Advanced Optimisation with Python
• Set Covering Problems
• Integer Programming Formulation • PuLP Modelling & Solution
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Nursing Roster – Question 1
Determine the minimum number of nurses required to cover all the requirements, knowing that a nurse works eight hours per day and that she is entitled to a break of two hours after she has worked for four hours.
Nursing Roster – Question 1
• There are 12 shifts each 24-hour day
• Each nurse works two consecutive shifts then has a break for one shift followed by another two shifts. For example, a nurse starting with shift 1 would work shifts 1, 2, break for 3 and then work for shifts 4 and 5.
• Following on the above, at any shift we will only have the nurses who started their shifts in that shift, the previous shift, and 3 and 4 shifts earlier, hence we can define a set WORK as {0, -1, -3, -4}.
• Every 24 hours we start again with shift 1. So shift 1 follows shift 12. For example, a nurse starting with shift 10 will work 10, 11, break for 12, work 1, and 2. We will need to use mod (%) function to find the right shifts to consider.
Nursing Roster – Question 1
startt : Number of nurses starting work in time period t
Nursing Roster – Question 2
The service only has 80 nurses, which is not sufficient with the given requirements. Nurses can work two additional hours per day as overtime. These two additional hours follow immediately after the last four hours, without any break. Determine the schedule of the nurses in this service that minimizes the number of nurses working overtime.
Nursing Roster – Question 2
overtt : Number of nurses starting work in time period t and working overtime
CCTV surveillance
What is the minimum number of cameras that have to be installed to survey all the streets of this zone and where should they be placed?
CCTV surveillance
placen : 1 if a camera is located at location n
streets = {
(1,2), (1,3),
(2,39), (2,41),
(3,4), (3,11), (3,12), (3,16), (4,5), (4,6), (4,9), (6,7), (6,8),
(12,13), (12,15), (13,14),
(14,15), (14,18), (15,16), (15,19), …
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