Vehicle Routing in Reverse Logistics

1
Vehicle Routing in Reverse Logistics

• Lixi Zhang (Presented by Doina Olaru)
• PhD StudentUWA
• PATREC Research Forum
• 4 September 2007

2
Contents

• Introduction
• Importance of Transport in Logistics
• Problem Description
• Implementation and Findings
• Conclusions and Future Research

3
About the VRPSDP

• VRP with simultaneous delivery and pick-up
  (VRPSDP) identified as a special research area
  that has not received sufficient attention in the
  past.
• Simple model of VRPSDP, highlighting the main
  differences between traditional vehicle routing
  problems in forward and reverse logistics.

4
Importance of Transport in Logistics

• In many cases, transport cost major part of the
  total cost in a supply chain (e.g., transport
  costs ? 40 to 50 of total logistics costs and 4
  to 10 of the product selling price)

5
Importance of Transport in Logistics (Cont.)

• Cubitt (2002) outlined five possibilities for
  achieving transport efficiency with positive
  impact on logistics
• ?? Reducing the number of shippers
• ?? Negotiation of rates with carriers
• ?? Reducing administration costs
• ?? Maximising equipment use
• ?? Consolidating shipments.

6
Importance of Transport in Logistics (Cont.)

• Inbound logistics, intra-organisational
  movements, outbound logistics, and recovery and
  recycling

Types of Logistics/Transport Links (Source
Adapted from Monczka, Trent, and Handfield, 2003,
pp.550)
7
Problem Description

• Most customers are willing to be served with a
  single stop with both pick-up and delivery
  instead of separately trips for the pick-up and
  delivery.
• VRP is known to be an NP-hard problem ? the
  VRPSDP is an NP-hard problem too

8
Problem Description (Cont.)

• A set of customers i
• ? customer i requires a delivery, a pick-up
  operation or both of a certain amount of goods
  (di) or waste (pi) ONE visit for both
  operations
• Service - provided by a set of vehicles of
  limited capacity C
• ? vehicle leaves the warehouse (DC) carrying
  goods total amount to deliver and returns to
  the warehouse carrying an amount of waste total
  amount to be picked-up

9
Applications in Industry

• Gaur (2001), Gaur and Fisher (2004) - delivery
  scheduling problem in a supermarket chain in
  Netherlands
• Angelelli and Speranza (2002) - unique vehicle
  routing model of three waste collection systems
• Privé, Renaud, Boctor and Laporte (2006) -
  distribution of soft drinks and collection of
  recyclable containers in a Quebec-based company
• De Magalhães and de Sousa (2006) - pharmaceutical
  goods in the North Centre of Portugal
• Alshamrania et al. (2007) - simultaneous design
  of delivery routes and returns strategies for
  blood distribution of the American Red Cross

10
Modelling approach

• Genetic algorithms (GA) robust, efficient
  algorithms to search the universe of solutions
  for a problem based on an evolutionary model.
• Main benefit of GA they find good solutions for
  nonlinear problems by simultaneously exploring
  space of solutions and exploiting promising areas
  operations inspired by natural evolution
  (crossover, mutation, and selection).

11
Example GA crossover

• Chromosomes line up and swap the portions of
  their genetic code beyond the crossover point.

12
Implementation and findings
13
Implementation and findings (Cont.) Warehouse 1
coordinates (10,10)
14
Implementation and findings (Cont.)

• Objective function (OF)
• Di total distance travelled by vehicles from
  the warehouse to the customers to deliver and
  pick-up goods.
• Pt penalty for not being able to arrive to the
  customer (or to the warehouse) on the time
  window. Thus, the objective function is to
  minimise
• M M
• ?Di and ? Pt (M is the number of
  the vehicles)
• i1 t1
• subject to limited capacities and travel times

15
Scenarios
16
Scenario 1a Pick-up deliver with different
vehicles

• Separate vehicles for delivery and pick-up
• No preferred time (800 1700)
• Five runs have been carried out with different
  initial solution points ? lowest objective
  function value 146 with penalty 0

17
Scenario 1a Solution
18
Scenario 1a Solution
Vehicle 1 Vehicle 2 Vehicle 3
C7 (Delivery 1035 AM) (Pickup 1152 AM)
C9 (Delivery 1128 AM) (Pickup 1226 PM)
C8 (Delivery 1212 PM) (Pickup 128 PM)
C6 (Delivery 1014 AM) (Pickup 1032 AM)
DC
C4 (Delivery 1028 AM) (Pickup 1120 AM)
C5 (Delivery 942 AM) (Pickup 1005 AM)
C3 (Delivery 830 AM) (Pickup 830 AM)
C2 (Delivery 912 AM) (Pickup 905 AM)
19
Scenario 2a Pick-up and deliver with same vehicle
simultaneously

• All three vehicles deliver goods with forward and
  backward movement at the same time.
• No preferred time for customers is from
  8001700.
• A solution has the lowest objective function 62
  with penalty value 0.
• Scenario 2a has lower OF (better use of the
  vehicles) compared to scenario 1a

20
Scenario 2a Solution
21
Scenario 2a Solution
Vehicle 1 Vehicle 2 Vehicle 3
C7 (Delivery/Pickup 830 AM)
C9 (Delivery/ Pickup 900 AM)
C8 (Delivery/ Pickup 1032 AM)
C6 (Delivery/ Pickup 954 AM)
C4 (Delivery/ Pickup 830 AM)
DC
C5 (Delivery/ Pickup 1146 AM)
C3 (Delivery/ Pickup 1003 AM)
C2 (Delivery/ Pickup 1044 AM)
22
Scenario 1b,2b Same as above but with a smaller
order size

• Scenario 1b Objective function 77 Scenario 2b
  OF 67 Because of a smaller total order size of
  goods, this scenario only needs one vehicle for
  pick-up. This demonstrates that the GA model can
  automatically scale down the requirement of
  vehicles if customer demand is not high.

23
Scenario 1b Solution
24
Scenario 1b Solution
Vehicle 1 Vehicle 2 Vehicle 3
C7 (Delivery 933 AM Pickup 830 AM)

C9 (Delivery 1003 AM)
C8 (Delivery 1018 AM)
C6 (Delivery 900 AM)
DC
C4 (Delivery 830 AM)
C5 (Delivery 1027 AM)
C3 (Delivery 931 AM)
C2 (Delivery 1000 AM Pickup 1001 AM)
25
Scenario 2b Solution
26
Scenario 2b Solution
Vehicle 1 Vehicle 2 Vehicle 3
C9 (Delivery/Pickup 1158 AM)
C7 (Delivery/Pickup 1039 AM)
C8 (Delivery/Pickup 1143 AM)
C6 (Delivery/Pickup 1025 AM)
DC
C4 (Delivery/Pickup 1111 AM)
C5 (Delivery/Pickup 1002 AM)
C3 (Delivery/Pickup 830 AM)
C2 (Delivery/Pickup 901 AM)
27
Scenario 3 Same as 1a and 1b scenarios but with
narrow time windows

• Solution 3a
• OF 132.6 with penalty 11.65
• Solution 3b
• OF 81.2 and the penalty 12.16.

28
Scenario 3a Solution
29
Scenario 3a Solution
Vehicle 1 Vehicle 2 Vehicle 3
C9 (Delivery 1119 AM Pickup 1205 PM)
C7 (Delivery 1039 AM Pickup 1132 AM)
C8 (Delivery 1203 PM Pickup 107 PM)
C6 (Delivery 1017 AM Pickup 1103 AM)
C4 (Delivery 830 AM Pickup 830 AM)
DC
C5 (Delivery 942 AM Pickup 1038 AM)
C3 (Delivery 1000 AM Pickup 942 AM)
C2 (Delivery 1021 AM, Pickup 1005 AM)
30
Scenario 3b Solution
31
Scenario 3b Solution
Vehicle 1 Vehicle 2 Vehicle 3
C9 (Delivery/Pickup 1109 AM)
C7 (Delivery/Pickup 1003 AM)
C8 (Delivery/Pickup 1242 PM)
C6 (Delivery/Pickup 1019 AM)
C4 (Delivery/Pickup 830 AM)
DC
C5 (Delivery/Pickup 914 AM)
C3 (Delivery/Pickup 830 AM)
C2 (Delivery/Pickup 917 AM)
32
Summary results
33
Findings and Future Research

• Essential finding ? simultaneous pick-up and
  delivery can reduce OF (i.e., travel
  distance/cost)
• Significant improvement compared to forward and
  backward movements done separately.
• The penalty value result of the fact that time
  constraints can not be fully satisfied.
• The small case study shows sensitivity to a
  variety of situations in delivering customer
  orders with different order sizes and different
  patterns of the time windows.

34
Findings and Future Research (Contd)

• Size main limitation
• Further work will extend the model for real world
  large size problem.
• Deterministic demand
• Further work necessary for stochastic GA
• Fleet characteristics - heterogeneity
• Future research will apply GA for VRPSDP
  considering heterogeneous vehicles different
  types of goods for deliveries and pick-ups.
• Agent-based approach
• Future research needed to hybridise GA and ABM

35

• Thank you for your attention