In a nurse rostering problem, there are 15 nurses that must be scheduled for the next 30 days in ane of the units of the hospital. The following Table implies some information on the characteristics of these nurses:
able[[ able[[Nurse],[Number]],Gender,Age, able[[Skill level],[(10 for the best, 1 for the worst)]], able[[Experience],[(in years)]], able[[Managerial],[background],[(Yes, or No)]]],[1,Female,24,1,2,No],[2,Female,45,1,10,Yes],[3,Male,28,4,1,No],[4,Male,67,4,23,Yes],[5,Female,34,2,13,Yes],[6,Female,64,8,20,No],[7,Male,35,2,5,No],[8,Male,63,5,23,No],[9,Female,25,6,1,No],[10,Male,34,7,9,No],[11,Male,37,1,15,No],[12,Male,55,9,15,Yes],[13,Female,55,7,20,No],[14,Female,67,3,2,Nos],[15,Female,23,9,,]]
In this Table, the first column shows the index of nurses. The second and third column show the gender and the age of nurses. The fourth column shows the how proficient the nurses are. Higher skill levels show that nurses are more skilled compared to others. The fifth column shows the number of years that the nurse has worked in this hospital. Finally, the last column shows whether or not the nurse has ever managed other nurses as the nurse manager for a reasonable amount of time in the past.
(6)/(9)
An operations research analyst has already formulated a nurse rostering problem for these nurses using the nurse scheduling model presented in Lecture 3. However, after showing the results to the nurse manager, she has asked to address some other details that are explained in the rest of this question. To formulate the requested constraints, you are supposed to use the following decision variable:
Decision variables
x_(red )=1 if nurse n has shift s on day d;0 otherwise.
All of the following situations must be formulated as hard constraints.
Part a) On each day, in each shift, at most two of the nurses working in the shift must have managerial background. Write a constraint to formulate this assumption. (3 points)
Part b) Nurses $4 and $6 have family problems and therefore do not like to work together in the same shift on any day. Write a constraint to formulate this assumption. (3 points)
Part c) To respect the diversity in the hospital, on each day, in each shift, the number of male nurses cannot be more than 2 persans less than the number of female nurses. Write a constraint to formulate this situation. (3 points)
Part d) The 15th day in the rostering horizon coincides with a long holiday that people will have more outdoor activity and as a result more emergency cases will arrive in the hospital. Therefore, in the morning shift of this day, at least 2 nurses with skill levels of 4 or better must be working in the hospital. Write a constraint to formulate this assumption. (3 points)
Part e) On each day, the average skil level of nurses working in different shifts must be at least 5.5 or higher.
Write a constraint to formulate this assumption. (3 points)
Part f) To maintain a high quality of care for patients, on each day, in each shift, the number of nurses with at least 12 years work experience in this hospital must be cannot be less than 6 persons. Write a constraint to formulate this assumption. (3 points)
In a nurse rostering problem, there are 15 nurses that must be scheduled for the next 30 days in one of the units of the hospital. The following Table implies some information on the characteristics of these nurses:
Nurse Gender Number
Age
Skill level Experience (10 for the best, 1 for the worst) (in years)
background (Yes, or No) No Yes No Yes Yes No No No No No No Yes No Yes No
1
Female 24 Female 45 Male 28 Male 9 Female 34 Female 64 Male 35 Male 63 Female 25 Male 34 Male 37 Male 55 Female Ss Female 67 Female 23
1 1
2 10
2 3 4
23 13 20 5 23 1 5 9 15 15 20 2
5 6
2 8 2 5 6
7 8
9 10 11 12 13 14 15
1 9 7
9
In this Table, the first column shows the index of nurses. The second and third column show the gender and the age of nurses. The fourth column shows the how proficient the nurses are. Higher skill levels show that nurses are more skilled compared to others. The fifth column shows the number of years that the nurse has worked in this hospital. Finally, the last column shows whether or not the nurse has ever managed other nurses as the nurse manager tor a reasonable amount of time in the past.
6/9
nurse scheduling model presented in Lecture 3. However, after showing the results to the nurse manager, she has asked to address some other details that are explained in the rest of this question. To formulate the requested constraints, you are supposed to use the following decision variable: Decision variables Xnsd = 1 if nurse n has shift s on day d; 0 otherwise. All of the following situations must be formulated as hard constraints.
Part a) On each day, in each shift, at most two of the nurses working in the shift must have managerial background. Write a constraint to formulate this assumption. (3 points) Part b) Nurses #4 and a6 have family problems and therefore do not like to work together in the same shift
Part c) To respect the diversity in the hospital, on each day, in each shift, the number of male nurses cannot be more than 2 persons less than the number of female nurses. Write a constraint to formulate this situation. (3 points)
outdoor activity and as a result more emergency cases will arrive in the hospital. Therefore, in the morning shift of this day, at least 2 nurses with skill levels of 4 or better must be working in the hospital. Write a constraint to formulate this assumption. (3 points) Part e) On each day, the average skill level of nurses working in different shifts must be at least 5.5 or higher. Write a constraint to formulate this assumption. (3 points) Part f) To maintain a high quality of care for patients, on each day, in each shift, the number of nurses with at least 12 years work experience in this hospital must be cannot be less than 6 persons. Write a constraint to formulate this assumption. (3 points)