ANT/OR. An Optimisation Model for Staff Planning in a Home Care Organisation

Transcription

1 University of Antwerp Operations Research Group ANT/OR An Optimisation Model for Staff Planning in a Home Care Organisation P.A. Maya Duque 1,2 M. Castro 1 P. Goos 1 K. Sörensen 1 1 Faculty of Applied Economics, Operations Research Group ANT/OR University of Antwerp 2 Faculty of Engineering, Universidad de Antioquia

2 Outline 1 Problem Description 2 Mathematical formulation 3 Solution strategy 4 Computational results 4.1 Service level optimization 4.2 Travelled distance optimization 4.3 A specific case: Region of Leuven 5 Conclusions 2/22

3 Outline 1 Problem Description 2 Mathematical formulation 3 Solution strategy 4 Computational results 4.1 Service level optimization 4.2 Travelled distance optimization 4.3 A specific case: Region of Leuven 5 Conclusions 3/22

4 Problem description 4/22

5 Problem Description Two objective functions Service level Total travelled distance Three decisions involved Allocating Scheduling Routing 5/22

6 Problem description 6/22

7 Outline 1 Problem Description 2 Mathematical formulation 3 Solution strategy 4 Computational results 4.1 Service level optimization 4.2 Travelled distance optimization 4.3 A specific case: Region of Leuven 5 Conclusions 7/22

8 Mathematical formulation Decision variable x ik { 1, patient i is served using the scheme k in S i 0, Otherwise 8/22

9 Mathematical formulation max f 1 = Service level (1) min f 2 = Total travelled distance (2) s.t. x ik = 1 i P (3) k S i a jt ik h ix ik 4 j C, t T (4) i P j k S i a jt ik h ix ik c jw j C, w = 1... W (5) t T w i P j k S i x ik {0, 1} i P, k S i (6) 9/22

10 Problem description 10/22

11 Problem description 11/22

12 Outline 1 Problem Description 2 Mathematical formulation 3 Solution strategy 4 Computational results 4.1 Service level optimization 4.2 Travelled distance optimization 4.3 A specific case: Region of Leuven 5 Conclusions 12/22

13 Solution strategy Easy to understand Flexible Objective hierarchy Initialisation Patient feasible schemes 1 Service level optimisation Set partitioning heuristic 2 Total distance optimisation Randomised local search 13/22

14 Outline 1 Problem Description 2 Mathematical formulation 3 Solution strategy 4 Computational results 4.1 Service level optimization 4.2 Travelled distance optimization 4.3 A specific case: Region of Leuven 5 Conclusions 14/22

15 Instances Region Code Number of Number of Required Available patients caregivers hours hours Kalmthout Zoersel Mechelen Leuven Lubbeek Herentals /22

16 Parameter tuning Notation α Number of schemes generated for each patient. β Number of most suitable caregivers. γ probability that the same assignment of caregivers. to time slots is repeated for all weeks. κ Number of iterations. A full factorial experiment with three levels per factor is used to tune the parameters All parameters have a significant impact both on the service level and on the computing time α is set to 2000, β is set to 3 and γ is set to 1 16/22

17 Service level optimization Region κ Total service Total Total time Computing level (%) suitab. (%) pref.(%) time (s) Kalmthout Zoersel Mechelen Leuven Lubbeek Herentals /22

18 Parameter tuning Notation η Length of the swap candidate list δ Maximum allowed decrease percentage of the service level. α Number of schemes generated for each patient. β Number of most suitable caregivers. λ Number of iterations. A full factorial experiment with three levels per factor is used to tune the parameters All parameters but η have a significant impact α is set to 2000, β is set to 5 and η is set to 3 18/22

19 Travelled distance optimization Region λ % decrease in the service level δ Kalmthout Zoersel Mechelen Leuven Lubbeek Herentals Average /22

20 Results for the region of Leuven Solution Iter. δ Service Patient-CG Time slot Distance (%) level (%) preference (%) preference (%) Improv. (%) Initial Dist. Improved /22

21 Outline 1 Problem Description 2 Mathematical formulation 3 Solution strategy 4 Computational results 4.1 Service level optimization 4.2 Travelled distance optimization 4.3 A specific case: Region of Leuven 5 Conclusions 21/22

22 We studied the home care planning problem faced by Landelijke Thuiszorg We propose a mathematical formulation and a solution strategy Our solution strategy is flexible, simple and easy to understand The results show that our approach has an excellent performance when it comes to optimising the service level Our approach reduces the total travelled distance while keeping the decrease in service acceptable This algorithm will constitute the core optimisation component of a DSS to be developed by the organisation 22/22