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

Contents Introduction Literature review Problem Statement 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 planning Head 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 2011 18 19 20 … A B C D E Reqs. 5M 6D 3N 4-S1 3-S2 ... 7D 2N 6-S1 5-S2 7M 5D 4N 5-S1 4-S2 M: Morning (6-14) D: Day (14-22) N: Night (22-6) S1: Skill-1 S2: Skill-2

Introduction - Nurse Rostering concerns arranging the available nursing personnel to work requirements. Short to medium planning period Nurse December 2011 18 19 20 … A M B D C N E Reqs. 5M 6D 3N 4-S1 3-S2 ... 7D 2N 6-S1 5-S2 7M 5D 4N 5-S1 4-S2 M: Morning (6-14) D: Day (14-22) N: Night (22-6) S1: Skill-1 S2: Skill-2

Nurse Rostering Problem December 2011 18 19 20 … A M B D C N E Reqs. Day-shift after night shift Many constraints Quality = the violation of soft constraints The lower the better M = Morning (6-14), D = Day (14-22), N = Night (22-6)

Nurse Rostering Problem - More on Soft Constraints Work requirements Coverage constraints Secondary skill constraints Personnel requests C asks days off at 20/12 Series constraints Max consecutive nights Counter constraints 40 hours /week Successive series Refer to Bilgin et al. (2010) for more detail

Nurse Rostering Problem - More on Soft Constraints Work requirements Coverage constraints Secondary skill constraints Personnel requests C asks days off at 20/12 Series constraints Max consecutive nights Counter constraints 40 hours /week Successive series NP-hard Problem Used metaheuristics (VNS & ALNS ) Refer to Bilgin et al. (2010) for more detail

Current practice Work requirements Statistical forecasting Personnel structure (PS) Nurse to patient ratio Rostering problem Metaheuristics … Roster quality Usually fixed

Current practice Work requirements Statistical forecasting Personnel structure (PS) Nurse to patient ratio Rostering problem Metaheuristics … Roster quality Usually fixed Understaffing Overstaffing Conflicting constraints Undesired condition

Current practice Work requirements Statistical forecasting Personnel structure (PS) Nurse to patient ratio Rostering problem Metaheuristics … Roster quality Usually fixed How we can change PS  good quality roster? Understaffing Overstaffing Conflicting constraints Undesired condition

Literature review No 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 statement How to investigate the suitability of a personnel structure while considering the roster quality?

Three proposed examinations Problem statement How to investigate the suitability of a personnel structure while considering the roster quality? Three proposed examinations Static check Roster quality component examination Simple neighbourhood examination

(1) Static check Personnel structure Rostering Problem Resources Work requirements Ratio= 𝑊𝑜𝑟𝑘 𝑟𝑒𝑞𝑢𝑖𝑟𝑒𝑚𝑒𝑛𝑡𝑠 𝑅𝑒𝑠𝑜𝑢𝑟𝑐𝑒𝑠 Can be more detailed, e.g. ratio for weekend Ratio persubgroup= 𝑊𝑜𝑟𝑘 𝑟𝑒𝑞𝑢𝑖𝑟𝑒𝑚𝑒𝑛𝑡𝑠 𝑅𝑒𝑠𝑜𝑢𝑟𝑐𝑒𝑠

(1) Static check Personnel structure Rostering Problem Resources Work requirements Ratio= 𝑊𝑜𝑟𝑘 𝑟𝑒𝑞𝑢𝑖𝑟𝑒𝑚𝑒𝑛𝑡𝑠 𝑅𝑒𝑠𝑜𝑢𝑟𝑐𝑒𝑠 Discards many rostering constraints Can be more detailed, e.g. ratio for weekend Ratio persubgroup= 𝑊𝑜𝑟𝑘 𝑟𝑒𝑞𝑢𝑖𝑟𝑒𝑚𝑒𝑛𝑡𝑠 𝑅𝑒𝑠𝑜𝑢𝑟𝑐𝑒𝑠

(2) Roster quality component examination Roster solution Bilgin et al.(2010)’s algorithm Rostering Problem Personnel Structure 1

(2) Roster quality component examination Roster solution Bilgin et al.(2010)’s algorithm Rostering Problem Personnel Structure 1 2 𝑅𝑜𝑠𝑡𝑒𝑟 𝑞𝑢𝑎𝑙𝑖𝑡𝑦= 𝐶 𝐶 𝑆𝑘𝑖𝑙 𝑙 1 +𝐶 𝐶 𝑆𝑘𝑖𝑙 𝑙 2 +…+𝐶 𝐶 𝑆𝑘𝑖𝑙 𝑙 𝑛 + 𝑆𝑆 𝑆𝑘𝑖𝑙 𝑙 1 + 𝑆𝑆 𝑆𝑘𝑖𝑙 𝑙 2 +…+ 𝑆𝑆 𝑆𝑘𝑖𝑙 𝑙 𝑛 + 𝑃𝑆 𝑆𝑘𝑖𝑙 𝑙 1 + 𝑃𝑆 𝑆𝑘𝑖𝑙 𝑙 2 +…+ 𝑃𝑆 𝑆𝑘𝑖𝑙 𝑙 𝑛 + 𝑆 𝑆𝑘𝑖𝑙 𝑙 1 + 𝑆 𝑆𝑘𝑖𝑙 𝑙 2 +…+ 𝑆 𝑆𝑘𝑖𝑙 𝑙 𝑛 + 𝐶 𝑆𝑘𝑖𝑙 𝑙 1 + 𝐶 𝑆𝑘𝑖𝑙 𝑙 2 +…+ 𝐶 𝑆𝑘𝑖𝑙 𝑙 𝑛 Coverage Constraints Secondary Skill Personnel requests Series Counter

(2) Roster quality component examination 3 CR SS PS S C 1 2 … n % 2 𝑅𝑜𝑠𝑡𝑒𝑟 𝑞𝑢𝑎𝑙𝑖𝑡𝑦= 𝐶 𝐶 𝑆𝑘𝑖𝑙 𝑙 1 +𝐶 𝐶 𝑆𝑘𝑖𝑙 𝑙 2 +…+𝐶 𝐶 𝑆𝑘𝑖𝑙 𝑙 𝑛 + 𝑆𝑆 𝑆𝑘𝑖𝑙 𝑙 1 + 𝑆𝑆 𝑆𝑘𝑖𝑙 𝑙 2 +…+ 𝑆𝑆 𝑆𝑘𝑖𝑙 𝑙 𝑛 + 𝑃𝑆 𝑆𝑘𝑖𝑙 𝑙 1 + 𝑃𝑆 𝑆𝑘𝑖𝑙 𝑙 2 +…+ 𝑃𝑆 𝑆𝑘𝑖𝑙 𝑙 𝑛 + 𝑆 𝑆𝑘𝑖𝑙 𝑙 1 + 𝑆 𝑆𝑘𝑖𝑙 𝑙 2 +…+ 𝑆 𝑆𝑘𝑖𝑙 𝑙 𝑛 + 𝐶 𝑆𝑘𝑖𝑙 𝑙 1 + 𝐶 𝑆𝑘𝑖𝑙 𝑙 2 +…+ 𝐶 𝑆𝑘𝑖𝑙 𝑙 𝑛 Coverage Constraints Secondary Skill Personnel requests Series Counter

(3) Simple neighbourhood examination 1 𝑆 𝑖 𝑆 𝑗 Current .. 𝑛 𝑖 𝑛 𝑗 Skill based Neighbor_1 𝑛 𝑖 ±𝑐 Neighbor_2 𝑛 𝑗 ∓𝑑 FTE type Neighbor_3 Neighbor_4 Comb. Neighbor_5 1 6 14 5 12 1 7 14 4 12 1 6 15 5 12

(3) Simple neighbourhood examination 1 𝑆 𝑖 𝑆 𝑗 Current .. 𝑛 𝑖 𝑛 𝑗 Skill based Neighbor_1 𝑛 𝑖 ±𝑐 Neighbor_2 𝑛 𝑗 ∓𝑑 FTE type Neighbor_3 Neighbor_4 Comb. Neighbor_5 2 Roster solutions Bilgin et al.(2010)’s algorithm Rostering Problem Personnel Structure Generate 5 problem instances Run the algorithm 5 replications

Simple neighbourhood examination 1 𝑆 𝑖 𝑆 𝑗 Current .. 𝑛 𝑖 𝑛 𝑗 Skill based Neighbor_1 𝑛 𝑖 ±𝑐 Neighbor_2 𝑛 𝑗 ∓𝑑 FTE type Neighbor_3 Neighbor_4 Comb. Neighbor_5 2 Roster solutions Bilgin et al.(2010)’s algorithm Rostering Problem Personnel Structure Generate 5 problem instances Run the algorithm 5 replications Tabulate Pairwise Wilcoxon Test Boxplot 3

Implementation example Emergency ward 4 weeks

Emergency ward (1) static check & (2) roster quality Ratio= 𝑊𝑜𝑟𝑘 𝑟𝑒𝑞𝑢𝑖𝑟𝑒𝑚𝑒𝑛𝑡𝑠 𝑅𝑒𝑠𝑜𝑢𝑟𝑐𝑒𝑠 G1-Skill 1 G2-Skill 2 G3-Skill 3 G4-Skill 4 0.95 0.85 Reasonable, provide some extra time for vacation/illness

Emergency ward (1) static check & (2) roster quality Ratio= 𝑊𝑜𝑟𝑘 𝑟𝑒𝑞𝑢𝑖𝑟𝑒𝑚𝑒𝑛𝑡𝑠 𝑅𝑒𝑠𝑜𝑢𝑟𝑐𝑒𝑠 G1-Skill 1 G2-Skill 2 G3-Skill 3 G4-Skill 4 0.95 0.85 Reasonable, provide some extra time for vacation/illness 2 The lower the better Soft constraint violations Coverage constraint Secondary skill Counter Series Skill 1 Skill 2 Skill 3 Skill 4 1.6% 2.2% 64.0% 16.1% 10.2% 2.9% Skill 4 understaffed

Emergency ward (3) Simple neighbourhood examination   G1 G2 G3 G4 Emergency (1) First Skill 1 16 4 6 The lower the better

Emergency ward (3) Simple neighbourhood examination   G1 G2 G3 G4 Emergency (1) First Skill 1 16 4 6 Wilcoxon test produces very low p-values, close to zero. Difference significant Lower the better Add skill type 2, 3, and 4

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.