Research interests Viviane Gascon Vietnam 2010

Nurse scheduling Viviane Gascon and Éric Gagné

Laboratoire interdisciplinaire de recherche et d’intervention dans les services de santé Nurse scheduling: home care nurses of a medical clinic Nurses are assigned to one of the sectors covered by the clinic. Nurses are assigned to one of the sectors covered by the clinic. Full time and part time nurses. Full time and part time nurses. Nurses work on weekends every 4 or 5 weeks. Nurses work on weekends every 4 or 5 weeks. Nurses are on duty every 7 weeks. Nurses are on duty every 7 weeks. Hard constraints : Hard constraints : Nurses work a number of days specified by their category (full time or part time). Nurses work a number of days specified by their category (full time or part time). A nurse must work in her assigned sector. A nurse must work in her assigned sector.

Laboratoire interdisciplinaire de recherche et d’intervention dans les services de santé Nurse scheduling: soft constraints The demand/surplus of nurses must be spread among the working days. The demand/surplus of nurses must be spread among the working days. At least one nurse must work in each sector for every working day of the week. At least one nurse must work in each sector for every working day of the week. The maximum number of consecutive working days must not exceed 5 days. The maximum number of consecutive working days must not exceed 5 days. The Holidays must be fairly spread among nurses. The Holidays must be fairly spread among nurses. Nurses’ requirements for days off and vacations should be satisfied. Nurses’ requirements for days off and vacations should be satisfied patterns must be avoided (no working day between two days off) patterns must be avoided (no working day between two days off).

Laboratoire interdisciplinaire de recherche et d’intervention dans les services de santé Nurse scheduling: objectives Minimize deviations for the six soft constraints Minimize deviations for the six soft constraints Maximize number of nurses working on Mondays and Fridays. Maximize number of nurses working on Mondays and Fridays. Goal programming problem

Laboratoire interdisciplinaire de recherche et d’intervention dans les services de santé Nurse scheduling: mathematical model Variables Variables

Laboratoire interdisciplinaire de recherche et d’intervention dans les services de santé Nurse scheduling: solving method Each aggregate objective function is given a priority. Each aggregate objective function is given a priority. Nurses on duty, on duty during a Holiday and nurses’ schedules from the previous planning period are known. Nurses on duty, on duty during a Holiday and nurses’ schedules from the previous planning period are known. An adapted Tabu search approach was used An adapted Tabu search approach was used

Routing home care nurses Bouazza Elbenani, Jacques Ferland and Viviane Gascon

Laboratoire interdisciplinaire de recherche et d’intervention dans les services de santé Routing home care nurses A public clinic plan visits to patients who need medical treatments at home; A public clinic plan visits to patients who need medical treatments at home; Each patient on the list must be visited on a given day; Each patient on the list must be visited on a given day; The territory covered by the clinic is divided into sectors; The territory covered by the clinic is divided into sectors; Each sector is assigned to some nurses; Each sector is assigned to some nurses; Each nurse is assigned to a sector. Each nurse is assigned to a sector. A nurse assigned to a specific sector can visit patients from another sector, if necessary; A nurse assigned to a specific sector can visit patients from another sector, if necessary; The clinic can use nurses from the recall list; The clinic can use nurses from the recall list; The problem considers constraints of the vehicle routing problem with time windows…. and more. The problem considers constraints of the vehicle routing problem with time windows…. and more.

Laboratoire interdisciplinaire de recherche et d’intervention dans les services de santé Routing home care nurses problem VRP problem with time windows and multiple vehicles? + Continuity of care by nurses If blood samples, return to the clinic earlier List of patients constantly evolving each patient is visited once by a nurse each nurse comes back to the clinic she left no subtour routes’ length is limited

Laboratoire interdisciplinaire de recherche et d’intervention dans les services de santé Home care nurses: specific constraints Continuity of care: Continuity of care: A patient should always be visited by the same nurse. This constraint is modeled by a penalty cost introduced in the objective function when a patient is not visited by his/her regular nurse. Blood sample constraints : Blood sample constraints : If a blood sample is taken before 10h00 the nurse must go back to the clinic before 10h00 to drop the blood sample; If a blood sample is taken between 10h00 and 11h00 the nurse must go back to the clinic before 11h00 to drop the blood sample.

Laboratoire interdisciplinaire de recherche et d’intervention dans les services de santé Home care nurses: objectives Main objective : minimize total distance Secondary objectives : minimize use of nurses from the recall list; minimize use of nurses from the recall list; penalize the visit of a patient by another nurse than his/her regular nurse; penalize the visit of a patient by another nurse than his/her regular nurse; penalize the visit of a patient by a nurse from another sector than his/her usual sector. penalize the visit of a patient by a nurse from another sector than his/her usual sector. minimize number of patients not visited minimize number of patients not visited Each nurse being assigned to a sector, a problem can be defined for each sector. The global problem takes into account the fact that a nurse can visit patients from another sector than hers.

Laboratoire interdisciplinaire de recherche et d’intervention dans les services de santé Home care nurses: solving method Tabu search approach Phase 1: Solve the sector problems Phase 2: Solve the global problem

Laboratoire interdisciplinaire de recherche et d’intervention dans les services de santé Analysis of a blood sample process Viviane Gascon, Mathilde Bélanger and Katie Hébert

Laboratoire interdisciplinaire de recherche et d’intervention dans les services de santé Problem overview  Hospital with no appointments for blood samples  Two types of patients  with priority (coumadin, hyperglycemia)  standards  High demand : average of 350 patients every day  High waiting time for patients  Technologists are unsatisfied with their work  Patients are unsatisfied with the service

Laboratoire interdisciplinaire de recherche et d’intervention dans les services de santé Patient’s trajectory

Laboratoire interdisciplinaire de recherche et d’intervention dans les services de santé ANALYSE DES DONNÉES ET RÉSULTATS Temps d’attente et de service moyen selon les jours de la semaine Sciences de la gestion CounterBlood CounterBlood 00:01:2900:03:0200:02:0500:03:20 PriorityStandards Average service times CounterBlood CounterBlood Min 00:00:0000:00:1600:00:0000:00:23 Max 00:17:0701:41:3602:06:4202:18:44 Ave. 00:02:3900:21:4300:38:4900:41:40 Waiting times PriorityStandards PriorityStandards Min 00:02:5400:04:07 Max 01:47:0104:04:15 Ave. 00:28:4301:26:34 Leading times

Laboratoire interdisciplinaire de recherche et d’intervention dans les services de santé Point d’équilibre Arrival of « coumadin »

Laboratoire interdisciplinaire de recherche et d’intervention dans les services de santé SIMULATION MODEL With simulation techniques we can model a process and propose scenarios.  Basic model : models the real process from data collected  Three scenarios : the objective is to reduce total waiting time and total leading time Distribution laws for service times

Laboratoire interdisciplinaire de recherche et d’intervention dans les services de santé BASIC SIMULATION MODEL Total mean leading time (min)PrioStd Observed time28,0785,75 Basic model28,4284,69 Difference1,25%-1,24%

Laboratoire interdisciplinaire de recherche et d’intervention dans les services de santé SCENARIOS  Scenario 1 : Modify technologists and clerks’ working schedules, all technologists must serve patients with priority, adjust arrival rate of patients  Scenario 2 : Scenario 1 plus reduce time between service for counters and for the blood samples themselves  Scenario 3 : Scenario 2 plus a higher reduction for the times between service, reduce the number of technologists by one and reduce the distance traveled by patients to go to the technologists’ room. Minutes% % Observed time2886 Scenario % % Scenario % % Scenario % % PrioStd Total mean leading time Results