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Agenda

A Real-life Application of a Multi Depot Heterogeneous Dial-a-Ride Problem for Patient Transportation in Austria Patrick Hirsch and Marco Oberscheider Institute of Production and Logistics University of Natural Resources and Life Sciences, Vienna IN3-HAROSA Workshop. Agenda. Introduction

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Agenda

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  1. A Real-life Application of a Multi Depot Heterogeneous Dial-a-Ride Problem for Patient Transportation in AustriaPatrick Hirsch and Marco OberscheiderInstitute of Production and LogisticsUniversity of Natural Resources and Life Sciences, ViennaIN3-HAROSA Workshop

  2. Agenda • Introduction • Problem Description • Method • Numerical Studies • Conclusion and Outlook

  3. Introduction • Projects for Home-Health Care • Public and Private Transport • Rural and Urban Areas • Daily and Weekly Scheduling • Synchronized Tasks / Precedence Constraints • Assignment Constraints (qualification, language,…) • Time-dependent Travel Times (public transport) • Scenarios with Natural Hazards • Austrian Red Cross as Project-partner → Rich Vehicle Routing Problem (VRP)

  4. Problem Overview • Optimization of Patient Transportation – No Emergency Services • Austrian Red Cross • Ex-Post Analysis • Dial-A-Ride Problem • Multiple Depots • Pick-up and Delivery Locations • Heterogeneous Car Fleet • Aim  get a schedule for a single day • Implementation: Set Partitioning Problem  Initial Solution Heuristic Tabu Search Metaheuristic P3 P1 D2 D1 B4 P2 P4 P6 D3 D4 B1 P7 P5 B B2 B3 D P D6 D7 P8 D5

  5. Problem Overview – Vehicles • Auxiliary Ambulance • „Casual“ car • Transport of mobile patients • One paramedic • Patient Transport Ambulance • Special car - equipment • Stretcher, patient seat and wheelchair place • Two paramedics

  6. Problem Overview - Model Objective: Minimize the operation time (= handling and driving time) of the used vehicles Constraints: • Each request has to be served • Time windows at pick-up and delivery locations • Maximum ride times • Given shifts and mandatory breaks • The order to return to the home-depot if idle • Capacities of the vehicles • Exclusive use: e.g. radiation therapy or mental-health problems • Auxiliary ambulance: Up to three mobile patients • Patient transport ambulance: Two patients allowed – only one stretcher available

  7. Problem Overview – Possible Solution P3 P1 D2 D1 P2 P4 P6 D3 D4 B1 P7 P5 B2 D6 D7 D5 P8

  8. Method

  9. Method Example 1-2-2-1 → 50 Minutes 1-2-1-2 → 45 Minutes 1-1 → 25 Minutes 2-2 → 30 Minutes 3-3 → 15 Minutes 3-2-3-2 → 55 Minutes 1-2-2-3-1-3 → 90 Minutes …

  10. Method Example 1-2-2-1 → 50 Minutes 1-2-1-2 → 45 Minutes 1-1 → 25 Minutes 2-2 → 30 Minutes 3-3 → 15 Minutes 3-2-3-2 → 55 Minutes 1-2-2-3-1-3 → 90 Minutes …

  11. Method Example 1-2-1-2 → 45 Minutes 1-1 → 25 Minutes 2-2 → 30 Minutes 3-3 → 15 Minutes 3-2-3-2 → 55 Minutes 1-2-2-3-1-3 → 90 Minutes …

  12. Method Example 1-2-1-2 → 45 Minutes 3-3 → 15 Minutes

  13. Tabu Search Algorithm based on the Unified Tabu Search method from Cordeau et al. (2001) task moves with local reoptimization – insert the task at the cost-optimal position in the new tour fixed tabu durations – depending on the number of tasks and vehicles aspiration criteria – attribute related intermediate infeasible solutions penalization of worsening candidate solutions by adding costs which are dependent on how often an attribute was used in a solution  diversification strategy “Standard” Tabu Search (TS) implies the whole neighborhood of a solution time-consuming and not suitable for large problem instances Method Metaheuristic Solution Approach (1)

  14. Tabu Search with Alternating Strategy Static (TSAS-stat) (Gronalt and Hirsch, 2007) motivated by “Granular Tabu Search” (Toth and Vigo (2003)) concentrates on “bad” connections in current solutions sort the links according to their duration in a descending order select a predefined number of links starting from the one with the longest duration only these links are chosen to be removed in neighbor solutions – other links can only be modified if a task from a removed link is inserted after a certain number of iteration steps with a limited neighborhood an iteration step with full neighborhood search is set Tabu Search with Alternating Strategy Dynamic (TSAS-dyn) (Hirsch, 2011) if there is no improvement in the solution quality for a predefined number of iteration steps → change the neighborhood structure automatically an iteration step with full neighborhood search is set after a predefined number of iteration steps MethodMetaheuristic Solution Approach (2)

  15. Numerical Studies – Parameters (1) • Real-Life Data - Three Scenarios (days) • 24 Hours • Eight Hour Shifts • 30 minutes time windows • Allowed maximum ride time depends on shortest path • SP < 10 min → 10 min • 10 min ≤ SP ≥ 30 min → 100 % • SP > 30 min → 30 min • 10 % exclusive transports

  16. Numerical Studies – Parameters (2) • Manipulation time depends on • vehicle type • mobility of patient (stretcher, wheelchair or mobile) • hospital/ward • two patients having the same pick-up or delivery location (parallelization possible?) • Manipulation times are based on statistical analysis of > 80,000 patient transports • Driving speed of vehicles:

  17. Numerical Studies – Map (1)

  18. Numerical Studies – Map (2)

  19. Numerical Studies – Initial Solution (1) • Small dataset (221 patient transports) tested yet • With given parameters the used routing would not be feasible • Shifts → manually altered • Combinations (TW, MRT) • Comparison only possible to a certain degree • Initial solution heuristic uses two versions to determine the best vehicle for the next task: • Vehicles have to return to their base if idle • G…total driving time = dt(depot,pick-up) • D…total driving time = dt(delivery,depot) + dt(depot,pick-up) • Example: • If G → Red vehicle will perform 3 • If D → Green vehicle will perform 3 1 2 10 min 15 min 20 min 3

  20. Numerical Studies – Initial Solution (2) NE…No exclusive transports 40…Time windows of 40 minutes +5….Extension of maximum ride times of 5 minutes

  21. Conclusions and the Way Forward • Combinations as input for Set Partitioning Problem • Formation of Tasks • Manipulation times are dependent on the transported patients • Feasible combinations are strongly dependent on • Length of Time Window • Maximum Ride Time • Short computation time to get a feasible result with initial solution heuristic (~ 1 second) • TS and TSAS (static and dynamic) • implementation  work in process • the two different initial solution heuristics indicate the potential for improvement heuristics

  22. Thank you for your attention!

  23. References • Cordeau J.-F., Laporte G., Mercier A., 2001. A unified tabu search heuristic for vehicle routing problems with time windows. Journal of the Operational Research Society 52, 928-936. • Gronalt M., Hirsch P., 2007. Log-Truck scheduling with a tabu search strategy. In: Doerner, K.F., Gendreau, M., Greistorfer, P., Gutjahr, W.J., Hartl, R.F., Reimann, M. (Eds.), Metaheuristics - Progress in Complex Systems Optimization, 65-88; Springer, New York. • Hirsch P., 2011. Minimizing empty truck loads in round timber transport with tabu search strategies. International Journal of Information Systems and Supply Chain Management 4(2), 15-41. • Toth P., Vigo D., 2003. The Granular Tabu Search and Its Application to the Vehicle Routing Problem. INFORMS Journal on Computing 15(4), 333-346.

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