Three personnel structure examinations for improving nurse roster quality

Three personnel structure examinations for improving nurse roster qualityKomarudin, G. Vanden Berghe, M.-A. Guerry, and T. De Feyter

Contents Introduction

Personnel structure Nurse rostering problem

Literature review Problem Statement Three proposed examinations Implementation example Conclusion and future research

Introduction - Personnel structure represents the number and the

composition of distinct personnel subgroups

used for (long term) manpower planning

Introduction - Personnel structure represents the number and the

composition of distinct personnel subgroups

used for (long term) manpower planningHead Nurse

Nurse with Skill

1

Nurse with Skill

2

Nurse with Skill

3

Trainee Nurse

1 12 15 5 7

Introduction - Nurse Rostering concerns arranging the available nursing

personnel to work requirements. Short to medium planning period

Nurse

December 201118 19 20 …

ABCDE…

Reqs. 5M6D3N

4-S13-S2...

5M7D2N

6-S15-S2

…

7M5D4N

5-S14-S2

…

M: Morning (6-14)D: Day (14-22)N: Night (22-6)

S1: Skill-1S2: Skill-2

Introduction - Nurse Rostering concerns arranging the available nursing

personnel to work requirements. Short to medium planning period

M: Morning (6-14)D: Day (14-22)N: Night (22-6)

S1: Skill-1S2: Skill-2

Nurse

December 201118 19 20 …

A M M MB D D DC N N DD NE M M…

Reqs. 5M6D3N

4-S13-S2...

5M7D2N

6-S15-S2

…

7M5D4N

5-S14-S2

…

Nurse

December 201118 19 20 …

A M M MB D D DC N N DD NE M M…

Reqs.

Nurse Rostering Problem

Many constraints Quality = the violation of soft constraints

The lower the betterM = Morning (6-14), D = Day (14-22), N = Night (22-6)

Day-shift after

night shift

Nurse Rostering Problem -More on Soft Constraints

Work requirements

Coverage constraint

s

Secondary skill

constraintsPersonnel requests

C asks days off at

20/12

Series constraint

sMax

consecutive nights

Counter constraint

s40 hours

/week

Successive series

Refer to Bilgin et al. (2010) for more detail

Nurse Rostering Problem -More on Soft Constraints

• NP-hard Problem Used metaheuristics (VNS & ALNS )

Work requirements

Coverage constraint

s

Secondary skill

constraintsPersonnel requests

C asks days off at

20/12

Series constraint

sMax

consecutive nights

Counter constraint

s40 hours

/week

Successive series

Refer to Bilgin et al. (2010) for more detail

Current practice

Roster quality

Rostering problemMetaheuristics …

Personnel structure (PS)Nurse to patient ratio

Work requirementsStatistical forecasting

Usually fixed

Current practice

Roster quality

Rostering problemMetaheuristics …

Personnel structure (PS)Nurse to patient ratio

Work requirementsStatistical forecasting

• Understaffing• Overstaffing• Conflicting

constraints

Undesired condition

Usually fixed

Current practice

Roster quality

Rostering problemMetaheuristics …

Personnel structure (PS)Nurse to patient ratio

Work requirementsStatistical forecasting

Usually fixed

• Understaffing• Overstaffing• Conflicting

constraints

Undesired condition

How we can change PS good quality roster?

Literature reviewNo Approach Paper Review

1 Staffing and rostering sequentially

• Abernathy, et al. (1973)

• Ozcan (2009)

• restrict the possibilities at the rostering level suboptimal solutions

2 Integrated staffing and rostering

• Venkataraman & Brusco (1996)

• Mundschenk & Drexl (2007)

• Li et al. (2007)• Beliën et al. (2011)

• Constraints is rather limited, compared to nurse rostering

• (some) only tries to meet the aggregate requirements, without actually produce schedule

3 Part-time/ Annualized workers

• Bard & Purnomo (2005)

• Corominas, et al. (2007)

• only determine the number of additional workers

• May not available

Problem statementHow to investigate the suitability of a

personnel structure while considering the roster quality?

Three proposed examinations1. Static check2. Roster quality component examination3. Simple neighbourhood examination

Problem statementHow to investigate the suitability of a

personnel structure while considering the roster quality?

(1) Static checkPersonnel structure

Rostering Problem

Resources Work requirements

Ratio=𝑊𝑜𝑟𝑘𝑟𝑒𝑞𝑢𝑖𝑟𝑒𝑚𝑒𝑛𝑡𝑠𝑅𝑒𝑠𝑜𝑢𝑟𝑐𝑒𝑠

Ratio persubgroup=𝑊𝑜𝑟𝑘𝑟𝑒𝑞𝑢𝑖𝑟𝑒𝑚𝑒𝑛𝑡𝑠𝑅𝑒𝑠𝑜𝑢𝑟𝑐𝑒𝑠

Can be more detailed, e.g. ratio for weekend

(1) Static checkPersonnel structure

Rostering Problem

Resources Work requirements

Ratio=𝑊𝑜𝑟𝑘𝑟𝑒𝑞𝑢𝑖𝑟𝑒𝑚𝑒𝑛𝑡𝑠𝑅𝑒𝑠𝑜𝑢𝑟𝑐𝑒𝑠

Ratio persubgroup=𝑊𝑜𝑟𝑘𝑟𝑒𝑞𝑢𝑖𝑟𝑒𝑚𝑒𝑛𝑡𝑠𝑅𝑒𝑠𝑜𝑢𝑟𝑐𝑒𝑠

Can be more detailed, e.g. ratio for weekend

Discards many rostering constraints

Roster solution

Bilgin et al.

(2010)’s algorithm

RosteringProblem

PersonnelStructure

(2) Roster quality component examination1

Coverage ConstraintsSecondary Skill

Personnel requestsSeries

Counter

Roster solution

Bilgin et al.

(2010)’s algorithm

RosteringProblem

PersonnelStructure

(2) Roster quality component examination1

2

(2) Roster quality component examinationCR SS PS S C

1 2 … n 1 2 … n 1 2 … n 1 2 … n 1 2 … n

% % % % % % % % % % % % % % % % % % % %

3

Coverage ConstraintsSecondary Skill

Personnel requestsSeries

Counter

2

[ 1 6 1 4 5 12 ]

[ 1 7 1 4 4 12 ]

[ 1 6 1 5 5 12 ]

(3) Simple neighbourhood examination

Current .. .. ..Skill

basedNeighbor_1 .. .. ..Neighbor_2 .. .. ..

FTE type

Neighbor_3 .. .. ..Neighbor_4 .. .. ..

Comb. Neighbor_5 .. .. ..

1

(3) Simple neighbourhood examination

Roster solutions

Bilgin et al.

(2010)’s algorithm

RosteringProblem

PersonnelStructure

Generate 5 problem instances Run the algorithm 5 replications

Current .. .. ..Skill

basedNeighbor_1 .. .. ..Neighbor_2 .. .. ..

FTE type

Neighbor_3 .. .. ..Neighbor_4 .. .. ..

Comb. Neighbor_5 .. .. ..2

1

Simple neighbourhood examination

Roster solutions

Bilgin et al.

(2010)’s algorithm

RosteringProblem

PersonnelStructure

Generate 5 problem instances Run the algorithm 5 replications

Current .. .. ..Skill

basedNeighbor_1 .. .. ..Neighbor_2 .. .. ..

FTE type

Neighbor_3 .. .. ..Neighbor_4 .. .. ..

Comb. Neighbor_5 .. .. ..

Tabulate

Pairwise Wilcoxon

Test

Boxplot

2

3

1

Implementation example Emergency ward

4 weeksWard Skill 1 Skill 2 Skill 3 Skill 4 Total Nurse Emergency Primary skill 1 16 4 6 27 Secondary skill 20

Subgroup Pattern (Primary skill – secondary skill)

No Of Nurses

Subgroup 1 (G1) Skill 1 1 Subgroup 2 (G2) Skill 2 – Skill 4 16 Subgroup 3 (G3) Skill 3 – Skill 4 4 Subgroup 4 (G4) Skill 4 6 Total 27

Emergency ward(1) static check & (2) roster quality

Ratio=𝑊𝑜𝑟𝑘𝑟𝑒𝑞𝑢𝑖𝑟𝑒𝑚𝑒𝑛𝑡𝑠𝑅𝑒𝑠𝑜𝑢𝑟𝑐𝑒𝑠

1G1-Skill

1G2-Skill

2G3-Skill

3G4-Skill

40.95 0.85 0.85 0.85

Reasonable, provide some extra time for vacation/illness

Emergency ward(1) static check & (2) roster quality

Ratio=𝑊𝑜𝑟𝑘𝑟𝑒𝑞𝑢𝑖𝑟𝑒𝑚𝑒𝑛𝑡𝑠𝑅𝑒𝑠𝑜𝑢𝑟𝑐𝑒𝑠

1G1-Skill

1G2-Skill

2G3-Skill

3G4-Skill

40.95 0.85 0.85 0.85

Reasonable, provide some extra time for vacation/illness

Coverage constraint Secondary skill Counter SeriesSkill

1Skill 2

Skill 3

Skill 4

Skill 1

Skill 2

Skill 3

Skill 4

1.6% 2.2% 64.0%

16.1%

10.2% 2.9%

Skill 4 understaffed

Soft constraint violations2 The lower

the better

The lower the better

Emergency ward(3) Simple neighbourhood examination3 Ward   G1 G2 G3 G4

Emergency (1) First Skill 1 16 4 6

Lower the better

Emergency ward(3) Simple neighbourhood examination3 Ward   G1 G2 G3 G4

Emergency (1) First Skill 1 16 4 6

Add skill type 2, 3, and 4

Wilcoxon test produces very low p-values, close to zero.

Difference significant

Conclusion and future research Three examinations provide:

constraints that cannot be satisfied with the given personnel structure and

alternative personnel structures that enable better quality rosters.

Future research develop an optimization approach to find

the most preferable personnel structure

References Abernathy, W. J., Baloff, N., Hershey, C. J. & Wandel, S., 1973. A

Three-Stage Manpower Planning and Scheduling Model-A Service Sector Example. Operations Research, 21(3), pp. 693-711.

Bard, J. F. & Purnomo, H. W., 2005. A column generation-based approach to solve the preference scheduling problem for nurses with downgrading. Socio-Economic Planning Sciences, 39(3), pp. 193-213.

Beliën, J., Cardoen, B. & Demeulemeester, E., 2011.. Improving workforce scheduling of aircraft line maintenance at Sabena Technics. Interfaces. In Press.

Bilgin, B., De Causmaecker, P., Rossie, B. & Vanden Berghe, G., 2010. Local search neighbourhoods for dealing with a novel nurse rostering model. Annals of Operations Research, pp. 1-25.

Corominas, A., Lusa, A. & Pastor, R., 2007. Planning production and working time within an annualised hours scheme framework. Annals of Operations Research, 155(1), pp. 5-23.

References Li, Y., Chen, J. & Cai, X., 2007. An integrated staff-sizing

approach considering feasibility of scheduling decision. Annals of Operations Research, 155(1), pp. 361-390.

Mundschenk, M. & Drexl, A., 2007. Workforce planning in the printing industry. International Journal of Production Research, 45(20), pp. 4849-4872.

Ozcan, Y. A., 2009. Quantitative Methods in Health Care Management: Techniques and Applications. 2nd ed. San Fransisco: Jossey-Bass.

Venkataraman, R. & Brusco, M. J., 1996. An integrated analysis of nurse staffing and scheduling policies. 24(1), pp. 57-71.