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The Dynamic Vehicle Routing Problem with A-priori Information

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. Outline. The Dynamic Traveling Repairman Problem (DTRP). Simulation of the Partially DTRP (PDTRP).

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The Dynamic Vehicle Routing Problem with A-priori Information

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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.

  2. 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.

  3. 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.

  4. 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.

  5. 9:34 A simple example • A single vehicle serves 5 advance request customers and…? Depot

  6. 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.

  7. 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.

  8. 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.

  9. 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?

  10. 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.

  11. 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?

  12. Measuring the dynamism • The degree of dynamism (dod) measure (Lund et. al 1996): • I.e. in the example from before - dod = 1/(5+1) = 16 %

  13. 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.

  14. Simulation results - PDTRP FCFS -SQM FCFS NN-FCFS-SQM PART Nearest Neighbor

  15. 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. A-priori DTSPTW (1) • =0.1 • =0.2 • =0.25 • =0.5

  16. 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. A-priori DTSPTW (2) The objective is to minimize a weighted sum of the distance and the lateness.

  17. 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.

  18. A-priori DTSPTW (4)

  19. A-priori DTSPTW (5)

  20. 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.

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