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Nurse Scheduling-IGP 1
I N T E R G E R G O A L P R O G R A M M I N G
13.04.14
NURSE SCHEDULING
Prepared by-Sowmiyan Morri
Swapnil SoniDoMS, IISc
Course-Applied Operations Research
Instructor-Prof M Mathirajan
2Nurse Scheduling-IGP
Index
Introduction to Nurse Scheduling Scheduling problem Motivation to adopt OR technique
Research and Literature work Literature Review The Paper
The Paper Parameters Problem Statement Problem Formulation
Notations & Decision Variables Constraints Objective Function
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Programming in LINGO (Optimization
tool)
Result Conclusion
Achievements The way forward Applications
Pilot Study at Health Centre, IISc Parameters Constraints Result
References
3
Introduction to Nurse Scheduling
13.04.14Nurse Scheduling-IGP
Motivation for applying Operations Research for Nurse Scheduling
Cyclical Nurse Schedule
Constraints
Hospitals requirement
Nurses’ preferences
Conventional RegisterQuestion on:
• Tedious•Time •Accuracy•Fairness
Mathematical ModelingAdvantages on:
• Tedious•Time •Accuracy•Fairness
Prescriptive Model
Cause Response
Variables of 1st order Linear
Variables with Binary values Integer
Constraints with priorities Goal
Liner Integer Goal Programming
Operations Research
4Nurse Scheduling-IGP
Literature Review
13.04.14
Authors Reference Literature Limitations
Arthur & Ravindran
Arthur, J. L., & Ravindran, A., A Multiple Objective Nurse SchedulingModel, IIE Transactions, 13(1), pp. 55-60, 1981
Research on modelling Nurse Scheduling using goal programming has been studied which focused on two phases:•Phase 1 is to assign the working days and days off for each nurse while•Phase 2 is to assign the shift types of their working days
•Small set of constraints •Limited problem dimensions with the size of nurses is 4
Musa & Saxena
Musa, A. A., & Saxena, U., Scheduling Nurses Using Goal-ProgrammingTechniques, IIE Transactions, 16(3), pp. 216 – 221, 1984
Used a 0-1 goal programming thatapplied to one unit of a hospital with the considerations of the hospital policies and nurses’ preferences
•2 week planning period •1 one single shift
Ozkarahan & Bailey
Ozkarahan, I. & Bailey, J.E., Goal Programming Model Subsystem of AFlexible Nurse Scheduling Support System, IIE Transactions, 20(3), pp.306-316, 1988.
Nurse scheduling modelling showed theflexibility of goal programming in handling various goals which fulfilled the hospital’s objectives and the nurses’ preferences.
•Small set of constraints
5Nurse Scheduling-IGP 13.04.14
Authors Reference Literature Limitations
Azaiez & Al Sharif
Berrada, I., Ferland, J. A., & Michelon, P., A Multi-objective Approach toNurse Scheduling with Both Hard and Soft Constraints, Socio-EconomicPlanning Sciences, 30(3), pp. 183-193, 1996
Used the 0-1 goal programming approach with the considerations of hospital’s objectives as hard constraints and the nurses’ preferences as soft constraints to develop the schedules
•No cyclic scheduling
Harvey and Kiragu
Harvey, H.M., & Kiragu, M., Cyclic and Non-cyclic Scheduling of 12 hShift Nurses by Network Programming, European Journal of OperationalResearch, 104, pp. 582-592, 1998
Presented a mathematical model for cyclic and non-cyclic scheduling of 12hours shift nurses. The model is quite flexible and can accommodate a varietyof constraints
• With small requirements which are not appropriate to embed in real situations
Chan and Weil
Chan, P. & Weil, G., Cyclical Staff Scheduling Using Constraint LogicProgramming, Lecture Notes on Computer Sciences 2079, pp. 159-175,2001
Use of work cycles with various constraints to producetimetables of up to 150 people
•Small set of constraints
Literature Review
6Nurse Scheduling-IGP
The Paper
13.04.14
Author From
Ruzzakiah JenalSchool of Information Technology, Faculty of Science and Information Technology,Universiti Kebangsaan Malaysia, Selangor, Malaysia
Wan Rosmanira Ismail School of Mathematical Sciences, Faculty of Science and Technology,Universiti Kebangsaan Malaysia, Selangor, Malaysia
Liong Choong Yeun
Ahmed Oughalime
Published By LPPM ITB, ISSN: 1978-3043
Accepted for Publication April 13th, 2011
7Nurse Scheduling-IGP
The Paper -Parameters
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Number of Nurses 18
Number of Days 21
Number of Shifts: 3 (Morning, Evening & Night)
Number of Decision Variables 18 X 21 X 4 (3 shifts+1 Off) = 1512
Type of Decision Variables Binary (0-1)
Parameters:
One Ward 18 nurses 3 Shifts
Morning ShiftAt least 4 nurses
Evening ShiftAt least 4
nurses
Night ShiftExactly 3 nurses
7:00 am-2:00pm
2:00pm-9:00pm
9:00pm-7:00am
8Nurse Scheduling-IGP 13.04.14
Problem StatementObjective:
Cyclic Nurse Scheduling: To allot shifts to each Nurse for each day thereby generating a schedule of working days and days off for each nurse in a ward of a hospital.
Physical Constraints:
(A) Hard ConstraintMeeting management objectives
(B)Soft constraintsSatisfaction of employees(Nurses), work/life balance
Logical Constraints:
(C) Cyclic SchedulingA cyclic schedule consists of a set of work patterns which is rotated among a group of workers over a set of scheduling horizon. At the end of the scheduling horizon each worker would have completed each pattern exactly once.
Advantages:• Fairness among nurses• Considers nurses preferences • Lead to maximizing satisfaction• Help Nurses to provide Quality of services
“The right employees at the right time and at the right cost while achieving a high level of employee job satisfaction”
9Nurse Scheduling-IGP
Problem Statement
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Morning Shift
?=0,1Nurse
Demand1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Days
1 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 42 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 43 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 44 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 45 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 46 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 47 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 48 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 49 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 4
10 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 411 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 412 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 413 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 414 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 415 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 416 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 417 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 418 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 419 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 420 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 421 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 4
Total Shift ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?
Similarly for:Evening, Day & Off Shift
This Excel sheet is linked with LINGO to feed the inputs for ‘Data Sets’ & ‘Attributes’ and get output for all ‘Decision Variables’
10Nurse Scheduling-IGP 13.04.14
Constraints•Hard Constraints (Management)•Soft Constraints (Nurse Specific)
Hard Constraints
•Each unit is covered by 3 shifts for 24 hours a day and 7 days a week.•Minimum staff level requirement must be satisfied.•Each nurse works at most one shift a day.•Avoid any isolated days patterns of “off-on-off”.•Each nurse must have three days off after having three consecutive night
shifts.•Each nurse works between 12 to 14 days per schedule.•Each nurse works not more than 6 consecutive days.•Evening shift constitutes at least 25% of total workload.•Morning shift constitutes at least 30% of total workload.
Soft Constraints
•Avoid working in an evening shift followed by a morning shift or a nightshift the next day.
•Avoid working in a morning shift followed by an evening shift or a night shift the next day.
•Each nurse has at least one day off in one weekend.•All nurses have the same amount of total workload.
Problem Formulation-Constraints Description
Hard Constraints-Must be satisfied
Soft Constraint-May be violated
Goal Programmin
g
11Nurse Scheduling-IGP
NotationsThe following notations are used to specify the model: n = number of days in the schedule (n = 21) m = number of nurses available for the unit of interest (m = 18) i = index for days, i = 1…n k = index for nurses, k = 1…m Pi = staff requirement for morning shift of day i, i = 1…n Ti = staff requirement for evening shift of day i, i = 1…n Mi = staff requirement for night shift of day i, i = 1…n
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Problem Formulation- Notation & Decision Variables
Decision Variables
12Nurse Scheduling-IGP
Hard Constraints:
Set 1: Minimum staff level requirement must be satisfied: For Morning shift (Where Pi=4)
For Evening shift (Where Ti=4)
For Night shift (Where Mi=3)
Set 2: Each nurse works only one shift a day:13.04.14
Problem Formulation-Constraints
….“n” equations
….“n” equations
….“n” equations
….“n*m” equations
13Nurse Scheduling-IGP
Hard Constraints:
Set 3: Avoid any isolated days patterns of “off-on-off” :
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Problem Formulation-Constraints (continued..)
….“(n-2)*m” equations
Day1 Day2 Day3Off On OffC1 X2/Y2/Z2 C3 Sum
Unacceptable1 1 1 3
Acceptable0 0 0 00 0 1 10 1 0 10 1 1 21 0 0 11 0 1 21 1 0 2
Yes No
1414
Nurse Scheduling-IGP
Hard Constraints:
Set 4: Each nurse works 3 consecutive days of night shift and followed by 3 days off. Each nurse will be assigned to their night shifts and off days as follow:
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Problem Formulation-Constraints (continued..)
….“m” equations
15Nurse Scheduling-IGP
Hard Constraints:
Set 5: Each nurse works between 12 to 14 days per schedule:
13.04.14
Problem Formulation-Constraints (continued..)
….“2*m” equations
For each Nurse total Sum of all working shift should lie between 12 & 14
16Nurse Scheduling-IGP
Hard Constraints: Set 6: Each nurse works not more than 6 consecutive days:
Each Nurse has to have at least 1 “Off” in 7 consecutive days
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Problem Formulation-Constraints (continued..)
Cases for 7 Consecutive days for Kth Nurse
Case-1
Case-2
Case-3
Case-4
Case-5
Case-6
Case-7
Case-8
Case-9
Case-10
Case-11
Case-12
Case-13
Case-14
Case-15
Case-16
Case-17
Case-18
Case-19
Case-20
Case-21
Days
1 K K+1 K+1 K+1 K+1 K+1 K+12 K K K+1 K+1 K+1 K+1 K+13 K K K K+1 K+1 K+1 K+14 K K K K K+1 K+1 K+15 K K K K K K+1 K+16 K K K K K K K+17 K K K K K K K 8 K K K K K K K 9 K K K K K K K
10 K K K K K K K 11 K K K K K K K 12 K K K K K K K 13 K K K K K K K 14 K K K K K K K 15 K K K K K K K 16 K K K K K K K 17 K K K K K K K 18 K K K K K K K 19 K K K K K K K 20 K K K K K K K 21 K K K K K K K
7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7
Due to Cyclic constraint, Nurse “K” has to take position of “K+1” in each next cycle
1717
Nurse Scheduling-IGP
Set 6: Each nurse works not more than 6 consecutive days For 1st 15 Days, 18 Nurses (in following eq “i” can take maximum of 15 value)
For next 6 days, 17 Nurses (in following eq “k” can take maximum of 17 value)
For next 6 days, 18th Nurses 13.04.1413.04.141
7Nurse Scheduling-IGP
6 ….“(n-6)*m” equations
Problem Formulation-Constraints (continued..)
….“6*(m-1)” equations
….6 equations
18Nurse Scheduling-IGP
Set 7: Evening shift constitutes at least 25% of total workload:
Sum of all Evening shifts for a nurse >=25% of Total worked shifts
Set 8: Morning shift constitutes at least 30% of total workload:
o Sum of all Morning shifts for a nurse >=30% of Total worked shifts
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Problem Formulation-Constraints (continued..)
0.25* ….“m” equations
0.30* ….“m” equations
19Nurse Scheduling-IGP
Soft Constraints:
Soft constraints are arising out of Nurses’ preferences so these can be treated as Goals for our Integer Liner Programming.
The deviation for each goal are christened: ρ : Positive Deviation η : Negative Deviation
Set 1: Avoid working in an evening shift followed by a morning shift or a night shift the next day:
13.04.14
Day1 Day2Evening Morning/Night
Y1 X2/Z2 SumUnacceptable
1 1 2Acceptable
0 0 00 1 11 0 1
Yes No
Problem Formulation-Constraints (continued..)
20Nurse Scheduling-IGP
Set 1: Avoid working in an evening shift followed by a morning shift or a night shift the next day:
For 1st 20 Days, 18 Nurses (in following eq “i” can take maximum of 20 value)
For 21st & 1st days, 17 Nurses (in following eq “k” can take maximum of 17 value)
For 21st & 1st days, 18th & 1st Nurses
13.04.1413.04.14Nurse Scheduling-IGP
….“(n-1)*m” equations
Problem Formulation-Constraints (continued..)
….“(m-1)” equations
….1 equation
Goal-1: Minimize
=
=
=
21Nurse Scheduling-IGP
Set 2: Avoid working in an Morning shift followed by a Evening shift or a night shift the next day:
For 1st 20 Days, 18 Nurses (in following eq “i” can take maximum of 20 value)
For 21st & 1st days, 17 Nurses (in following eq “k” can take maximum of 17 value)
For 21st & 1st days, 18th & 1st Nurses
13.04.1413.04.14Nurse Scheduling-IGP
….“(n-1)*m” equations
Problem Formulation-Constraints (continued..)
….“(m-1)” equations
….1 equation
Goal-2: Minimize
=
=
=
22Nurse Scheduling-IGP
Set 3: Each nurse has at least one weekend off:
Sum of above heighted weekends >=1 (for each Nurse)
13.04.14
Problem Formulation-Constraints (continued..)
Nurse1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Days
1 2 3 4 5 6 7 8 9
10 11 12 13 14 15 16 17 18 19 20 21
Each Nurse has to have at least one Off here out of highlighted 3 weekends
….“m” equations
Goal-3: Minimize
=
23Nurse Scheduling-IGP
Set 4: All nurses have the same amount of total workload: In Hard Constraint Set-5, it has been seen that Management preference for
total work load should be between 12 & 14. But Nurses prefer to have equal work load. Thus trade off is to have work load of 13 for each nurse.
Sum of all shifts for each Nurse = 13
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Problem Formulation-Constraints (continued..)
….“m” equations
Goal-4: Minimize
Binary Constraints: For each nurse and for each shift (Morning, Evening, Night, Off), value can be either 1 or 0.
24Nurse Scheduling-IGP 13.04.14
Problem Formulation-Objective Function:
Preemptive Goal Programming for this model:
Subject to:
• Hard constraints• Soft constraints• Binary Constraints• Non-negativity constraints
25Nurse Scheduling-IGP
Programming in LINGO
13.04.14
Defining Sets
Import & Export of Data with Excel
26Nurse Scheduling-IGP
Program Execution
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27Nurse Scheduling-IGP
Time Line Analysis
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1 2 3 4 5 6 7 80
500
1000
1500
2000
2500
3000
3500
4000
4500
No. of Variables Vs Time to solve
Tim
e to
sol
ve (
in M
inut
es)
(for 21 Days)
Exponential increase in time to solve the problem w.r.t. No. of Nurses
28Nurse Scheduling-IGP
Result-Optimal Solution
13.04.14
OVERALL SCHEDULE
Nurse Total Nurses in Morning
Shift
Total Nurses in Evening
Shift
Total Nurses in Night
Shift
Total Nurses in all Shifts1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Days
1 N OFF OFF OFF E E N OFF M E E M N OFF M M OFF OFF 4 4 3 112 N OFF M OFF E E N OFF E E OFF OFF N OFF M M M OFF 4 4 3 113 N OFF M OFF E OFF N OFF OFF E M OFF N OFF E E M M 4 4 3 114 OFF E E E OFF N OFF M M OFF E N OFF M OFF OFF M N 4 4 3 115 OFF E E E M N OFF E M M OFF N OFF M OFF OFF OFF N 4 4 3 116 OFF E E OFF M N OFF E OFF M OFF N OFF M E OFF M N 4 4 3 117 E E OFF M N OFF OFF E M OFF N OFF M M E OFF N OFF 4 4 3 118 E E M M N OFF OFF OFF M OFF N OFF E E E M N OFF 4 5 3 129 OFF E E M N OFF M M OFF OFF N OFF E E OFF M N OFF 4 4 3 11
10 E OFF E N OFF OFF M M E N OFF M OFF OFF M N OFF E 4 4 3 1111 E M OFF N OFF OFF E M E N OFF M OFF E M N OFF E 4 5 3 1212 OFF M OFF N OFF M E M OFF N OFF M E E OFF N OFF E 4 4 3 1113 OFF M N OFF M M OFF E N OFF M E E OFF N OFF OFF E 4 4 3 1114 OFF M N OFF M E E E N OFF M OFF OFF M N OFF OFF E 4 4 3 1115 E OFF N OFF OFF E E OFF N OFF M E M M N OFF M OFF 4 4 3 1116 E N OFF E M OFF OFF N OFF M E E M N OFF M E OFF 4 5 3 1217 OFF N OFF E M M OFF N OFF E OFF E OFF N OFF M E M 4 4 3 1118 M N OFF OFF E M M N OFF E M OFF OFF N OFF E OFF E 4 4 3 1119 N OFF OFF M OFF M N OFF M E E OFF N OFF M E E OFF 4 4 3 1120 N OFF E M OFF OFF N OFF E OFF E M N OFF M OFF E M 4 4 3 1121 N OFF E E OFF M N OFF OFF M OFF M N OFF OFF E E M 4 4 3 11
Total Morning Shifts 1 4 3 5 6 6 3 5 6 4 5 6 3 6 6 6 5 4Total Evening Shifts 6 6 7 5 4 4 4 5 4 6 5 4 4 4 4 4 5 6
Total Night Shifts 6 3 3 3 3 3 6 3 3 3 3 3 6 3 3 3 3 3Total Off's 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8
Total Working Days 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13
Hard Constraints1) Demand is met
2) Each nurse works at most one shift a day
3) Avoid any isolated days patterns of “off-on-off”.
4) Each nurse must have three days off after having three consecutive night
5) Each nurse works between 12 to 14 days per schedule.
6) Each nurse works not more than 6 consecutive days
7) Evening shift constitutes at least 25% of total workload
Soft Constraints1) Avoid working in an evening shift followed by a morning shift or a nightshift the next day
3) Each nurse has at least one day off in one weekend.
4) All nurses have the same amount of total workload
29Nurse Scheduling-IGP
Conclusion
Achievements
The developed model with various constraints and goals using the 0-1 goal programming technique gives the optimum solution that showed both the hard constraints and soft constraints are satisfied.
The pattern will be rotated among the nurses and each nurse will be working according to each schedule’s pattern. After completing 18 schedules, then each nurse will revisit the starting schedule.
Cyclical nurse scheduling rotates equally through the desirable and undesirable work stretches among the nurses and requires relatively less scheduling effort of the head nurse.
The schedule satisfies the factors of completeness and continuity. While the fairness factor is dealt with since the schedule’s pattern is going to rotate among the nurses.
All nurses will have the opportunity to work with the satisfactory and unsatisfactory schedule’s patterns.
With this cyclical scheduling, it gives nurses more control over their work life because they know the type of shift schedule in the future which should have a positive effect on their job satisfaction.
13.04.14
30Nurse Scheduling-IGP
The way forward
New schedule will only need to be produced when changes occur in its average daily staff requirements.
For further research, one of possible work is to embed the model into user friendly software that would be easy to use and reliable.
The model also should be extended to account for other important scheduling aspects such as requested day off in order to being acceptable to all parties.
Applications
Transportation Call centres Health care Emergency services Civic services and utilities Venue management Financial services Hospitality and tourism Manufacturing
13.04.14
Conclusion (continued..)
Nurse Scheduling-IGP 31
HEALTH CENTRE, IISc
13.04.14
PILOT STUDY- NURSE SCHEDULING
Photo courtesy: Ms. D. Choudhary
32Nurse Scheduling-IGP
Pilot Study at Health Centre IISc
13.04.14
Number of Nurses 11
Number of Days 14 (2 Weeks)
Number of Shifts: 3 (Morning, Day & Night)
Number of Decision Variables 11 X 14 X 4 (3 shifts+1 Off) = 616
Type of Decision Variables Binary (0-1)
Health Centre 11 nurses 3 Shifts
Morning ShiftAt least 5 nurses
Evening ShiftAt least 2
nurses
Night ShiftExactly 1 nurses
6:00 am-1:00pm
1:00pm-8:00pm
8:00pm-6:00am
33Nurse Scheduling-IGP 13.04.14
Constraints•Hard Constraints (Management)•Soft Constraints (Nurse Specific)
Hard Constraints
•Each unit is covered by 3 shifts for 24 hours a day and 7 days a week.•Minimum staff level requirement must be satisfied.•Each nurse works at most one shift a day.•Each nurse works not more than 6 consecutive days.• Each nurse can’t have more than 3 holidays fortnightly.
Soft Constraints
•Avoid working in Night shift followed by Morning shift or Evening shift of the next day.
•Each nurse has at least one day off in one weekend. (could not be met)
Problem Formulation-Constraints Description
Hard Constraints-Must be satisfied
Soft Constraint-May be violated
Goal Programmin
g
34Nurse Scheduling-IGP
Execution & Result
13.04.14
OVERALL SCHEDULE PROPOSED FOR HEALTH CENTRE, IISc
Nurses Total Nurses in Morning
Shift
Total Nurses in Evening
Shift
Total Nurses in
Night Shift
Total Nurses in all Shifts1 2 3 4 5 6 7 8 9 10 11
Days
1 E E M M M N M E M E E 5 5 1 11
2 E M E E M N M E E M M 5 5 1 11
3 M N M E OFF OFF OFF M M M E 5 2 1 8
4 M N OFF E M E M OFF OFF M M 5 2 1 8
5 M OFF E E M E E N M M M 5 4 1 10
6 OFF E M OFF E M M N M M OFF 5 2 1 8
7 OFF M M E OFF M E N M OFF M 5 2 1 8
8 M M OFF N E OFF M OFF M M E 5 2 1 8
9 E M M OFF M E OFF N OFF M M 5 2 1 8
10 M N M E M E M OFF M E OFF 5 3 1 9
11 N OFF M M E M E M E OFF M 5 3 1 9
12 N E M M OFF M OFF E M M M 6 2 1 9
13 OFF N E OFF M E M M E M M 5 3 1 9
14 M OFF OFF M M E M M OFF E N 5 2 1 8
Total Morning Shifts 6 4 8 4 8 4 8 4 8 9 8
Total Evening Shifts 3 3 3 6 3 6 3 3 3 3 3
Total Night Shifts 2 4 0 1 0 2 0 4 0 0 1
Total Off's 3 3 3 3 3 2 3 3 3 2 2
Total Working Days 11 11 11 11 11 12 11 11 11 12 12
Hard Constraints1) Demand is met
2) Each nurse works at most one shift a day
3) Each nurse works not more than 6 consecutive days
4) Each nurse can’t have more than 3 holidays fortnightly
Soft Constraints1) Avoid working in Night shift followed by Morning shift or Evening shift of the next day
35Nurse Scheduling-IGP 13.04.14
Websites www.lindo.com www.journal.itb.ac.id
Research Papers A Cyclic Nurse Schedule using Goal Programming By Ruzzakiah Jenal et.al. A Multiple Objective Nurse Scheduling Model By Arthur & Ravidran Scheduling Nurses Using Goal-Programming Techniques By Musa & Saxena Goal Programming Model Subsystem of A Flexible Nurse Scheduling Support System
By Ozkarahan & Bailey
Books An Introduction to Management Science By Anderson Sweeney Williams
Tools used Microsoft Encarta (Encyclopedia for offline references) Microsoft Excel (Data embedding) Industrial LINGO (Linear Integer Programming)
References
Nurse Scheduling-IGP 13.04.1436
Thank you!
They said it….
“There’s a fundamental distinction between strategy and operational effectiveness” (Michael Porter)
Leanings….
• Practical application of Operations Research• Optimization Software- LINGO and its limitations• Literature Review of Research Paper