Vehicle Routing

1
Vehicle Routing Scheduling

• Cluster Algorithms
• Improvement Heuristics
• Time Windows

2
Cluster Algorithms

• Select certain customers as seed points for
  routes.
• Farthest from depot.
• Highest priority.
• Equally spaced.
• Grow routes starting at seeds. Add customers
• Based on nearest neighbor or nearest insertion
• Based on savings.
• Based on minimum angle.
• Re-optimize each route (solve a TSP for customers
  in each route).

3
Cluster with Nearest Neighbor
Suppose each vehicle capacity 4 customers
depot
Select 3 seeds
4
Cluster with Nearest Neighbor
Suppose each vehicle capacity 4 customers
depot
Add nearest neighbor
5
VRP Improvement Heuristics

• Start with a feasible route.
• Exchange heuristics within a route.
• Switch position of one customer in the route.
• Switch 2 arcs in a route.
• Switch 3 arcs in a route.
• Exchange heuristics between routes.
• Move a customer from one route to another.
• Switch two customers between routes.

6
K-opt Exchange

• Replace k arcs in a given route by k new arcs so
  the result is a route with lower cost.
• 2-opt Replace 4-5 and 3-6 by 4-3 and 5-6.

Original route
3
1
2
4
5
depot
6
7
3-opt Exchange

• 3-opt Replace 2-3, 5-4 and 4-6 by 2-4, 4-3 and
  5-6.

Original route
3
1
2
5
4
depot
6
8
Improvement Heuristics
Cluster with Nearest Neighbor
depot
depot
Optimized routes
Starting routes
9
Time Windows

• Problems with time windows involve routing and
  scheduling.

3,2-4
3,2-4
1, 9-12
2,1-3
4,10-2
5,8-10
Customer number
depot
6,9-12
Start and end of time window (200 pm - 400 pm)
10
Clustering and Time Windows

• Cluster customers based on location and time
  window.
• Design routes for each cluster.

3,2-4
1, 9-12
2,1-3
4,3-5
5,8-11
depot
6,9-12
11
Savings Method with Time Windows

• Start with n one stop routes from depot to each
  customer.
• Calculate all savings for joining two customers
  and eliminating a trip back to the depot.
• Sij Ci0 C0j - Cij
• Order savings from largest to smallest.
• Form route by linking customers according to
  savings if time windows are satisfied.

12
Savings Method with Time Windows

• Order savings from largest to smallest.
• S35
• S34
• S45
• S36
• S56
• S23
• S46
• S24
• S25
• S12
• S26
• S13
• etc.

13
Savings Method with Time Windows
One hour travel time between any two customers.
Half hour delivery time at each customer.
Largest savings S35
Leave depot 1000 Arrive at 5 1100 Leave 5
1130 Arrive at 3 200
3,2-4
1, 9-12
2,1-3
4,10-2
5,8-11
Next largest savings S34 , S45 , S36 , S56
depot
6,9-12
14
Savings Method with Time Windows
One hour travel time between any two customers.
Half hour delivery time at each customer.
S56
Leave depot 830 Arrive at 6 930 Leave
6 1000 Arrive at 5 1100 Leave 5
1130 Arrive at 3 200
3,2-4
1, 9-12
2,1-3
4,10-2
5,8-11
depot
Next largest savings S23 , S46 , S24
6,9-12
15
Savings Method with Time Windows
One hour travel time between any two customers.
Half hour delivery time at each customer.
Leave depot 830 Arrive at 6 930 Leave
6 1000 Arrive at 5 1100 Leave 5
1130 Arrive at 3 200
Leave depot 1230 Arrive at 4 130 Leave 4
200 Arrive at 2 300
S24
3,2-4
1, 9-12
2,1-3
4,10-2
5,8-11
Need S16 or S14. Will customer 1 fit on black or
red route?
depot
6,9-12
16
Savings Method with Time Windows
One hour travel time between any two customers.
Half hour delivery time at each customer.
Leave depot 830 Arrive at 6 930 Leave
6 1000 Arrive at 5 1100 Leave 5
1130 Arrive at 3 200
S14
3,2-4
1, 9-12
2,1-3
4,10-2
Leave depot 1100 Arrive at 1 1200 Leave 1
1230 Arrive at 4 130 Leave 4
200 Arrive at 2 300
5,8-11
depot
6,9-12