Three personnel structure examinations for improving nurse roster quality
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Three personnel structure examinations for improving nurse roster qualityKomarudin, G. Vanden Berghe, M.-A. Guerry, and T. De Feyter
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Contents Introduction
Personnel structure Nurse rostering problem
Literature review Problem Statement Three proposed examinations Implementation example Conclusion and future research
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Introduction - Personnel structure represents the number and the
composition of distinct personnel subgroups
used for (long term) manpower planning
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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
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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
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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
…
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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
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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
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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
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Current practice
Roster quality
Rostering problemMetaheuristics …
Personnel structure (PS)Nurse to patient ratio
Work requirementsStatistical forecasting
Usually fixed
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Current practice
Roster quality
Rostering problemMetaheuristics …
Personnel structure (PS)Nurse to patient ratio
Work requirementsStatistical forecasting
• Understaffing• Overstaffing• Conflicting
constraints
Undesired condition
Usually fixed
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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?
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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
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Problem statementHow to investigate the suitability of a
personnel structure while considering the roster quality?
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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?
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(1) Static checkPersonnel structure
Rostering Problem
Resources Work requirements
Ratio=𝑊𝑜𝑟𝑘𝑟𝑒𝑞𝑢𝑖𝑟𝑒𝑚𝑒𝑛𝑡𝑠𝑅𝑒𝑠𝑜𝑢𝑟𝑐𝑒𝑠
Ratio persubgroup=𝑊𝑜𝑟𝑘𝑟𝑒𝑞𝑢𝑖𝑟𝑒𝑚𝑒𝑛𝑡𝑠𝑅𝑒𝑠𝑜𝑢𝑟𝑐𝑒𝑠
Can be more detailed, e.g. ratio for weekend
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(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
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Roster solution
Bilgin et al.
(2010)’s algorithm
RosteringProblem
PersonnelStructure
(2) Roster quality component examination1
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Coverage ConstraintsSecondary Skill
Personnel requestsSeries
Counter
Roster solution
Bilgin et al.
(2010)’s algorithm
RosteringProblem
PersonnelStructure
(2) Roster quality component examination1
2
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(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
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[ 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
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(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
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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
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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
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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
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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
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The lower the better
Emergency ward(3) Simple neighbourhood examination3 Ward G1 G2 G3 G4
Emergency (1) First Skill 1 16 4 6
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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
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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
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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.
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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.