1 The Dynamic Vehicle Routing Problem with A-priori Information ROUTE2000 Thursday August 17th 2000...
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1
The Dynamic Vehicle Routing Problem
with A-priori Information ROUTE2000
Thursday August 17th 2000
Allan Larsen
The Department of Mathematical Modelling,
The Technical University of Denmark.
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Outline
• The Dynamic Traveling Repairman Problem (DTRP).
• Simulation of the Partially DTRP (PDTRP).
• Using a-priori information in a Dynamic Traveling Salesman Problem with Time Windows (ADTSPTW).
• Closing comments.
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Real-life routing issues
• The traditional VRP does not consider:
– Customers calling in requesting service during the day of operation.
– Time-dependent travel times.
– Varying customer demands and on-site service times.
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Static Contra Dynamic Vehicle Routing
• Static Vehicle Routing:
– All informations relevant to the planning of the routes are known to the planner before the routing process begins.
– Informations relevant to the routing do not change after the routes have been constructed.
• Dynamic Vehicle Routing:– Not all informations relevant to the planning of the routes are known by the planner when the routing process begins.– Informations can change after the initial routes have been
constructed.
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A simple example
• A single vehicle serves 5 advance request customers and…?
9:34
Depot
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Dynamic vehicle dispatching problems
• Serves one customer at the time.
• Examples:
– Emergency services (police, fire and ambulance services).
– Taxi cab services.
• Low response time are important - i.e. minimize the waiting time.
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Dynamic Vehicle Routing Problems
• Services a pool of customers.
• Queueing often occurs.
• Examples:
– Pick-up and delivery of long-distance courier mail (UPS, FedEx, DHL etc.)
– Distribution of heating oil to private households.
– Transportation of elderly and handicapped people.
• Keeping routing costs low is important - i.e. minimize the route length.
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Traditional solution approaches
• Re-optimization - i.e. solve a static VRP each time new information is received.
• Try to find a feasible spot in the routes to insert the new request.
– Defer the inclusion of the new request until the latest possible moment in time.
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Research issues
• How does the level of dynamism influence the performance of the solution methods?
• Is it possible to increase the performance of the solution methods if we obtain a-priori information on future requests?
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The Dynamic Traveling Repairman Problem
• Introduced by Bertsimas & Van Ryzin (1989).
– All requests are dynamic and generated according to a Poisson process.
– The requests are independently and uniformly distributed over a quadratic service region.
– The repairman travels at constant speed.
– Find routing policies so that the expected system time (waiting time + service time) is minimized.
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The Partially Dynamic Traveling Repairman Problem
• Modification of the DTRP
– We assume a subset of the requests are known in advance.
– The travel costs are minimized.
• Issues addressed:
– What is the relations between system performance and the level of dynamism?
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Measuring the dynamism
• The degree of dynamism (dod) measure (Lund et. al 1996):
requestsofnumbertotalrequestsimmediateofnumber
dod • I.e. in the example from before - dod = 1/(5+1) = 16 %
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Simulation of the PDTRP
• The requests are dispersed over a 10 x 10 km service region.
• The vehicle travels at 40 km/h.
• Generated 100 instances of problems with {0, 5, 10, …, 100} % dynamism each with an average of 40 customers.
• On-site service times were generated using a log-normal distribution (average of 3 min. & variance of 5 min.)
• All results are average values of these 100 instances.
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Simulation results - PDTRP
FCFS -SQM
FCFS
PARTNN-FCFS-SQM
Nearest Neighbor
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A-priori DTSPTW (1)
• Motivated by the pick-up and delivery of long-distance courier mail.
– Modelled as a Dynamic Traveling Salesman Problem with Time Windows.
• The service area is divided into a number subregions.
• We assume that the arrival intensity (λ) of each sub-region is known in advance.
λ=0.1 λ=0.2
λ=0.5 λ=0.25
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A-priori DTSPTW (2)
• We assume that a set of idle points, IP, is given.
– Each idle point serves as a “resting location” for the vehicle to go to when it is idle.
The objective is to minimize a weighted sum of the distance and the lateness.
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A-priori DTSPTW (3)
• Propose three simple repositioning policies:
– NEAREST-IP: Go to the closest IP.
– BUSIEST-IP: Go to the IP with the highest λ-value.
– HI-REQ: Go to the IP with the highest expected number of requests.
• A threshold parameter is chosen in order to avoid unnecessary traveling.
• Performed extensive simulation with various levels of dynamism and temporal characteristics.
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A-priori DTSPTW (4)
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A-priori DTSPTW (5)
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Closing comments
• Findings:
– Linear relationship between the degree of dynamism and the route costs for PDTRP.
– Modest performance improvements were achieved for a-priori information based repositioning policies.
• Further research:
– Multiple vehicles.
– Diversion.