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INTERGER GOAL PROGRAMMING 13.04.14 Nurse Scheduling-IGP NURSE SCHEDULING Prepared by- Sowmiyan Morri Swapnil Soni DoMS, IISc Course- Applied Operations Research Instructor- Prof M Mathirajan 1

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- I N T E R G E R G O A L P R O G R A M M I N G 13.04.14Nurse Scheduling-IGP NURSE SCHEDULING Prepared by- Sowmiyan Morri Swapnil Soni DoMS, IISc Course- Applied Operations Research Instructor- Prof M Mathirajan 1
- 2 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 13.04.14Nurse Scheduling-IGP 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 Register Question on: Tedious Time Accuracy Fairness Mathematical Modeling Advantages 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
- 4 Literature Review 13.04.14Nurse Scheduling-IGP Authors Reference Literature Limitations Arthur & Ravindran Arthur, J. L., & Ravindran, A., A Multiple Objective Nurse Scheduling Model, 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-Programming Techniques, IIE Transactions, 16(3), pp. 216 221, 1984 Used a 0-1 goal programming that applied 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 A Flexible Nurse Scheduling Support System, IIE Transactions, 20(3), pp. 306-316, 1988. Nurse scheduling modelling showed the flexibility of goal programming in handling various goals which fulfilled the hospitals objectives and the nurses preferences. Small set of constraints
- 5 13.04.14Nurse Scheduling-IGP Authors Reference Literature Limitations Azaiez & Al Sharif Berrada, I., Ferland, J. A., & Michelon, P., A Multi-objective Approach to Nurse Scheduling with Both Hard and Soft Constraints, Socio- Economic Planning Sciences, 30(3), pp. 183- 193, 1996 Used the 0-1 goal programming approach with the considerations of hospitals 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 h Shift Nurses by Network Programming, European Journal of Operational Research, 104, pp. 582-592, 1998 Presented a mathematical model for cyclic and non-cyclic scheduling of 12 hours shift nurses. The model is quite flexible and can accommodate a variety of 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 Logic Programming, Lecture Notes on Computer Sciences 2079, pp. 159- 175, 2001 Use of work cycles with various constraints to produce timetables of up to 150 people Small set of constraints Literature Review
- 6 The Paper 13.04.14Nurse Scheduling-IGP Author From Ruzzakiah Jenal School 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
- 7 The Paper -Parameters 13.04.14Nurse Scheduling-IGP 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 Shift At least 4 nurses Evening Shift At least 4 nurses Night Shift Exactly 3 nurses 7:00 am-2:00pm 2:00pm-9:00pm 9:00pm-7:00am
- 8 13.04.14Nurse Scheduling-IGP Problem Statement Objective: 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 Constraint Meeting management objectives (B) Soft constraints Satisfaction of employees(Nurses), work/life balance Logical Constraints: (C) Cyclic Scheduling A 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
- 9 Problem Statement 13.04.14Nurse Scheduling-IGP Morning Shift ?=0,1 Nurse Demand 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Days 1 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 4 2 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 4 3 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 4 4 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 4 5 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 4 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 4 7 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 4 8 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 4 9 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 4 10 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 4 11 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 4 12 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 4 13 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 4 14 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 4 15 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 4 16 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 4 17 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 4 18 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 4 19 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 4 20 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 4 21 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 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
- 10 13.04.14Nurse Scheduling-IGP 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 Programming
- 11 Notations The 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 = 1n k = index for nurses, k = 1m Pi = staff requirement for morning shift of day i, i = 1n Ti = staff requirement for evening shift of day i, i = 1n Mi = staff requirement for night shift of day i, i = 1n 13.04.14Nurse Scheduling-IGP Problem Formulation- Notation & Decision Variables Decision Variables
- 12 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: 13.04.14Nurse Scheduling-IGP Problem Formulation-Constraints .n equations .n equations .n equations .n*m equations
- 13 Hard Constraints: Set 3: Avoid any isolated days patterns of off-on-off : 13.04.14Nurse Scheduling-IGP Problem Formulation-Constraints (continued..) .(n-2)*m equations Day1 Day2 Day3 Off On Off C1 X2/Y2/Z2 C3 Sum Unacceptable 1 1 1 3 Acceptable 0 0 0 0 0 0 1 1 0 1 0 1 0 1 1 2 1 0 0 1 1 0 1 2 1 1 0 2 Yes No
- 14 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: 13.04.1414Nurse Scheduling-IGP Problem Formulation-Constraints (continued..) .m equations
- 15 Hard Constraints: Set 5: Each nurse works between 12 to 14 days per schedule: 13.04.14Nurse Scheduling-IGP Problem Formulation-Constraints (continued..) .2*m equations For each Nurse total Sum of all working shift should lie between 12 & 14
- 16 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 13.04.14Nurse Scheduling-IGP 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+1 2 K K K+1 K+1 K+1 K+1 K+1 3 K K K K+1 K+1 K+1 K+1 4 K K K K K+1 K+1 K+1 5 K K K K K K+1 K+1 6 K K K K K K K+1 7 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
- 17 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 13.04.1417Nurse Scheduling-IGP 13.04.1417Nurse Scheduling-IGP 6 .(n-6)*m equations Problem Formulation-Constraints (continued..) .6*(m-1) equations .6 equations
- 18 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 13.04.14Nurse Scheduling-IGP Problem Formulation-Constraints (continued..) 0.25* .m equations 0.30* .m equations
- 19 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: : Positive Deviation : Negative Deviation Set 1: Avoid working in an evening shift followed by a morning shift or a night shift the next day: 13.04.14Nurse Scheduling-IGP Day1 Day2 Evening Morning/Night Y1 X2/Z2 Sum Unacceptable 1 1 2 Acceptable 0 0 0 0 1 1 1 0 1 Yes No Problem Formulation-Constraints (continued..)
- 20 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 13.04.14Nurse Scheduling-IGP 13.04.14Nurse Scheduling-IGP .(n-1)*m equations Problem Formulation-Constraints (continued..) .(m-1) equations .1 equation Goal-1: Minimize = = =
- 21 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 13.04.14Nurse Scheduling-IGP 13.04.14Nurse Scheduling-IGP .(n-1)*m equations Problem Formulation-Constraints (continued..) .(m-1) equations .1 equation Goal-2: Minimize = = =
- 22 Set 3: Each nurse has at least one weekend off: Sum of above heighted weekends >=1 (for each Nurse) 13.04.14Nurse Scheduling-IGP Problem Formulation-Constraints (continued..) Nurse 1 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 =
- 23 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 13.04.14Nurse Scheduling-IGP 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.
- 24 13.04.14Nurse Scheduling-IGP Problem Formulation-Objective Function: Preemptive Goal Programming for this model: Subject to: Hard constraints Soft constraints Binary Constraints Non-negativity constraints
- 25 Programming in LINGO 13.04.14Nurse Scheduling-IGP Defining Sets Import & Export of Data with Excel
- 26 Program Execution 13.04.14Nurse Scheduling-IGP
- 27 Time Line Analysis 13.04.14Nurse Scheduling-IGP 1 2 3 4 5 6 7 8 No of Nurses 5 6 7 8 9 10 11 12 Time to Solve (min) 16 19 81 134 212 901 1498 3980 0 500 1000 1500 2000 2500 3000 3500 4000 4500 Timetosolve(inMinutes) No. of Variables Vs Time to solve (for 21 Days) Exponential increase in time to solve the problem w.r.t. No. of Nurses
- 28 Result-Optimal Solution 13.04.14Nurse Scheduling-IGP 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 11 2 N OFF M OFF E E N OFF E E OFF OFF N OFF M M M OFF 4 4 3 11 3 N OFF M OFF E OFF N OFF OFF E M OFF N OFF E E M M 4 4 3 11 4 OFF E E E OFF N OFF M M OFF E N OFF M OFF OFF M N 4 4 3 11 5 OFF E E E M N OFF E M M OFF N OFF M OFF OFF OFF N 4 4 3 11 6 OFF E E OFF M N OFF E OFF M OFF N OFF M E OFF M N 4 4 3 11 7 E E OFF M N OFF OFF E M OFF N OFF M M E OFF N OFF 4 4 3 11 8 E E M M N OFF OFF OFF M OFF N OFF E E E M N OFF 4 5 3 12 9 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 11 11 E M OFF N OFF OFF E M E N OFF M OFF E M N OFF E 4 5 3 12 12 OFF M OFF N OFF M E M OFF N OFF M E E OFF N OFF E 4 4 3 11 13 OFF M N OFF M M OFF E N OFF M E E OFF N OFF OFF E 4 4 3 11 14 OFF M N OFF M E E E N OFF M OFF OFF M N OFF OFF E 4 4 3 11 15 E OFF N OFF OFF E E OFF N OFF M E M M N OFF M OFF 4 4 3 11 16 E N OFF E M OFF OFF N OFF M E E M N OFF M E OFF 4 5 3 12 17 OFF N OFF E M M OFF N OFF E OFF E OFF N OFF M E M 4 4 3 11 18 M N OFF OFF E M M N OFF E M OFF OFF N OFF E OFF E 4 4 3 11 19 N OFF OFF M OFF M N OFF M E E OFF N OFF M E E OFF 4 4 3 11 20 N OFF E M OFF OFF N OFF E OFF E M N OFF M OFF E M 4 4 3 11 21 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 4 Total 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 3 Total 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 Constraints 1) 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 Constraints 1) 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
- 29 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 schedules 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 schedules pattern is going to rotate among the nurses. All nurses will have the opportunity to work with the satisfactory and unsatisfactory schedules 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. 13.04.14Nurse Scheduling-IGP
- 30 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 13.04.14Nurse Scheduling-IGP Conclusion (continued..)
- HEALTH CENTRE, IIS c 13.04.14Nurse Scheduling-IGP PILOT STUDY- NURSE SCHEDULING 31 Photo courtesy: Ms. D. Choudhary
- 32 Pilot Study at Health Centre IISc 13.04.14Nurse Scheduling-IGP 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 Shift At least 5 nurses Evening Shift At least 2 nurses Night Shift Exactly 1 nurses 6:00 am-1:00pm 1:00pm-8:00pm 8:00pm-6:00am
- 33 13.04.14Nurse Scheduling-IGP 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 cant 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 Programming
- 34 Execution & Result 13.04.14Nurse Scheduling-IGP 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 Constraints 1) 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 cant have more than 3 holidays fortnightly Soft Constraints 1) Avoid working in Night shift followed by Morning shift or Evening shift of the next day
- 35 13.04.14Nurse Scheduling-IGP 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
- 13.04.14Nurse Scheduling-IGP 36 Thank you! They said it. Theres 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