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

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 worked Employee 1 0 Employee 2 0 Employee 3 0 Employee 4 0 Employee 5 0 Number of E shifts 0 0 0 0 0 0 0 Number of L shifts 0 0 0 0 0 0 0 Number of N shifts 0 0 0 0 0 0 0 Greet Vanden Berghe - Personnel rostering 2/24

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

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

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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

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

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

Modelling rostering problems Static horizon: only consider current scheduling period for evaluation Incorrectly computes constraint violations a scheduling period’s boundaries. Days worked Employee 1 E E E E 4 Employee 2 L L E E 4 Employee 3 N N N L 4 Employee 4 E N N N N 5 Employee 5 L L L L 4 Locally inconsistent constraint evaluation Greet Vanden Berghe - Personnel rostering 5/24

Modelling rostering problems Static horizon: only consider current scheduling period for evaluation Incorrectly computes constraint violations a scheduling period’s boundaries. Days worked Employee 1 E E E E 4 Employee 2 L L E E 4 Employee 3 N N N L 4 Employee 4 E N N N N 5 Employee 5 L L L L 4 Locally inconsistent constraint evaluation Greet Vanden Berghe - Personnel rostering 5/24

Modelling rostering problems Static horizon: only consider current scheduling period for evaluation Incorrectly computes constraint violations a scheduling period’s boundaries. Days worked Employee 1 E E E E 4 Employee 2 L L E E 4 Employee 3 N N N L 4 Employee 4 E N N N N 5 Employee 5 L L L L 4 Locally inconsistent constraint evaluation Greet Vanden Berghe - Personnel rostering 5/24

Modelling rostering problems Static horizon: only consider current scheduling period for evaluation Incorrectly computes constraint violations a scheduling period’s boundaries. Days worked Employee 1 E E E E 4 Employee 2 L L E E 4 Employee 3 N N N L 4 Employee 4 E N N N N 5 Employee 5 L L L L 4 Locally inconsistent constraint evaluation Greet Vanden Berghe - Personnel rostering 5/24

Modelling rostering problems Static horizon: only consider current scheduling period for evaluation Incorrectly computes constraint violations a scheduling period’s boundaries. Days worked Employee 1 E E E E 4 Employee 2 L L E E 4 Employee 3 N N N L 4 Employee 4 E N N N N 5 Employee 5 L L L L 4 Locally inconsistent constraint evaluation Greet Vanden Berghe - Personnel rostering 5/24

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

Greet Vanden Berghe - Personnel rostering 7/24

Modelling rostering problems Some constraints span multiple scheduling periods Globally inconsistent constraint evaluation Greet Vanden Berghe - Personnel rostering 8/24

Modelling rostering problems Some constraints span multiple scheduling periods Days worked Employee 1 4 E E E E Employee 2 L L E E 4 Employee 3 N N N L 4 Employee 4 E N N N N 5 Employee 5 L L L L 4 Globally inconsistent constraint evaluation Greet Vanden Berghe - Personnel rostering 8/24

Modelling rostering problems Some constraints span multiple scheduling periods Days worked Employee 1 E E E E 4 Employee 2 L L E E 4 Employee 3 4 N N N L Employee 4 E N N N N 5 Employee 5 L L L L 4 Globally inconsistent constraint evaluation Greet Vanden Berghe - Personnel rostering 8/24

Modelling rostering problems Some constraints span multiple scheduling periods Days worked Employee 1 E E E E 4 Employee 2 L L E E 4 Employee 3 4 N N N L Employee 4 E N N N N 5 Employee 5 L L L L 4 Globally inconsistent constraint evaluation Greet Vanden Berghe - Personnel rostering 8/24

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

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

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

Stepping horizon formulation Counters (global) min 5 bank holidays worked per year Series (local) . Forbidden shift changes no early shift after late shift Series with upper bound max 5 consecutive days worked Series with lower bound min 4 consecutive nights worked Greet Vanden Berghe - Personnel rostering 10/24

Stepping horizon formulation Counters (global) min 5 bank holidays worked per year Series (local) . Forbidden shift changes no early shift after late shift Series with upper bound max 5 consecutive days worked Series with lower bound min 4 consecutive nights worked Greet Vanden Berghe - Personnel rostering 10/24

Stepping horizon formulation Counters (global) min 5 bank holidays worked per year Series (local) . Forbidden shift changes no early shift after late shift Series with upper bound max 5 consecutive days worked Series with lower bound min 4 consecutive nights worked Greet Vanden Berghe - Personnel rostering 10/24

Local consistency Extend evaluation into previous scheduling period Example : An employee must not have isolated days off. Greet Vanden Berghe - Personnel rostering 11/24

Local consistency Extend evaluation into previous scheduling period Example : An employee must not have isolated days off. Greet Vanden Berghe - Personnel rostering 11/24

Local consistency Extend evaluation into previous scheduling period Example : An employee must not have isolated days off. Previous period Current period Sat Sun Mon Tue Wed Thu Fri Greet Vanden Berghe - Personnel rostering 11/24

Local consistency Extend evaluation into previous scheduling period Example : An employee must not have isolated days off. Previous period Current period Sat Sun Mon Tue Wed Thu Fri Additional constraint evaluations Greet Vanden Berghe - Personnel rostering 11/24

Local consistency Static horizon: MAX sr � � x i ( j + m ) k ≤ MAX sr ∀ i ∈ E, j ∈ { 1 , ..., d − MAX sr } m =0 k ∈ S sr Additional stepping horizon constraints: MAX sr − m m � � � � x ijk ≤ MAX sr ∀ i ∈ E, m ∈ { 1 , ..., MAX sr } x i ( ˜ ˜ d − j ) k + j =0 j =1 k ∈ S sr k ∈ S sr Greet Vanden Berghe - Personnel rostering 12/24

Local consistency Static horizon: MAX sr � � x i ( j + m ) k ≤ MAX sr ∀ i ∈ E, j ∈ { 1 , ..., d − MAX sr } m =0 k ∈ S sr Additional stepping horizon constraints: MAX sr − m m � � � � x ijk ≤ MAX sr ∀ i ∈ E, m ∈ { 1 , ..., MAX sr } x i ( ˜ ˜ d − j ) k + j =0 j =1 k ∈ S sr k ∈ S sr Greet Vanden Berghe - Personnel rostering 12/24