By Dr Simon Martin, Dr Djamila Ouelhadj,

1. Cooperative search for fair nurse rosters By Dr Simon Martin, Dr Djamila Ouelhadj, Logistics and Management Mathematics Group, Department of Mathematics University of Portsmouth Lion Gate Portsmouth PO1 3HE England +44 (0) 23 9284 6393 simon.martin@port.ac.uk

2. The Partners • Dr Simon Martin LMMG University of Portsmouth • Dr Djamila Ouelhadj LMMG University of Portsmouth • Dr Ender Özcan ASAP University Nottingham • Dr Greet Vanden Berghe KaHO University of Leuven • Pieter Smet KaHO University of Leuven

3. The Aims of this project • To use our agent based framework to solve the Nurse Rostering Problem • To research different models of fairness • To show that cooperation produces fairer results than a stand alone equivalent

4. The Nurse Rostering problem The Scheduling of hospital personnel is Particularly challenging because: • There are different staffing needs on different days and shifts • Staff work in shifts • Healthcare institutions work around the clock • The need for day and night shifts • The correct staff mix for each ward • Many different employment contracts • Part-time • Special arrangements • Fairness so that staff are happy

5. Its hard, NP- HARD! • Until recently this was all done by hand by a senior nurse and it took a significant amount of time each week! • Recently computer systems have been built to help solve this problem. However the problem is not always solvable in a sensible time-scale • This is known as NP-Hard. To tackle these issues we use techniques called heuristics

6. The Current Platform Launcher Agent Problem definition Cooperating Agent Cooperating Agent Cooperating Agent Cooperating Agent The Launcher Agent (LA) sends the same problem to each agent

7. The Current Platform Launcher Agent Cooperating Agent Cooperating Agent Cooperating Agent Agents cooperate by passing Best heuristics/edges

8. The Current Platform Launcher Agent Problem definition Cooperating Agent Cooperating Agent Cooperating Agent Cooperating Agent Each agent sends its best overall solution to the launcher agent. The LA takes the best And writes it to file

9. Models of Fairness The standard objective function MinWS = minimise the sum of the sum of all nurses violations New Fairness objective functions MinMax = minimise the number of nurses × worst nurse violation MinDev = minimise the sum of deviations from the average + the numbers of nurses × the mean roster quality MinError = minimise the sum of the differences of max roster value – min roster value a + the mean roster quality MinSS = minimise the sum of the squared violations associated with assigning a nurse to a given roster

10. Measuring Fairness Measuring fairness is done with the Jains Fairness function (Jain et al., 1984; Muhlenthaler and Wanka, 2012) It is the sum of the squared violations in assigning a nurse to a given roster divided by the number of nurses times the squared value of assigning a nurse to a roster Its values range from the worse case 1/N to 1 where N is the number of nurses to 1 where the roster is completely fair

11. Results

12. Conclusions • We applied our platform to produce fair and optimal nurse employment schedules. • We have developed a number of fairness models and fairness measures • We have shown that cooperation produces fairness rosters than stand alone equivalents

13. Papers Martin, S, Ouelhadj, D, Smet, P, Vanden Berghe, G, Özcan, E.,(2013) Cooperative search for fair nurse rosters. Expert Systems with Applications Smet, P, Vanden Berghe, G, Martin, S, Ouelhadj, D, Özcan, E., (2012) Fairness in nurse rostering. Annals of Operational Research