Institute of Production and Logistics – University of Natural Resources and Life Sciences, Vienna 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

Institute of Production and Logistics – University of Natural Resources and Life Sciences, Vienna Agenda  Introduction  Problem Description  Method  Numerical Studies  Conclusion and Outlook

Institute of Production and Logistics – University of Natural Resources and Life Sciences, Vienna 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)

Institute of Production and Logistics – University of Natural Resources and Life Sciences, Vienna 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 P2 P P1 D1 P3 D2 P5 P4 D5 P8 D6 D7 P6 P7 D4 D3 D B B2 B3 B1 B4

Institute of Production and Logistics – University of Natural Resources and Life Sciences, Vienna 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

Institute of Production and Logistics – University of Natural Resources and Life Sciences, Vienna 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

Institute of Production and Logistics – University of Natural Resources and Life Sciences, Vienna Problem Overview – Possible Solution B2 B1 P2 P1 D1 P3 D2 P6 P7 D4 D3 P8 D6 D7 P5 P4 D5

Institute of Production and Logistics – University of Natural Resources and Life Sciences, Vienna Method

Institute of Production and Logistics – University of Natural Resources and Life Sciences, Vienna Method Example → 50 Minutes → 45 Minutes 1-1 → 25 Minutes 2-2 → 30 Minutes 3-3 → 15 Minutes → 55 Minutes → 90 Minutes …

Institute of Production and Logistics – University of Natural Resources and Life Sciences, Vienna Method Example → 50 Minutes → 45 Minutes 1-1 → 25 Minutes 2-2 → 30 Minutes 3-3 → 15 Minutes → 55 Minutes → 90 Minutes …

Institute of Production and Logistics – University of Natural Resources and Life Sciences, Vienna Method Example → 45 Minutes 1-1 → 25 Minutes 2-2 → 30 Minutes 3-3 → 15 Minutes → 55 Minutes → 90 Minutes …

Institute of Production and Logistics – University of Natural Resources and Life Sciences, Vienna Method Example → 45 Minutes 3-3 → 15 Minutes

Institute of Production and Logistics – University of Natural Resources and Life Sciences, Vienna Method Metaheuristic Solution Approach (1)  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

Institute of Production and Logistics – University of Natural Resources and Life Sciences, Vienna Method Metaheuristic Solution Approach (2)  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

Institute of Production and Logistics – University of Natural Resources and Life Sciences, Vienna 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 Scenario# Patient Transports# Vehicles# Depots Maximum Medium Minimum

Institute of Production and Logistics – University of Natural Resources and Life Sciences, Vienna 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: Interstate highways Limited access highways Other highways Arterial roads Other streets 100 km/h85 km/h60 km/h45 km/h30 km/h

Institute of Production and Logistics – University of Natural Resources and Life Sciences, Vienna Numerical Studies – Map (1)

Institute of Production and Logistics – University of Natural Resources and Life Sciences, Vienna Numerical Studies – Map (2)

Institute of Production and Logistics – University of Natural Resources and Life Sciences, Vienna 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 min 10 min 20 min

Institute of Production and Logistics – University of Natural Resources and Life Sciences, Vienna Numerical Studies – Initial Solution (2) NE…No exclusive transports 40…Time windows of 40 minutes +5….Extension of maximum ride times of 5 minutes Version# VehiclesTotal Driving time [min.] Empty Driving time [min.] Working time [min.] Waiting time [min.] Real598,7804,02111,02317,837 V_G529,0653,94511,38217,478 V_D579,2033,83111,19817,662 V_G_NE508,7923,78911,11017,750 V_D_NE579,2143,68810,89017,970 V_G_NE_40468,3713,45310,51018,350 V_D_NE_40558,6303,45810,52518,335 V_G_NE_+5488,3483,34510,39918,461 V_D_NE_+5568,2343,21110,23718,623 V_G_+5508,6303,81111,06717,793 V_D_+5568,6493,48910,69118,169

Institute of Production and Logistics – University of Natural Resources and Life Sciences, Vienna 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

Institute of Production and Logistics – University of Natural Resources and Life Sciences, Vienna Thank you for your attention!

Institute of Production and Logistics – University of Natural Resources and Life Sciences, Vienna References  Cordeau J.-F., Laporte G., Mercier A., A unified tabu search heuristic for vehicle routing problems with time windows. Journal of the Operational Research Society 52,  Gronalt M., Hirsch P., 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., Minimizing empty truck loads in round timber transport with tabu search strategies. International Journal of Information Systems and Supply Chain Management 4(2),  Toth P., Vigo D., The Granular Tabu Search and Its Application to the Vehicle Routing Problem. INFORMS Journal on Computing 15(4),