Geetha Baskaran Andrzej Bargiela Rong Qu School of ... · W1 to w5 (Complex) Scheduling: W1 to W5...

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25th EUROPEAN CONFERENCE ON OPERATIONAL RESEARCH

GEETHA BASKARAN 08.06.12 – 11.06.12

Geetha Baskaran Andrzej Bargiela School of Foundation Studies School of Computer Science

University of Nottingham (Malaysia Campus) University of Nottingham (Malaysia Campus)

Rong Qu School of Computer Science

University of Nottingham (Jubilee Campus)


GEETHA BASKARAN

OVERVIEW OF PRESENTATION

 Introduction  Previous Studies  Nurse Rostering Problem  Information Granulation Rationale  Proposed Studies  Example of Nurse Rostering Problem  Proposed Solution  Computational Results  Conclusion

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INTRODUCTION

 The challenge of healthcare  Flexible healthcare staff schedules  Need for automated rostering

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GEETHA BASKARAN

 Early research – 1970’ties  Mathematical programming  Heuristics  Optimisation  ….  Data aggregation (granulation)

PREVIOUS STUDIES

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GEETHA BASKARAN

EXAMPLE OF NURSE ROSTERING PROBLEM

NRP Scheduling period = 5 weeks

16 nurses in ward

12 (FT) 36h nurses

All HC & SC are satisfied

1 (PT) 32h nurse

3 (PT) 20h nurses

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ORTEC studies (Dutch hospitals)


NURSE ROSTERING PROBLEM

Nurses

E D R N L

GEETHA BASKARAN

One Week Shift(One Nurse)

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patterns

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GEETHA BASKARAN


 Nurse rostering problem involves allocating the required workload to nurses subject to a number of constraints.

 Constraints are categorized into two groups;  Hard Constraints are those that must be

satisfied to obtain feasible solutions.  Eg:

3 3 3 1 E D N L

Demands need to be fulfilled

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Shifts and personal cover demand

E D N L

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1.  Demands need to be fulfilled

2.  For each day, 1 nurse may start only one shift. 3.  Within a scheduling period, a nurse is allowed to exceed the number of hours for

which he/she is available for his/her department by at most 4 hours. 4.  The maximum labor time per week is on average 36 hours over a period of 13

consecutive weeks if this period does not include work during night shifts. 5.  The maximum number of night shifts is 3 per period of 5 consecutive weeks. 6.  A nurse must receive at least 2 weekends off duty per 5 week period. A weekend

off duty lasts 60 hours including Saturday 00:00 to Monday 04:00. 7.  Following a series of at least 2 consecutive night shifts, a 42 hours rest is required. 8.  During any period of 24 consecutive hours, at least 11 hours of rest is required. A

night shift has to be followed by at least 14 hours rest. An exception is that once in a period of 21 days for 24 consecutive hours, the resting time may be reduced to 8 hours.

9.  The number of consecutive night shifts is at most 3. 10. The number of consecutive shifts (workdays) is at most 6. 11.  One of the full-time nurses requires not receiving any late shifts

Hard Constraints – ORTEC studies (Dutch hospitals)

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GEETHA BASKARAN

Feasible (Nurse 1)

Infeasible(Nurse 2)

  3 Nights

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HC = 9

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 Soft Constraints are typically time related constraints. They are desirable but not compulsory, and thus can be violated.

 Eg:

One Week Shift(One Nurse)

COST = 5

An early shift after a day shift should be avoided. 5

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GEETHA BASKARAN


1 For the period of Friday 23:00 to Monday 0:00, a nurse should have either no shifts or at least 2 1000 shifts (Complete Weekend).

2 Avoid sequence of shifts with length of 1 for all nurses. 1000 3a For nurses with availability of 30-36 hours per week, the length of a series of night shifts should be 1000

within the range [2, 3]. It could be part of, but not before, another sequence of shifts. 3b For nurses with availability of 0-30 hours per week, the length of a series of night shifts should be 1000

within the range [2, 3]. It could be part of, but not before, another sequence of shifts. 4 The rest after a series of day, early or late shifts is at least 2 days. 100 5a For nurses with availability of 30-36 hours per week, the number of shifts is within the range [4, 5] 10

per week. 5b For nurses with availability of 0-30 hours per week, the number of shifts is within the range [2, 3] 10

per week. 6a For nurses with availability of 30-36 hours per week, the length of a series of shifts should be within 10

the range of [4, 6]. 6b For nurses with availability of 0-30 hours per week, the length of a series of shifts should be within 10

the range [2, 3]. 7 For all nurse, the length of a series of early shifts should be within the range [2, 3]. It could be within 10

another series of shifts. 8  For all nurse the length of a series of late shifts should be within the range of [2, 3]. It could be within 10

another series of shifts. 9a An early shift after a day shift should be avoided. 5 9b An early shift after a late shift should be avoided. 5 9c A day shift after a late shift should be avoided. 5 10 A night shift after an early shift should be avoided. 1

Soft Constraints – ORTEC studies (Dutch hospitals) Soft Constraints Cost

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Penalties of the violations within blocks

Shifts and personal cover demand

E D N L

Succeeding shifts

N E D L Preceding ok n/f n/f n/f Shift E ok ok ok ok

D ok 5 ok ok L ok n/for 5* n/for 5* ok

9a An early shift after a day shift should be avoided. 5 9b An early shift after a late shift should be avoided. 5 9c A day shift after a late shift should be avoided. 5 10 A night shift after an early shift should be avoided. 1

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GEETHA BASKARAN

E

D

N

L

Reducing the number of shift types to be considered (2-stage approach)

Demand

N

d

d

Granulation of Shift Types

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R

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N N R R E E E E R R E D R R E E E D R R R N N R R E E E E R R E D R R E E D D R R R … …. N N R R E E D D R R E E R R E E E D R R R ….. ….. N N R R D D D D R R E E R R E E E D R R R ….. N N R R D L L L R R E E R R E E E D R R R ….. N N R R L L L L R R E E R R E E E D R R R …. ….

WEEK1 WEEK2 WEEK3

Offline preparation Process

Granulation of Shift Types

• Convert the problem space from {N,E,L,D,R} to a smaller space of {N,d,R}.

08.06.12 – 11.06.12

WEEK1 WEEK2 WEEK3

N N R R d d d d R R d d R R d d d d R R R


GEETHA BASKARAN

• The 18 feasible zero-cost shift patterns which were identified for the sample problem of a ward in a Dutch hospital Which satisfies All the constraints for the 36h nurses. These patterns will be used for the 32 h nurse also since it falls in the same category

Granulation of Shifts into Patterns

P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 P13 P14 P15 P16 P17 P18

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• The 15 feasible zero-cost shift patterns which were identified for the sample problem of a ward in a Dutch hospital Which satisfies All the constraints for the 20h nurses

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NNRRRRR RRNNRRR RDNNRRR RRRRNNN DDRRRRR RDDRRRR DDDRRRR RRDDRRR RDDDRRR RRRDDRR DRRDDRR RRDDDRR RRRRRDD DRRRRDD RRRRDDD

P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 P13 P14 P15


GEETHA BASKARAN


•  Use available patterns to satisfy demands.

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WEEK1 WEEK2 WEEK3

N N R R d d d d R R d d d d d d R R R D D

WEEK1 WEEK2 WEEK3

P3 P17 P12

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Previous research

Granulation Approach vs. Traditional Rostering

GEETHA BASKARAN

Convert dNR

schedule to EDL

Scheduling: W1 to w5 (Complex)

Scheduling:W1 to W5

EDLNR -> dNR->

Patterns in dNR space

EDLNR

Individual shifts

Prune converted patterns using (constraints 7-10)

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Granulation Approach

•  Granulation of the shift types (EDLNR dNR)

•  Granulation of shifts into patterns

•  “zero-cost patterns”

•  “non-zero-cost patterns”

•  Schedulling of patterns

•  Conversion of schedule in dNR into schedule in EDLNR

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GEETHA BASKARAN

The week 1 feasible scheduling sequence generated from the patterns generated on the different types of nurses and which satisfies all the constraints according to the types of nurses. Besides, these patterns satisfy the personnel cover requirements (9999966) for day and (1111111) for night shift.

Week 1 Schedule

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Week 1-5 Schedule

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dNR RESULT

Week 1-5 Schedule



EDLNR RESULT

Week 1-5 Schedule

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EDLNR RESULT

Week 1-5 Schedule



Solution Cost

5-weeks schedule 31-day schedule

Published ORTEC solution

NA 270

Proposed data granulation solution

250 160

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GEETHA BASKARAN

CONCLUSION

  Nurse rostering problem - detailed time constraints and different types of day-shifts represents computational challenge.

  The complexity of the problem is due to large solution space and the many constraints that need to be satisfied.

  The novel approach proposed here involves a simplification of the original problem by a sensible grouping of shift types and the grouping of the individual shifts into weekly sequences that can be used to derive schedules in this reduced problem space.

  Subsequently the schedules from the reduced problem space are translated into the original problem space by taking into account the constraints that could not be represented in the reduced space.

  The grouping of the shift types into a prototype shift and the grouping of shift sequences into weekly patterns used in scheduling are collectively referred to as information granulation

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GEETHA BASKARAN

QUESTION & ANSWER

THANK YOU

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GEETHA BASKARAN

Information Granulation Rationale

The concept of information granulation was first introduced by Zadeh in the

context of fuzzy sets in 1979 . The fundamental tasks of Granular Computing (GrC) is the construction of Information Granules, a process that is called “information granulation”. Some of the basic notions of granular computing are :

granules hierarchies levels

Example of Granulation Process by

Corrado Mencar

08.06.12 – 11.06.12

Geetha Baskaran Andrzej Bargiela Rong Qu School of ... · W1 to w5 (Complex) Scheduling: W1 to W5...

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