Employee 4 L L L L Employee 5 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Number of E shifts Number of L shifts Number of N shifts Days worked 4 4 4 5 4 Greet Vanden Berghe - Personnel rostering 2/24

slide-5
SLIDE 5

Greet Vanden Berghe - Personnel rostering 3/24

slide-6
SLIDE 6

Outline

1 Introduction 2 Modelling rostering problems 3 Stepping horizon formulations 4 Case study 5 Conclusions and future work Greet Vanden Berghe - Personnel rostering 4/24

slide-7
SLIDE 7

Modelling rostering problems

Static horizon: only consider current scheduling period for evaluation Incorrectly computes constraint violations a scheduling period’s boundaries. Locally inconsistent constraint evaluation

Greet Vanden Berghe - Personnel rostering 5/24

slide-8
SLIDE 8

Modelling rostering problems

Static horizon: only consider current scheduling period for evaluation Incorrectly computes constraint violations a scheduling period’s boundaries. Locally inconsistent constraint evaluation

Greet Vanden Berghe - Personnel rostering 5/24

slide-9
SLIDE 9

Modelling rostering problems

Static horizon: only consider current scheduling period for evaluation Incorrectly computes constraint violations a scheduling period’s boundaries.

E E E E Employee 1 L L E E Employee 2 N N N L Employee 3 E N N N N Employee 4 L L L L Employee 5 Days worked 4 4 4 5 4

Locally inconsistent constraint evaluation

Greet Vanden Berghe - Personnel rostering 5/24

slide-10
SLIDE 10

Modelling rostering problems

Static horizon: only consider current scheduling period for evaluation Incorrectly computes constraint violations a scheduling period’s boundaries.

E E E E Employee 1 L L E E Employee 2 N N N L Employee 3 E N N N N Employee 4 L L L L Employee 5 Days worked 4 4 4 5 4

Locally inconsistent constraint evaluation

Greet Vanden Berghe - Personnel rostering 5/24

slide-11
SLIDE 11

Modelling rostering problems

Static horizon: only consider current scheduling period for evaluation Incorrectly computes constraint violations a scheduling period’s boundaries.

E E E E Employee 1 L L E E Employee 2 N N N L Employee 3 E N N N N Employee 4 L L L L Employee 5 Days worked 4 4 4 5 4

Locally inconsistent constraint evaluation

Greet Vanden Berghe - Personnel rostering 5/24

slide-12
SLIDE 12

Modelling rostering problems

Static horizon: only consider current scheduling period for evaluation Incorrectly computes constraint violations a scheduling period’s boundaries.

E E E E Employee 1 L L E E Employee 2 N N N L Employee 3 E N N N N Employee 4 L L L L Employee 5 Days worked 4 4 4 5 4

Locally inconsistent constraint evaluation

Greet Vanden Berghe - Personnel rostering 5/24

slide-13
SLIDE 13

Modelling rostering problems

Static horizon: only consider current scheduling period for evaluation Incorrectly computes constraint violations a scheduling period’s boundaries.

E E E E Employee 1 L L E E Employee 2 N N N L Employee 3 E N N N N Employee 4 L L L L Employee 5 Days worked 4 4 4 5 4

Locally inconsistent constraint evaluation

Greet Vanden Berghe - Personnel rostering 5/24

slide-14
SLIDE 14

Related work

  • E.K. Burke, P. De Causmaecker, S. Petrovic, G. Vanden Berghe

(2001) Fitness evaluation for nurse scheduling problems, CEC

  • A. Ikegami, A. Niwa (2003) A subproblem-centric model and

approach to the nurse scheduling problem, Mathematical Programming

  • C.A. Glass, R.A. Knight (2010) The nurse rostering problem: A

critical appraisal of the problem structure, European Journal of Operational Research

Greet Vanden Berghe - Personnel rostering 6/24

slide-15
SLIDE 15

Greet Vanden Berghe - Personnel rostering 7/24

slide-16
SLIDE 16

Modelling rostering problems

Some constraints span multiple scheduling periods Globally inconsistent constraint evaluation

Greet Vanden Berghe - Personnel rostering 8/24

slide-17
SLIDE 17

Modelling rostering problems

Some constraints span multiple scheduling periods

E E E E Employee 1 L L E E Employee 2 N N N L Employee 3 E N N N N Employee 4 L L L L Employee 5 Days worked 4 4 4 5 4

Globally inconsistent constraint evaluation

Greet Vanden Berghe - Personnel rostering 8/24

slide-18
SLIDE 18

Modelling rostering problems

Some constraints span multiple scheduling periods

E E E E Employee 1 L L E E Employee 2 N N N L Employee 3 E N N N N Employee 4 L L L L Employee 5 Days worked 4 4 4 5 4

Globally inconsistent constraint evaluation

Greet Vanden Berghe - Personnel rostering 8/24

slide-19
SLIDE 19

Modelling rostering problems

Some constraints span multiple scheduling periods

E E E E Employee 1 L L E E Employee 2 N N N L Employee 3 E N N N N Employee 4 L L L L Employee 5 Days worked 4 4 4 5 4

Globally inconsistent constraint evaluation

Greet Vanden Berghe - Personnel rostering 8/24

slide-20
SLIDE 20

Modelling rostering problems

Stepping horizon: consider previous scheduling period(s) for evaluation Achieve consistency at two levels: Local: at the boundaries of the scheduling period Global: over multiple scheduling periods

Contribution

New IP formulations for main types of rostering constraints.

Greet Vanden Berghe - Personnel rostering 9/24

slide-21
SLIDE 21

Modelling rostering problems

Stepping horizon: consider previous scheduling period(s) for evaluation Achieve consistency at two levels: Local: at the boundaries of the scheduling period Global: over multiple scheduling periods

Contribution

New IP formulations for main types of rostering constraints.

Greet Vanden Berghe - Personnel rostering 9/24

slide-22
SLIDE 22

Modelling rostering problems

Stepping horizon: consider previous scheduling period(s) for evaluation Achieve consistency at two levels: Local: at the boundaries of the scheduling period Global: over multiple scheduling periods

Contribution

New IP formulations for main types of rostering constraints.

Greet Vanden Berghe - Personnel rostering 9/24

slide-23
SLIDE 23

Stepping horizon formulation

Counters (global) Series (local) Forbidden shift changes Series with upper bound Series with lower bound min 5 bank holidays worked per year . no early shift after late shift max 5 consecutive days worked min 4 consecutive nights worked

Greet Vanden Berghe - Personnel rostering 10/24

slide-24
SLIDE 24

Stepping horizon formulation

Counters (global) Series (local) Forbidden shift changes Series with upper bound Series with lower bound min 5 bank holidays worked per year . no early shift after late shift max 5 consecutive days worked min 4 consecutive nights worked

Greet Vanden Berghe - Personnel rostering 10/24

slide-25
SLIDE 25

Stepping horizon formulation

Counters (global) Series (local) Forbidden shift changes Series with upper bound Series with lower bound min 5 bank holidays worked per year . no early shift after late shift max 5 consecutive days worked min 4 consecutive nights worked

Greet Vanden Berghe - Personnel rostering 10/24

slide-26
SLIDE 26

Local consistency

Extend evaluation into previous scheduling period Example: An employee must not have isolated days off.

Greet Vanden Berghe - Personnel rostering 11/24

slide-27
SLIDE 27

Local consistency

Extend evaluation into previous scheduling period Example: An employee must not have isolated days off.

Greet Vanden Berghe - Personnel rostering 11/24

slide-28
SLIDE 28

Local consistency

Extend evaluation into previous scheduling period Example: An employee must not have isolated days off.

Previous period Current period Mon Tue Wed Thu Fri Sun Sat

Greet Vanden Berghe - Personnel rostering 11/24

slide-29
SLIDE 29

Local consistency

Extend evaluation into previous scheduling period Example: An employee must not have isolated days off.

Previous period Current period Additional constraint evaluations Mon Tue Wed Thu Fri Sun Sat

Greet Vanden Berghe - Personnel rostering 11/24

slide-30
SLIDE 30

Local consistency

Static horizon:

MAXsr

  • m=0
  • k∈Ssr

xi(j+m)k ≤ MAXsr ∀i ∈ E, j ∈ {1, ..., d − MAXsr} Additional stepping horizon constraints:

MAXsr−m

  • j=0
  • k∈Ssr

˜ xi( ˜

d−j)k+ m

  • j=1
  • k∈Ssr

xijk ≤ MAXsr ∀i ∈ E, m ∈ {1, ..., MAXsr}

Greet Vanden Berghe - Personnel rostering 12/24

slide-31
SLIDE 31

Local consistency

Static horizon:

MAXsr

  • m=0
  • k∈Ssr

xi(j+m)k ≤ MAXsr ∀i ∈ E, j ∈ {1, ..., d − MAXsr} Additional stepping horizon constraints:

MAXsr−m

  • j=0
  • k∈Ssr

˜ xi( ˜

d−j)k+ m

  • j=1
  • k∈Ssr

xijk ≤ MAXsr ∀i ∈ E, m ∈ {1, ..., MAXsr}

Greet Vanden Berghe - Personnel rostering 12/24

slide-32
SLIDE 32

Global consistency

Introduce two new concepts: Counter start value: CSV Counter remainder value: CRV Example: Each employee must work on five bank holidays per year. When solving the roster in July: CSV = number of bank holidays worked in January - June CRV = number of bank holidays in August - December

Greet Vanden Berghe - Personnel rostering 13/24

slide-33
SLIDE 33

Global consistency

Introduce two new concepts: Counter start value: CSV Counter remainder value: CRV Example: Each employee must work on five bank holidays per year. When solving the roster in July: CSV = number of bank holidays worked in January - June CRV = number of bank holidays in August - December

Greet Vanden Berghe - Personnel rostering 13/24

slide-34
SLIDE 34

Global consistency

Introduce two new concepts: Counter start value: CSV Counter remainder value: CRV Example: Each employee must work on five bank holidays per year. When solving the roster in July: CSV = number of bank holidays worked in January - June CRV = number of bank holidays in August - December

Greet Vanden Berghe - Personnel rostering 13/24

slide-35
SLIDE 35

Global consistency

Introduce two new concepts: Counter start value: CSV Counter remainder value: CRV Example: Each employee must work on five bank holidays per year. When solving the roster in July: CSV = number of bank holidays worked in January - June CRV = number of bank holidays in August - December

Greet Vanden Berghe - Personnel rostering 13/24

slide-36
SLIDE 36

Global consistency

Static horizon:

MINc ≤

  • j∈Dc
  • k∈Sc

xijk ≤ MAXc ∀i ∈ E Stepping horizon:

MINc − CRVc ≤ CSVc +

  • j∈Dc
  • k∈Sc

xijk ≤ MAXc ∀i ∈ E

Greet Vanden Berghe - Personnel rostering 14/24

slide-37
SLIDE 37

Global consistency

Static horizon:

MINc ≤

  • j∈Dc
  • k∈Sc

xijk ≤ MAXc ∀i ∈ E Stepping horizon:

MINc − CRVc ≤ CSVc +

  • j∈Dc
  • k∈Sc

xijk ≤ MAXc ∀i ∈ E

Greet Vanden Berghe - Personnel rostering 14/24

slide-38
SLIDE 38

Data sets

Static horizon data sets NSPLib (Vanhoucke and Maenhout, 2007) Nottingham (Brucker et al., 2010) INRC I (Haspeslagh et al., 2012) Stepping horizon data sets KAHO (Bilgin et al., 2012) INRC II (Thi Thanh Dang et al., 2015)

Greet Vanden Berghe - Personnel rostering 15/24

slide-39
SLIDE 39

Case study

Rostering nurses in a Belgian hospital 21 nurses 8 shifts 4 skills 3 types of contracts Data from January - December 2013

Greet Vanden Berghe - Personnel rostering 16/24

slide-40
SLIDE 40

Case study

Constraint Type Weight Maximum 0 early shifts 100000 Maximum 0 short shifts 100000 Maximum 0 long shifts 100000 Maximum 5 consecutive days worked Local 1500 Minimum 4 consecutive night shifts worked Local 1000 Maximum 7 consecutive night shifts worked Local 1000 Minimum 11 hours rest after a shift Local 1000 Minimum 5 late shifts 750 Maximum 7 late shifts 750 Required number of hours worked per year Global 50 Skills required 0, 1, 10

Greet Vanden Berghe - Personnel rostering 17/24

slide-41
SLIDE 41

Case study

Three approaches for generating one-year rosters Optimal Static horizon Stepping horizon

Greet Vanden Berghe - Personnel rostering 18/24

slide-42
SLIDE 42

Case study

Three approaches for generating one-year rosters Optimal Static horizon Stepping horizon

Greet Vanden Berghe - Personnel rostering 18/24

slide-43
SLIDE 43

Case study

Three approaches for generating one-year rosters Optimal Static horizon Stepping horizon

Greet Vanden Berghe - Personnel rostering 18/24

slide-44
SLIDE 44

Case study

Three approaches for generating one-year rosters Optimal Static horizon Stepping horizon

Greet Vanden Berghe - Personnel rostering 18/24

slide-45
SLIDE 45

Computational results — Global

Focus on required number of hours worked per year constraint

Optimal Static Stepping horizon horizon Group 1 0.1% 8.7% 5.5% Group 2 1.0% 8.1% 13.4% Group 3 29.4% 33.4% 50.2% Total 10.2% 16.7% 23.4%

Table: Difference between the required and actual hours worked

Greet Vanden Berghe - Personnel rostering 19/24

slide-46
SLIDE 46

Computational results — Global

Focus on required number of hours worked per year constraint

Optimal Static Stepping horizon horizon Group 1 0.1% 8.7% 5.5% Group 2 1.0% 8.1% 13.4% Group 3 29.4% 33.4% 50.2% Total 10.2% 16.7% 23.4%

Table: Difference between the required and actual hours worked

Greet Vanden Berghe - Personnel rostering 19/24

slide-47
SLIDE 47

Computational results — Global

Focus on required number of hours worked per year constraint

Optimal Static Stepping horizon horizon Group 1 0.1% 8.7% 5.5% Group 2 1.0% 8.1% 13.4% Group 3 29.4% 33.4% 50.2% Total 10.2% 16.7% 23.4%

Table: Difference between the required and actual hours worked

Greet Vanden Berghe - Personnel rostering 19/24

slide-48
SLIDE 48

Computational results — Global

Focus on required number of hours worked per year constraint

Optimal Static Stepping horizon horizon Group 1 0.1% 8.7% 5.5% Group 2 1.0% 8.1% 13.4% Group 3 29.4% 33.4% 50.2% Total 10.2% 16.7% 23.4%

Table: Difference between the required and actual hours worked

Greet Vanden Berghe - Personnel rostering 19/24

slide-49
SLIDE 49

Computational results — Global

Focus on required number of hours worked per year constraint

Figure: Difference between the required and actual hours worked

Greet Vanden Berghe - Personnel rostering 20/24

slide-50
SLIDE 50

Computational results — Global

Focus on required number of hours worked per year constraint

  • 60%
  • 30%

0% 30% 60% (a) Optimal

Figure: Difference between the required and actual hours worked

Greet Vanden Berghe - Personnel rostering 20/24

slide-51
SLIDE 51

Computational results — Global

Focus on required number of hours worked per year constraint

  • 60%
  • 30%

0% 30% 60%

  • 60%
  • 30%

0% 30% 60% (a) Optimal (b) Static horizon

Figure: Difference between the required and actual hours worked

Greet Vanden Berghe - Personnel rostering 20/24

slide-52
SLIDE 52

Computational results — Global

Focus on required number of hours worked per year constraint

  • 60%
  • 30%

0% 30% 60%

  • 60%
  • 30%

0% 30% 60%

  • 60%
  • 30%

0% 30% 60% (a) Optimal (b) Static horizon (c) Stepping horizon

Figure: Difference between the required and actual hours worked

Greet Vanden Berghe - Personnel rostering 20/24

slide-53
SLIDE 53

Computational results — Local

Focus on total number of violations

Constraint Optimal Static Stepping horizon horizon Maximum 5 consecutive days worked 62 Minimum 4 consecutive night shifts 17 1 Maximum 7 consecutive night shifts Minimum 11 hours rest after a shift 16 Total 95 1

Greet Vanden Berghe - Personnel rostering 21/24

slide-54
SLIDE 54

Computational results — Local

Focus on total number of violations

Constraint Optimal Static Stepping horizon horizon Maximum 5 consecutive days worked 62 Minimum 4 consecutive night shifts 17 1 Maximum 7 consecutive night shifts Minimum 11 hours rest after a shift 16 Total 95 1

Greet Vanden Berghe - Personnel rostering 21/24

slide-55
SLIDE 55

Computational results — Local

Focus on total number of violations

Constraint Optimal Static Stepping horizon horizon Maximum 5 consecutive days worked 62 Minimum 4 consecutive night shifts 17 1 Maximum 7 consecutive night shifts Minimum 11 hours rest after a shift 16 Total 95 1

Greet Vanden Berghe - Personnel rostering 21/24

slide-56
SLIDE 56

Computational results — Local

Focus on total number of violations

Constraint Optimal Static Stepping horizon horizon Maximum 5 consecutive days worked 62 Minimum 4 consecutive night shifts 17 1 Maximum 7 consecutive night shifts Minimum 11 hours rest after a shift 16 Total 95 1

Greet Vanden Berghe - Personnel rostering 21/24

slide-57
SLIDE 57

Computational results — Local

Figure: (a) Static horizon solution

Greet Vanden Berghe - Personnel rostering 22/24

slide-58
SLIDE 58

Computational results — Local

Figure: (a) Static horizon solution Figure: (b) Stepping horizon solution

Greet Vanden Berghe - Personnel rostering 22/24

slide-59
SLIDE 59

Conclusions and future work

Stepping horizon formulations for personnel rostering constraints IP formulations Empirical evaluation on case study Future work Anticipate future events: stochastic demand/employee availability, fixed assignments

Greet Vanden Berghe - Personnel rostering 23/24

slide-60
SLIDE 60

Conclusions and future work

Stepping horizon formulations for personnel rostering constraints IP formulations Empirical evaluation on case study Future work Anticipate future events: stochastic demand/employee availability, fixed assignments

Greet Vanden Berghe - Personnel rostering 23/24

slide-61
SLIDE 61

Greet Vanden Berghe - Personnel rostering 24/24