Lecture 03_Vehicle Routing Problem

Question 1

Parameters of VRP

Vehicle Routing Problem

Answer 1

One depot (without loss of generality) with index 0

n customers (i=1,2,…,n) with demand bi
* Complete deliveries in one tour (no split deliveries)

Distances between customers or depot and customers
dij, i=0,1,…,n; j=0,1,…,n (for simplification: symmetric)

K identical vehicles
* Capacity Q (volume, customers)
* Time restriction T

Question 2

Heuristics for VRP

Answer 2

**1. Route first, cluster second **
- determine giant tour without capacity constraints (TSP)
- go back to depot, if next customer cannot be visited with given capacity

2. Cluster first, route second: Sweep-method

3. Parallel clustering and routing; Savings method

Question 3

Sweep Method

Heuristic for VRP

Answer 3

• representation of the customers in sequence of their polar coordinates
• **work counter-clockwise
• first node selection is arbitrary** -> different results depending on start
• improve by 2-opt method possible

Cluster creation
- allocation
- capacity check
- creating the sequence: TSP

Question 4

Savings Procedure

Heuristic for VRP

Answer 4

• Starting point: Round trips (0,i,0)
  Saving by combination of 2 tours
• Take two end customers of two different tours
• Saving the distances of both end customers to the depot (d0i+d0j)

* Satisfy capacities sij = d0i + d0 j − dij

Question 5

VRP Heuristics

3 items

Answer 5

• Successive Insertion
• Sweep Method
• Savings Matrix

Minimize total distance while satisfying demand

Question 6

Compare the 3 different methods for solving the VRP

Answer 6

• Successive Insertion for one tour → Split the tour can lead to long distances to the depot
• Sweep Method useful if clusters are visible
• Sweep Method generates tour plans step by step
• Savings Method optimizes tour planning similar to the Successive Insertion for circle tours without the splitting problem and long distances to the depots

Question 7

What are the benefits that arise, when multiple service provider bundle their tours, e.g. within a city logistics cooperation?

Answer 7

• Less empty trucks drives
• The more nodes, the better the possibilities of distance optimization
• Better degree of capacity utilization → lower unit costs & less investment
• Relief of road transport infrastructure
• Specialization of the different service provider

Question 8

Savings Procedure
Step by Step

Answer 8

1. construct savings matrix using:
   s(ij) = d(0i) + d(0j) - d(ij)
2. start with highest savings node pair
3. start constructing route adding next highest node pair
4. Check whether node pair is feasible (only end customers)
5. Check capacity and demand restrictions