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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 a

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