Vehicle Routing & Scheduling: Developments & Applications in Urban Distribution

Assoc. Prof. Russell G. Thompson

Department of Infrastructure Engineeringrgthom@unimelb.edu.au

IIT Bombay 10th April 2014

Outline

Vehicle Routing and SchedulingCollaborative Freight SystemsB2CPerformance Based StandardsOngoing ResearchReferences

Vehicle Routing & Scheduling

Vehicle Routing Problem with Time Windows (VRPTW)

• Decision variables– schedules (trucks to customers)– routes (customer visiting order)

• Objective function: min. operating costs– Travel costs (time & distance)– Penalties (time windows)

• Constraints– Vehicle capacities– Customer time windows

Time windows and penalties

PenaltyCost ($)

i

e iArrivalTim e

i

l i

1

1

3rd Customer

2nd Customer

1st Customer

a1,(1,1)

Distance

Time

e(1,1)

w 1,(1,2)

t(1,0), (1,1)

s1,(1,1)

(1,0)Depot

(1,3)

ServiceTime

y1,(1,3)

WaitingTime

Delay Time

Travel Time

(1,2)

(1,1)

Depot

(1,0) e(1,2) e(1,3)l(1,1) l(1,2)l(1,3)a1,(1,2) a1,(1,3) a1,(1,0)L

d1,(1,1) d1,(1,2) d1,(1,3)

Metaheuristics

• Simulated Annealing (SA)

• Tabu Search (TS)

• Genetic Algorithms (GA)

have been successfully applied to VRPTW…

Tabu Search

• An intelligent problem solving technique based on flexible memory

• Neighbourhoods examined for new solutions some moves are tabu or forbidden

• Need to:– Define search history– Determine how to generate neighbourhood

solutions

Definitions

• A neighbourhood– set of solutions formed from current

solution using a simple operation

• Tabu list– set of moves that are not allowed to avoid

repetition

General Procedure

(i) determine initial solution, this become the current solution

(ii) if stopping criteria is not satisfied, generate neighbourhood solutions from the current solution, else finish

(iii) current solution is selected from non-tabu neighbourhood solutions found in

(ii), goto (ii)

Neighbourhood Generation Techniques

• Adjacency Exchange– Adjacent links for a tour are exchanged

• Insert Exchange– Tour links are randomly exchanged (2

usually)• Cross Exchange

– Segments of tours (multiple customers) are exchanged

Vehicle 1 Vehicle 2 Vehicle 1 Vehicle 2

Move

Move Operation

Vehicle 1 Vehicle 2 Vehicle 1 Vehicle 2

Exchange

Exchange Operation

Rule Determination

• Tabu Restrictions– Ban moves previously made– Can be conditional upon improvement

gained (aspiration criteria) • Selection Criteria

– Usually best neighbourhood solution is selected (even if no improvement gained)

Neigbourhood Example

Random Swap Tabu Search Example (Retail Customers)Route Cost ($)

Current Solution 0 5 9 1 8 12 11 3 6 4 10 7 2 0 430.46( 5,11) 0 11 9 1 8 12 5 3 6 4 10 7 2 0 525.25( 2, 5) * 0 2 9 1 8 12 11 3 6 4 10 7 5 0 422.95( 5, 9) 0 9 5 1 8 12 11 3 6 4 10 7 2 0 439.67( 8, 9) 0 5 8 1 9 12 11 3 6 4 10 7 2 0 456.96( 5, 4) 0 4 9 1 8 12 11 3 6 5 10 7 2 0 469.03(11,12) 0 5 9 1 8 11 12 3 6 4 10 7 2 0 435.64( 4,12) 0 5 9 1 8 4 11 3 6 12 10 7 2 0 468.34(12, 6) 0 5 9 1 8 6 11 3 12 4 10 7 2 0 442.43(12,10) 0 5 9 1 8 10 11 3 6 4 12 7 2 0 471.02( 8, 6) 0 5 9 1 6 12 11 3 8 4 10 7 2 0 432.43

Benefits of considering travel time variability in vehicle routing with time windows

0

2

4

6

8

10

12

14

16

-40 -30 -20 -10 0 10 20 30 40

Change in Mean Travel Speed (%)

Cost Savings (%)

Risk and Urban Distribution

2 International Patients registered…

Risk of delays modelled using stochastic programming & robust optimisation

Formed the basis for City Logistics modelling and intelligent transport systems research programs

Collaborative Distribution

• Shared storage location(s)• Networks restructured using advanced

vehicle routing & scheduling systems• Distribution to outlets by areas & priority• Substantial savings in transport costs (20-

30%)• Significant reduction in environmental &

social costs

Product Swaps

Distribute 500kg between each site

Vehicle capacity = 2000kg

Each site ≥ 1 vehicle

Transhipment possible at each site

Based on distributing electrical goods between retail shops in Melbourne

Concept could be applied to multiple carriers, horizontal collaboration (Fischer et al, 1995)

2 3

1 5

4

4 5 vehicles no transhipment

4 4 vehicles pickups at store w/o vehicle

2 3

1 5

4

4 vehicles with transhipment at stores

2 3

15

4

4

2 3

1 5

4

4 4 vehicles with transhipment at common location

Network Analysis

0

100

200

300

400

500

600

5 veh. 4 veh. Good 4 veh. Opt 4 veh. Trans

Configuation

Dis

tance T

ravelle

d (km

)

Collaborative Distribution in Melbourne

Independent Networks from suppliers

1

2

3

4

Collaborative Network

Around 20% saving in distance travelled

4

3

1

2

12

12

12

12

12

121

2

12

12

12

12

12

121

2

12 1

212

12

12

12 1

212

121

2

12

121

2

12 1

2

12

12

121

2

12

12

12

12

12

12

12

12

12

12

12

12

12

12

12

B2C Food Items

DensityHousehold

Characteristics

Area

Population

M arket Share Custom ers

T rip Frequency

Load

Hom e Deliveries Shop Sales

T im e W indow sDistanceT ravelled

VRS Deliveries

Delivery F leetCharacteristics

D istribution F leetCharacteristics

VRS D istribution

Single Urban DC

stores

m ediumdensity

low density

DC

Regional DC’s

VKT with 1 DC

Internet Sales0% 5% 10%

Suppliers to distribution centre 481.1 481.1 481.1Distribution to stores 458.5 458.5 426.9Stores and homes (customers) 24037 22835.3 21633Deliveries to homes 0 2805.9 6346.2Total 24977 26580.9 28888Increase (%) 6.4 15.7

VKT with regional DCs

Internet Sales0% 5% 10%

Suppliers to distribution centre 481.1 481.1 481.1Distribution to stores 458.5 458.5 426.9Stores and homes (customers) 24037 22835.3 21633Deliveries to homes from RDC’s 0 1077.1 1841.5Distribution to RDC’s from MDC 0 214.8 214.8Total 24977 25066.8 24598Change (%) 0.4 -1.5

E-commerce supermarket home delivery network

Extended length, 36 Mail Cages Rigid

Standard 12.5m, 3AR 23T vs High Productivity 4AR 14.85m 28T PBS Vehicle

+37% productivity

Depot Transfer Operation

Depot 1(LF=95%)

Depot 3(LF=90%)

Depot 2(LF=90%)

Depot 4

(LF=87%)

Multi Drop Operation

Depot Customer 1 Customer 2 Customer 3 Customer 4

Customer N

Domestic Postal Fleet Impacts

• Estimated Kilometre reduction 29%• Average Load Productivity increase 37%• Cost reduction -8% Rigid truck numbers -20%

(over 7 years) in Urban areas• Generated high interest and has attracted a

government and Industry scholarships

Ongoing Research

• Exact solution procedures• Pickup & Delivery with transfers• Intermodal networks (road & rail)• Flexible trailer combinations• Combining VRS with simulation (agent based

modelling)• Incorporating travel time information (dynamic

routes)

References

Hassall, K. and R.G. Thompson, (2011). Estimating the Benefits of Performance Based Standards Vehicles, Transportation Research Record, No. 2224, Journal of the Transportation Research Board, Transportation Research Board of the National Academies, Washington, D.C., 94-101.

Taniguchi, E. and R.G. Thompson (2003). Predicting the effects of city logistics schemes, Transport Reviews, Vol. 23, No. 4, 489-515.

Taniguchi, E. and R.G. Thompson (2002). Modeling City Logistics, Transportation Research Record, No. 1790, Transportation Research Board, National Research Council, Washington DC, 45-51.

Taniguchi, E., R.G. Thompson, T. Yamada and R. Van Duin, (2001). City Logistics – Network Modelling and Intelligent Transport Systems, Elsevier, Pergamon, Oxford, 260pp.

Taniguchi, E., Thompson, R.G. Yamada, T. (2012) ‘Emerging techniques for enhancing the practical application of city logistics models’, Procedia - Social and Behavioral Sciences, vol. 39, pp. 3-18.

Thompson, R.G. and R. van Duin (2002). Vehicle Routing and Scheduling, in Innovations in Freight Transport, (E. Taniguchi and R.G. Thompson, Eds.), 47-64, WIT Press, Southampton.

Thompson, R.G. and Hassall, K.P. (2012), A collaborative urban distribution network, Procedia - Social and Behavioral Sciences, vol. 39, pp. 230-240.

Thompson, R.G., E. Taniguchi and T. Yamada, (2011). Estimating Benefits of Considering Travel Time Variability in Urban Distribution, Transportation Research Record: Journal of the Transportation Research Board, Transportation Research Board of the National Academies, Washington, D.C., No. 2238, 86-96.

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