Optimization of patient transport dispatching in hospitals

Optimization of patient transport dispatching in hospitals Cyrille Lefèvre and Sophie Marquet Supervisors: Yves Deville and Gildas Avoine

1500 minutes

Thesis motivation MedSoc NPO asked us to conduct a study project around the management of patient transports Investigation in operational research to assess new approaches Possibility of using a positioning system to improve the dispatching With their help, we visited 2 hospitals Sainte-Elisabeth in Namur The CHU of Mont-Godinne 1

Punctuality is essential for patient transports In Sainte-Elisabeth hospital ( 300 beds), there are more than 100 transports/day Late transports cause: Patient inconvenience Domino effect on the following transports Underutilization of valuable resources Impact the logistic costs and the patients satisfaction 2

Lack of efficiency in patient transports Spatial allocation of the stretcher-bearers Uneven workload Centralization and computerization Lateness 20 min for 10% of the transports (Ste Elisabeth, Namur) Centralization, computerization and optimization That s where we kick in! 3

Thesis outcomes Modeling Offline optimization Online optimization Possibility of indoor positioning Vehicle routing problem, with equipment management Pickup and delivery problem Local search Linear programming Local search Found to be inadequate In addition, Development of a prototype system Experiments for parameter evaluation Experiments to assess the quality of the offline/online approach Proposed and tested improved offline approach 4

Optimization of patient transport dispatching 1. Problem description 2. Offline problem 3. Online problem 4. Indoor positioning system 5. Conclusion 5

Transport dispatching problem Transport request 2.*+,#3)4$+() The requests arrive dynamically Transport to complete!"#$%&'"() *+%&#(,-.") /(".(,-."0 1.#".") Every request is assigned to a stretcher-bearer at some point 6

Transport request Patient ID Pickup location Patient s location Delivery location Patient s destination Required equipment Stretcher or wheelchair Desired arrival time At the delivery location Earliest pickup time Earliest arrival at the pickup location Priority Medical unit 7

Atransportisasequenceofmanysteps Temporal progress!"#$"%&' ' ' Spatial progress 8

Atransportisasequenceofmanysteps Temporal progress!"#$"%&' ' (%%)*+,"+&' ' Spatial progress -$./#%*0,.12,(* 3'0$4'+5*0,.12,(* 6#++'()*%,7$2,(*!"#$%&'()*+,,&* The bearer remains at his position after the transport 8

Atransportisasequenceofmanysteps Temporal progress!"#$"%&' -#$).,"+&' /)01$.' (%%)*+,"+&' ' Spatial progress -$./#%*0,.12,(* 3'0$4'+5*0,.12,(* 6#++'()*%,7$2,(*!"#$%&'()*+,,&* The bearer remains at his position after the transport 8

Atransportisasequenceofmanysteps Temporal progress!"#$"%&' -#$).,"+&' /)01$.' Should be after earliest pickup time (%%)*+,"+&' /23"+&' /)01$.' Spatial progress -$./#%*0,.12,(* 3'0$4'+5*0,.12,(* 6#++'()*%,7$2,(*!"#$%&'()*+,,&* The bearer remains at his position after the transport 8

Atransportisasequenceofmanysteps Temporal progress!"#$"%&' -#$).,"+&' /)01$.' /23"+&' 456.768' (%%)*+,"+&' /23"+&' /)01$.' If after desired arrival time, the transport is late Spatial progress -$./#%*0,.12,(* 3'0$4'+5*0,.12,(* 6#++'()*%,7$2,(*!"#$%&'()*+,,&* The bearer remains at his position after the transport 8

Atransportisasequenceofmanysteps Temporal progress!"#$"%&' -#$).,"+&' /)01$.' 4"%)5"9' 255):2;' /23"+&' 456.768' (%%)*+,"+&' /23"+&' /)01$.' Lateness Spatial progress -$./#%*0,.12,(* 3'0$4'+5*0,.12,(* 6#++'()*%,7$2,(*!"#$%&'()*+,,&* The bearer remains at his position after the transport 8

Atransportisasequenceofmanysteps Temporal progress!"#$"%&' -#$).,"+&' /)01$.' /23"+&' 456.768' (%%)*+,"+&' /23"+&' /)01$.' -#$).,"+&' 456.768' Spatial progress -$./#%*0,.12,(* 3'0$4'+5*0,.12,(* 6#++'()*%,7$2,(*!"#$%&'()*+,,&* The bearer remains at his position after the transport 8

Aschedulethatminimizesthelateness Data Transport requests Number of available stretcher-bearers Number of stretchers/wheelchairs in each equipment room at the beginning of the day Travel times between all locations of interest Solution For each bearer, sequence of transports Time at which to begin the transport Equipment room to use Objective Minimize the sum of the latenesses of the transports, weighted by their priorities 9

2stagestoapprehendtheproblemdynamics Offline problem: All data known before the work day /0-0&!"#$%&& '$("%)*"+&,$-."#& Transport dispatcher 1"%)*"+& Online problem: Progressive data disclosure 320+(4"2-&2$5)$(-& Medical unit!"#$%&& '$("%)*"+&,$-."#& /0-0& 1)22$+-&("%)*"+& Transport dispatcher 320+(4"2-&-"&$6$7)-$& Available stretcher-bearer 10

Open field of research Ongoing research on the dispatching problem Up to now, mostly in offline The equipment management has not been approached before Our focus goes to the online problem, including the equipment management 11

Graph with several types of nodes Transport 1 1 Depot 2 Destination 2 3 Origin 3 4 4 Equipment rooms 13

Asetofroutes,minimizing Transports lateness priority 1 1 2 Destination 2 1 1 3 3 2 2 4 4 Depot 1 3 Origin 3 Depot 1 4 4 1 1 2 2 3 3 4 4 Depot 2 Equipment rooms 1 1 2 2 3 3 4 4 Depot 2 14

Asetofroutes,minimizing Transports lateness priority May change from one solution to another 1 1 2 2 3 3 Depot 1 Origin Depot 1 4 4 1 1 2 Destination 2 3 3 4 4 Depot 2 1 1 2 2 3 3 4 4 Same in every possible solution Equipment rooms 1 1 2 2 3 3 4 4 Depot 2 14

Travel and waiting times 1 1 Possible wait 2 Destination 2 1 1 2 1 3 9 5 6 4 3 2 11 2 7 2 4 4 3 Depot 1 Origin 3 Depot 1 Possible wait 4 4 Equipment rooms 1 1 arrival! earliest pickup time 2 13 2 1 1 3 3 7 1 4 4 4 2 1 8 2 3 3 3 5 2 Travel time Depot 2 4 4 Depot 2 15

This problem is similar to a vehicle routing problem VRP Given Vehicles with fixed capacity Customer locations Depot Find one route for each vehicle, such that Each customer is served once Each route begins and ends at the depot The total distance is minimal NP-hard optimization problem! 16

Amount of equipment in each equipment room nbavail(e, ρ, τ) = equipment of type e in room ρ at the beginning of the day equipment of type e taken out of room ρ before time τ + equipment of type e brought back to room ρ before time τ Equipment constraint nbavail(e, ρ, τ) 0 Violations can occur only when a bearer leaves an equipment room 17

Selected approach: Local Search Start 2-#130* /'0,1'-* Iteration Restart? +,(("-.* /'0,1'-* Small changes!"#$%&'(%'')* Best Intensify? Best solution? Keep in memory Neighbor selection 18

Zoom on central elements of the local search Operators 3 possible operators 1 operator chosen at each iteration to generate the neighborhood Tabu search Some neighbors are tabu, they cannot be selected Avoid cycling over the same solutions Best improvement Best non-tabu neighbor selected at each iteration Except if a tabu neighbor is the best solution seen so far 19

Equipment management: complex implementation Comet system Powerful but not flexible User-defined invariant 3D array Amount of equipment of each type in every room at the start/end of each transport Braided AVL tree Order between the starts and ends of the transports 20

Experimentation on the offline prototype Calibration of the parameters Many local search parameters Program behavior Sensibility to the problem size Context Grid with 35 machines (Condor) Lack of real life data 21

Frozen transports The current time keeps evolving during the search Every transport that begins before the current time in the best solution found so far is frozen in the solution Cannot be moved in the solution Cannot change equipment room Frozen Depot Origin Destination Equipment room Past Future Time Current time 23

Rolling horizon Because of the highly dynamical nature of the problem, a time horizon is used to limit the number of transports manipulated by the local search over or currently executed (frozen in the solution) horizon not in the solution manipulated by the local search (not frozen in the solution) earliest pickup times time 24

Insertion of new transports Outer-fit Earliest-pickup time any other earliest pickup time Select the route with the smallest elapsed time (end of the last transport) Insert the transport at the end of the route Inner-fit Earliest-pickup time < at least one other Select the route with the smallest total lateness Insert the transport at the best possible position 25

Comparison of 3 different approaches Online 0 Earliest pickup times Time 26

Comparison of 3 different approaches Online 0 Earliest pickup times Time Offline with global disclosure 0 Earliest pickup times Time 26

Comparison of 3 different approaches Online 0 Earliest pickup times Time Offline with global disclosure 0 Earliest pickup times Time Offline with progressive disclosure 0 Earliest pickup times Time 26

The online approach works better than the offline one, even with progressive disclosure Online Progressive Offline Global Instances 1 331 411 483 2 233 319 371 3 336 < 395 < 485 4 435 536 680 5 502 589 659 Problems twice as hard as in Sainte-Elisabeth 27

Explanations for this difference 9 8 Iterations per second 7 6 5 4 3 2 1 Online Offline, global disclosure Offline, progressive disclosure Intern structures and invariants Neighborhoods 0 0 10 20 30 40 50 Added transports 28

Anewoffline approach, based on the online approach Offline All transports total run time n th transport "#$%#&!! Schedule over n transports Schedule over all transports The current time and the optimization time should be specified whenever a transport is added to the solution 29

The dispatching system can work without IPS Contributions of the IPS Estimation of the travel times (statistics) Alternatives Recording of the stretcher-bearers movements for a few weeks (statistics) Map of the hospital Detection of a gap between the travel times of a transport and the estimated travel times Temporary suboptimal dispatching 31

The dispatching system can work without IPS Contributions of the IPS Positioning of the stretcherbearers when they have no transport to execute Alternatives Temporary suboptimal dispatching Error detection in the equipment management Occasional verification of the amount of equipment per equipment room We find the ratio contributions/price too low 32

Possible extensions Possibility to leave the equipment with the patient between transports Breaks of the stretcher-bearers Reaction to other dynamic events Deleted or modified request Gap between the measured and predicted travel times 34

Conclusion Transport dispatching problem Optimization Central to everyday hospital life Highly dynamic, similar to a VRP (NP-hard) Even more difficult due to equipment management Offline and online models The prototype works well on large problems Very promising online approach Indoor positioning Few contributions compared with the cost 35

11 minutes