The Dynamic Vehicle Routing Problem with A-priori Information

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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?

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)

• I.e. in the example from before - dod 1/(51)
  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
NN-FCFS-SQM
PART
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 (?) of each
  sub-region is known in advance.

• 0.1

• 0.2

• 0.25

• 0.5

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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
  ?-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.