models and algorithms for manpower planning and ......manpower planning and personnel rostering...

Models and Algorithms for Manpower Planning andPersonnel Rostering:

Towards An Integrated Approach

KomarudinDepartment of Business Technology and Operations

Vrije Universiteit [email protected]

Promotor: Prof. dr. Marie-Anne Guerry

February 19, 2015

Backgrounds Research motivation

Research backgrounds

Personnelplanningresearch

Over/underqualified

personnel1

Unattractiveworking

schedule2 Qualifiedpersonnelshortage3

Ageingworkforce4

1 International Labour Organization. 2014. Skills mismatch in Europe.2 New York Times. Aug. 14, 2014. Starbucks to Revise Policies to End IrregularSchedules for Its 130,000 Baristas.3 The European Commission. 2012. Employment and Social Developments in Europe2012.4 Erixon & van der Marel. 2011. What is driving the rise in health care expenditures?An inquiry into the nature and causes of the cost disease.

(BUTO) Integrated Manpower Planning & Personnel Rostering February 19, 2015 2 / 34

Backgrounds Research motivation

Research backgrounds

Personnelplanningresearch

Over/underqualified

personnel1

Unattractiveworking

schedule2 Qualifiedpersonnelshortage3

Ageingworkforce4

ResearchLimitation

Quantitativeapproach

Focus oncorporate/

organization

1 International Labour Organization. 2014. Skills mismatch in Europe.2 New York Times. Aug. 14, 2014. Starbucks to Revise Policies to End IrregularSchedules for Its 130,000 Baristas.3 The European Commission. 2012. Employment and Social Developments in Europe2012.4 Erixon & van der Marel. 2011. What is driving the rise in health care expenditures?An inquiry into the nature and causes of the cost disease.


Overview

Overview of Our Work

Manpower Planningand

Personnel Rostering

PersonnelRostering

individualfairness

(Chap. 6)

Manpowerplanning

StochasticModel

(Chap. 5)

Balancingthreecriteria

(Chap. 4)

Integratedmodel

Optimizationapproach(Chap. 3)

Three-stepevaluation(Chap. 2)


Introduction Manpower planning

Manpower planning

Manpower planning

aims to meet medium-to-long term human resource requirements

involves personnel supply-and-demand prediction

controls recruitments, personnel transition and wastage (depending on thechosen strategy)

Hospital

90 30 652015Personnelstructure



Manpower planning

Manpower planning




Hospital


2016

t + ..

95 35 75



Manpower planning

Manpower planning




Hospital


2016

t + ..

95 35 75

Recruitment

Wastage


Introduction Personnel Rostering

Personnel rostering

Personnel rostering

short term planning to allocate personnel into shifts

involves coverage requirements, legal and personal constraints

aims to meet coverage requirements and avoid unattractive rosters.

Feb.2015 CoverageReqs.

Resttime

AbsenceRequest

PersonnelContract

ConsecutiveShift



Personnel rostering - Illustration

Nurse February 2015 Score1 2 3 4 5 6 7 . . . 28

. . .

Cov. 4 4 4 5 5 5 4 4Req. 5 4 4 4 4 5 5 4

3 2 2 2 2 3 2 3Score



Personnel rostering - Illustration


. . .

Cov. 4 4 4 5 5 5 4 4Req. 5 4 4 4 4 5 5 4

3 2 2 2 2 3 2 3

Score

Over/UnderCoveraged

AbsenceRequest

UnattractiveRoster


Integrated model (Chaps. 2 & 3)

Integrated model (Chaps. 2 & 3)


Personnel Rostering

PersonnelRostering

individualfairness

(Chap. 6)

Manpowerplanning

StochasticModel

(Chap. 5)


(Chap. 4)

Integratedmodel




Integrated model (Chaps. 2 & 3) Motivation and Contribution

Challenges and Motivation

Personnel Planning

Personnel supply-demand projection

t

demand

Manpowerplanning

Personnelrostering

Dept.1 Dept.2 Dept.3

Conductedsequentially

Different timeframe

Potentially producepoor results

Our motivation:provide feedbacks

90 30 652015

2016 95 35 75




Personnel Planning


t

demand

Manpowerplanning

Personnelrostering


Poor rosters


Different timeframe



90 30 652015

2016 95 35 75




Personnel Planning


t

demand

Manpowerplanning

Personnelrostering


Poor rosters

feedback


Different timeframe



90 30 652015

2016 95 35 75



Contributions

The State-of-The-Art:

No Approach References Review1 Sequential plan-

ningAbernathy et al. (1973);Ozcan (2009)

Suboptimal solu-tions

2 Integratedstaffing androstering

Mundschenk and Drexl(2007); Belien et al. (2012)

Constraints arerather limited; Lesspersonalized rosters

3 Part-time/Annualizedpersonnel

Bard and Purnomo (2006);Corominas and Pastor(2010)

Only temporary so-lution

4 Staff allocation Haspeslagh (2012); Maen-hout and Vanhoucke (2013)

Focus only on staffallocation



Contributions


No Approach References Review1 Sequential plan-

ningAbernathy et al. (1973);Ozcan (2009)

Suboptimal solu-tions

2 Integratedstaffing androstering

Mundschenk and Drexl(2007); Belien et al. (2012)

Constraints arerather limited; Lesspersonalized rosters

3 Part-time/Annualizedpersonnel

Bard and Purnomo (2006);Corominas and Pastor(2010)

Only temporary so-lution

4 Staff allocation Haspeslagh (2012); Maen-hout and Vanhoucke (2013)

Focus only on staffallocation

Our Contributions:

Three-step approach for limited personnel structure modification.

Optimization approach for arbitrary personnel structure modification.


Integrated model (Chaps. 2 & 3) Three-step approach

Three-step approach (Chap. 2)

Step 1. Consistency check

Compare the required and the available resources

Disregard many rostering constraints







Step 2. Quality evaluation of the current personnelstructure

Solve the rostering problems

Identify which personnel group inappropriate








Solve the rostering problems

Identify which personnel group inappropriate

Step 3. Quality evaluation of the neighboring personnelstructures

Small modification to the personnel structure

Evaluate the roster qualities

Currentpersonnel-structure

Neighbor 2Neighbor 1 Neighbor 3


Integrated model (Chaps. 2 & 3) Optimization approach (Chap. 3)

Optimization approach (Chap. 3)

Response surface meth. (RSM)

Sampling the neighborhood of thecurrent solution

Perform regression analysis to findnew direction

Newsolution

Neighborhoodsampling

Regression

Initialsolution

generate


Integrated model (Chaps. 2 & 3) Optimization approach (Chap. 3)

Optimization approach (Chap. 3)

Response surface meth. (RSM)

Sampling the neighborhood of thecurrent solution

Perform regression analysis to findnew direction

Simulated Annealing (SA)

Local search to generateneighboring solutions

Move to the best neighboringsolution with a certain probability

Newsolution

Neighborhoodsampling

Regression

Initialsolution

generate

Currentsolution

Localsearch

Accept withSA criteria

Initialsolution

move to


Integrated model (Chaps. 2 & 3) Case study

Case studies

The data set originating from real-world nurse rostering problems is takenfrom Bilgin et al. (2012).

The three-step approach is provided for the Emergency ward only

No Ward Abbr. k∑

FTE qvT s0 ,T

s1(R(n))

1 Emergency Em 8 26.25 17,3092 Geriatrics Gr 8 17.06 11,4233 Meal Preparations MP 8 16.84 13,2234 Psychiatry Ps 9 16.50 8,7335 Reception Re 9 13.75 14,4476 Palliative Care PC 20 21.70 130,579

k : Number of subgroups∑FTE : The current total of full time equivalent in the ward

qvT s0 ,T

s1(R(n)) : The value of the roster quality (the smaller the better)



Case study results (three-step approach)


Subgroup: 1 2 3 4

Ratio: 0.95 0.85 0.85 0.85


Coverage constraint:Skill type 1: 1.6%Skill type 3: 2.2%

Skill type 4: 80.1%Counter constraint: 10.2%Series constraint: 2.9%

Ratio =Required resourcesAvailable resources

Proportion of thetotal weighted con-

straint violations



Case study results (three-step approach)


Subgroup: 1 2 3 4

Ratio: 0.95 0.85 0.85 0.85


Coverage constraint:Skill type 1: 1.6%Skill type 3: 2.2%

Skill type 4: 80.1%Counter constraint: 10.2%Series constraint: 2.9%

Ratio =Required resourcesAvailable resources

Reasonable, some slackfor vacation/illness

Proportion of thetotal weighted con-

straint violations

Skill 4 understaffed



Step 3. Quality evaluation of the neighboring personnel structures

Increase the number of nurses with skill type 2, 3 or 4.



Optimization approach (RSM & SA)

No Ward∑

FTE RSM SA

qvT s0 ,T

s1(R(n)) ratio ¯∑

FTE qvT s0 ,T

s1(R(n)) ratio ¯∑

FTE

1 Em 26.25 13,176 76.13% 29.20 13,301 76.85% 29.35

2 Gr 17.06 4,508 39.47% 15.05 3,728 32.64% 15.35

3 MP 16.84 4,436 33.54% 15.05 3,949 29.86% 15.33

4 Ps 16.50 5,182 59.34% 14.35 4,060 46.49% 14.20

5 Re 13.75 9,750 67.49% 14.65 10,212 70.69% 14.45

6 PC 21.7 50,583 38.74% 17.42 20,111 15.40% 15.85

Small modification on the total FTE can lead to a better roster quality

SA performs slightly better


Manpower planning (Chaps. 4 & 5)

Overview Chapters 4 & 5


Personnel Rostering

PersonnelRostering

individualfairness

(Chap. 6)

Manpowerplanning

StochasticModel

(Chap. 5)


(Chap. 4)

Integratedmodel





Challenge and motivations

What if the desiredpersonnel structure isdifficult to reach?

How we ensure that thepromotion policy does notharm the personnelmotivation?

How we deal withuncertainties?

90 30 652015

2016

t + ..

95 35 75

Recruitment

Wastage

Motivation: develop models andalgorithms for manpower planning problems



Contributions


The degree of desirability and the degree of attainability have beenintroduced in Guerry (1999); De Feyter and Guerry (2009)

Previous approaches use an unrestricted promotion strategy that can lead topersonnel dissatisfaction (Song and Huang, 2008; Nilakantan et al., 2011)

No method has been proposed to find the most beneficial manpower planningpolicy with stochastic wastage (Davies, 1982; Guerry, 1993)



Contributions


The degree of desirability and the degree of attainability have beenintroduced in Guerry (1999); De Feyter and Guerry (2009)

Previous approaches use an unrestricted promotion strategy that can lead topersonnel dissatisfaction (Song and Huang, 2008; Nilakantan et al., 2011)

No method has been proposed to find the most beneficial manpower planningpolicy with stochastic wastage (Davies, 1982; Guerry, 1993)

Our contributions

Introduce MIP models for manpower planning problems that include thepromotion steadiness degree (Chap. 4 & 5)

Introduce a stochastic optimization problem and its complexity analysis todeal with wastage uncertainties (Chap. 5)


Manpower planning (Chaps. 4 & 5) MP with three criteria - Chap. 4

Manpower planning with three criteria (Chap. 4)

Optimizing three criteria

The degree of attainabilityαni (t)(si ) =

0, if si < sLL,i or si > sUL,isi−sLL,i

ni (t)−sLL,i , if sLL,i ≤ si ≤ ni (t)si−sUL,i

ni (t)−sUL,i , if ni (t) ≤ si ≤ sUL,i

The degree of desirability βi (ni (t))

The degree of promotion steadinessγij(fij(t − 1, t))

Difference between n(t)and the attainable set

Difference betweenn(t) and the desiredpersonnel structure

Difference between thepersonnel transition and the’common’ promotion policy



The model of Chap. 4


Mixed integer nonlinear program (MINLP)

Piecewise linear approximation (PLA) to handle nonlinearity

The model is solved using an iterated PLA



The model of Chap. 4


Mixed integer nonlinear program (MINLP)

Piecewise linear approximation (PLA) to handle nonlinearity

The model is solved using an iterated PLA

Set lower &upper bounds

Increase #segments

Solve PLA model

Low ac-curacy?

Yes



Experiments for model of Chap. 4

PLA IPLANo Problem k κ aComp. time κ aComp. time1 P03 3 0.633 2.67 0.633 1.092 P04 4 0.547 15.57 0.547 11.043 P05 5 0.111 11.64 0.111 1.134 P10 10 0.466 18.45 0.466 1.765 P11 11 0.627 20.00 0.627 20.556 P12 12 0.601 b3600.00 0.601 13.507 P20 20 c 0.307 3601.778 P25 25 c 0.000 32.579 P30 30 c 0.184 2.74

aIn secondsbSolver is terminated after 1 hourcSolver terminates: out of memory without encountering a feasible solution

κ: the overall objective function value

with similar value of κ, IPLA model is more efficient than the PLA


Manpower planning (Chaps. 4 & 5) MP with stochastic wastage - Chap. 5

Manpower planning with stochastic wastage (Chap. 5)

Optimizing partially stochastic system

The degree of desirability

The degree of promotion steadiness

wastage is considered stochastic, following aprobability distribution

Difference betweenn(t) and the desiredpersonnel structure

Difference between thepersonnel transition and the’common’ promotion policy


Manpower planning (Chaps. 4 & 5) MP with stochastic wastage - Chap. 5

Partially stochastic system

The stochastic wastage is modeled using a finite number of scenarios

The MIP model is solved using a MIP solver

The problem is proved to be NP-hard based on reduction from 3-SAT

Case study with 3 subgroups

Using the deterministic case w = w, then the result is tested under stochasticcase w, the overall degree κ = 0.78099.

Using the stochastic case wi with 1000 scenarios, the overall degreeκ = 0.8019


Personnel rostering (Chapter 6)

Overview Chapter 6


Personnel Rostering

PersonnelRostering

individualfairness

(Chap. 6)

Manpowerplanning

StochasticModel

(Chap. 5)


(Chap. 4)

Integratedmodel




Personnel rostering (Chapter 6) Motivation and Contribution



. . .

Cov. 4 4 4 5 5 5 4 4Req. 5 4 4 4 4 5 5 4

3 2 2 2 2 3 2 3

Score





. . .

Cov. 4 4 4 5 5 5 4 4Req. 5 4 4 4 4 5 5 4

3 2 2 2 2 3 2 3

ScoreLow individual

fairness

Motivation:incorporate fairness in personnel rostering model



Contributions


Approach ReviewThe maximum and the range (Stolletzand Brunner, 2012; Smet et al., 2012)

Neglect most of theindividual penalties

The absolute deviation and thesquared deviation (Pesant and Regin,2005; Smet et al., 2012)

Tends to level all in-dividual penalties

The sum of squared (Martin et al.,2013),

Positive trade-off isnot always preferred

Jain’s index (Martin et al., 2013). Tends to increase in-dividual penalties

Nurse Score

. . .



Contributions


Approach ReviewThe maximum and the range (Stolletzand Brunner, 2012; Smet et al., 2012)

Neglect most of theindividual penalties

The absolute deviation and thesquared deviation (Pesant and Regin,2005; Smet et al., 2012)

Tends to level all in-dividual penalties

The sum of squared (Martin et al.,2013),

Positive trade-off isnot always preferred

Jain’s index (Martin et al., 2013). Tends to increase in-dividual penalties

Nurse Score

. . .

Our Contribution is the lexicographic objective function:

Minimize all individual penalties

maximize fairness by allowing positive trade-off.



Improving fairness

Minimizing the lexicographic objective function

PLexi is defined as a permutation of all individual penalties, sorted in anon-increasing order.

PLexi = (P ′H,1,P′H,2, ..,P

′H,n) s.t. P ′H,1 ≥ P ′H,2 ≥ ... ≥ P ′H,n



Experiments for lexicographic objective function

TP-PLexi generally produces vectors PLexi that are lexicographically smallerthan the ones produced by other approaches


Conclusions & Future Work


Conclusions

The models and algorithms presented are able to improve thepersonnel planning process

The models and algorithms are beneficial in improving thepersonnel motivation by:

Providing sufficient personnel with the right personnel-mix(Integrated model)Ensuring the career progression expectation (manpowerplanning model)Fair working schedule (personnel rostering model)

Future research

multi-level and multi-scale integrated personnel planning

global optimization approach



Thank you for your attention!


Bibliography

References I

William J. Abernathy, Nicholas Baloff, John C. Hershey, and Sten Wandel. AThree-Stage Manpower Planning and Scheduling Model–A Service-SectorExample. Operations Research, 21(3):693–711, 1973.

Jonathan F. Bard and Hadi W. Purnomo. Incremental changes in the workforce toaccommodate changes in demand. Health Care Management Science, 9(1):71–85, February 2006.

Jeroen Belien, Brecht Cardoen, and Erik Demeulemeester. Improving workforcescheduling of aircraft line maintenance at Sabena Technics. Interfaces, 42(4):352–364, 2012.

Burak Bilgin, Patrick De Causmaecker, Benoıt Rossie, and Greet Vanden Berghe.Local search neighbourhoods for dealing with a novel nurse rostering model.Annals of Operations Research, 194(1):33–57, 2012.

Albert Corominas and Rafael Pastor. Replanning working time under annualisedworking hours. International Journal of Production Research, 48(5):1493–1515,March 2010. ISSN 0020-7543. doi: 10.1080/00207540802582227. URLhttp://www.tandfonline.com/doi/abs/10.1080/00207540802582227.


http://www.tandfonline.com/doi/abs/10.1080/00207540802582227

Bibliography

References II

G. S. Davies. Control of grade sizes in partially stochastic markov manpowermodel. Journal of Applied Probability, 19:439–443, 1982.

Tim De Feyter and Marie-Anne Guerry. Evaluating Recruitment Strategies UsingFuzzy Set Theory in Stochastic Manpower Planning. Stochastic Analysis andApplications, 27(6):1148–1162, 2009.

Marie-Anne Guerry. The probability of attaining a structure in a partiallystochastic model. Advances in applied probability, 25(4):818–824, 1993.

Marie-Anne Guerry. Using Fuzzy Sets in Manpower Planning. Journal of AppliedProbability, 36(1):155–162, 1999.

Stefaan Haspeslagh. Negotiation at the short and mid term level supported byanalysis of nurse rostering problems. PhD thesis, Computer Science, Kulak,2012.

Broos Maenhout and Mario Vanhoucke. An integrated nurse staffing andscheduling analysis for longer-term nursing staff allocation problems. Omega,41(2):485–499, 2013.


Bibliography

References III

Simon Martin, Djamila Ouelhadj, Pieter Smet, Greet Vanden Berghe, and EnderOzcan. Cooperative search for fair nurse rosters. Expert Systems withApplications, 40:6674–6683, 2013.

Martin Mundschenk and Andreas Drexl. Workforce planning in the printingindustry. International Journal of Production Research, 45(20):4849–4872,October 2007.

K. Nilakantan, J.K. Sankaran, and BG Raghavendra. A proportionality model ofMarkov manpower systems. Journal of Modelling in Management, 6(1):100–122, 2011.

Yasar A. Ozcan. Quantitative methods in health care management: techniquesand applications. Jossey-bass, San Fransisco, second edition, 2009.

Gilles Pesant and Jean-Charles Regin. Spread: A balancing constraint based onstatistics. In Peter van Beek, editor, Principles and Practice of ConstraintProgramming - CP 2005, volume 3709 of Lecture Notes in Computer Science,pages 460–474. Springer Berlin Heidelberg, 2005.


Bibliography

References IV

Pieter Smet, Simon Martin, Djamila Ouelhadj, Ender Ozcan, and Greet VandenBerghe. Investigation of fairness measures for nurse rostering. In theInternational Conference on the Practice and Theory of Timetabling (PATAT2012), pages 369–372, 2012.

Haiqing Song and Huei-Chuen Huang. A successive convex approximation methodfor multistage workforce capacity planning problem with turnover. EuropeanJournal of Operational Research, 188(1):29–48, 2008.

Raik Stolletz and Jens O. Brunner. Fair optimization of fortnightly physicianschedules with flexible shifts. European Journal of Operational Research, 219(3):622–629, 2012.


models and algorithms for manpower planning and ......manpower planning and personnel rostering...

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