The overlapping case in an integrated staffing and rostering formulation

1. The overlapping case in an integrated staffing and rostering formulation Komarudin, M.-A. Guerry, G. VandenBerghe, and T. De Feyter

2. Contents • Introduction • Personnel structure • Nurse rostering problem • Literature review • Roster Quality Staffing (RQS) Problem • Subgroup formulation • Overlapping rostering constraint • Illustration • Conclusion and future research

3. Introduction - Personnel structure • represents the number and the composition of distinct personnel subgroups • used for (long term) manpower planning

4. 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-1 S2: Skill-2

5. Nurse Rostering Problem 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)

6. Nurse Rostering Problem -More on Soft Constraints • NP-hard Problem Used metaheuristics (VNS & ALNS ) Refer to Bilgin et al. (2010) for more detail

7. Motivation Usually fixed

8. Motivation Usually fixed How we can determine PS  good quality roster? Feedback Undesired condition • Understaffing • Overstaffing • Conflicting constraints

9. Literature review

10. Roster Quality Staffing (RQS) Problem statement How to investigate the suitability of a personnel structure while considering the roster quality? Roster quality Personnel structure Roster

11. Three-step approach Roster Quality Staffing (RQS) Problem statement • Static check • Roster quality component examination • Simple neighbourhood examination How to investigate the suitability of a personnel structure while considering the roster quality? Roster quality Personnel structure Roster

12. New formulation Subgroup formulation Overlapping rostering constraint

13. Defining subgroups on RQS 1 • Characteristics to differentiate subgroups : the set of characteristics for subgroup is the -th characteristic of subgroup . • Example:

14. Subgroup formulations on RQS • Exactly-same characteristics based , • Main-characteristic based , beneficial if the main-characteristic has a high penalty weight.

15. Subgroup formulation on RQS (application) • Multiple wards • Float unit personnel • Cross-trained personnel • Example:

16. 2 Overlapping personnel constraints • Subgroup-specific vs. overlapping • Overlapping: associated with two or moresubgroups. • Example: • coverage requirements for skill C • tutorship, etc.

17. Models for overlapping rostering constraints • possessed by at least two subgroups, e.g. coverage reqs. for float unit , , and . • partiallypossessed by at least two subgroups, e.g. tutorship , , , and . 1 – Substitution (OR) 2 – Complementary (AND) Characteristics of subgroup i Characteristics of overlapping rostering constraint l

18. Application on three-step approach Three proposed examinations: • Static check • Roster quality component examination • Overlapping rostering constraints • Simple neighbourhood examination Subgroup formulation  three examinations

19. Illustration • Emergency ward taken from Bilgin et al. (2012) • 4 weeks Exactly-same subgroup based

20. Emergency ward(1) static check & (2) roster quality 1 Reasonable, provide some extra time for vacation/illness

21. Emergency ward(1) static check & (2) roster quality 1 Reasonable, provide some extra time for vacation/illness 2 The lower the better Soft constraint violations Skill 4 understaffed Substitution overlapping constraint G2, G3 & G4

22. Emergency ward(3) Simple neighbourhood examination 3 The lower the better

23. Emergency ward(3) Simple neighbourhood examination 3 Wilcoxon test produces very low p-values, close to zero. Difference significant Add G2, G3 & G4 Skill 4 understaffed

24. Conclusion Conclusions: • Subgroup formulation provides more general formulation: • multi-ward, float unit, cross-trained, etc. • Overlapping rostering constraint: • clarifies the source of a low roster quality • RQS problem can be decomposed into smaller problems Future directions: • develop an optimization approach to find the most preferable personnel structure • Integrate with manpower planning

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