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Vehicle Routing & Scheduling. Multiple Routes Construction Heuristics Sweep Nearest Neighbor, Nearest Insertion, Savings Cluster Methods Improvement Heuristics Time Windows. Multiple Routes. Capacitated VRP: vehicles have capacities. Weight, Cubic feet, Floor space, Value.

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vehicle routing scheduling
Vehicle Routing & Scheduling
  • Multiple Routes
  • Construction Heuristics
    • Sweep
    • Nearest Neighbor, Nearest Insertion, Savings
    • Cluster Methods
  • Improvement Heuristics
  • Time Windows
multiple routes
Multiple Routes
  • Capacitated VRP: vehicles have capacities.
    • Weight, Cubic feet, Floor space, Value.
  • Deadlines force short routes.
    • Pickup at end of day.
    • Deliver in early morning.
  • Time windows
    • Pickup.
    • Delivery.
    • Hard or Soft.
multiple route solution strategies
Multiple Route Solution Strategies
  • Find feasible routes.
    • Cluster first, route second.
      • Cluster orders to satisfy capacities.
      • Create one route per cluster. (TSP for each cluster)
    • Route first, cluster second.
      • Create one route (TSP).
      • Break route into pieces satisfying capacities.
    • Build multiple routes simultaneously.
  • Improve routes iteratively.
sweep algorithm
Sweep Algorithm
  • Draw a ray starting from the depot.
  • Sweep clockwise (or counter-clockwise) and add customers to the route as encountered.
  • Start a new route when vehicle is full.
  • Re-optimize each route (solve a TSP for customers in each route).
sweep algorithm5

depot

depot

Sweep Algorithm

Suppose each vehicle capacity = 4 customers

nearest neighbor nearest insertion savings algorithms
Nearest Neighbor, Nearest Insertion & Savings Algorithms
  • Similar to for TSP, but keep track of demand on route.
  • Start new route when vehicle is full.
  • Re-optimize each route (solve a TSP for customers in each route).
nearest neighbor algorithm

First route

depot

depot

Nearest Neighbor Algorithm

Suppose each vehicle capacity = 4 customers

nearest neighbor algorithm8

Second route

Third route

depot

depot

Nearest Neighbor Algorithm

Suppose each vehicle capacity = 4 customers

cluster algorithms
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).
cluster with minimum angle

depot

Add customers with minimum angle

Cluster with Minimum Angle

Suppose each vehicle capacity = 4 customers

depot

Select 3 seeds

cluster with minimum angle11
Cluster with Minimum Angle

Suppose each vehicle capacity = 4 customers

depot

Add customers with minimum angle

cluster with minimum angle12
Cluster with Minimum Angle

Suppose each vehicle capacity = 4 customers

depot

Add customers with minimum angle

vrp improvement heuristics
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.
improvement heuristics
Improvement Heuristics

Cluster with Minimum Angle

depot

depot

Starting routes

“Optimized” routes

time windows
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

(2 pm - 4 pm)

routing example with time windows
Routing Example with Time Windows

One hour travel time between any two customers.

Half hour delivery time at each customer.

3,[2-4]

1, [9-12]

2,[1-3]

4,[10-2]

5,[8-11]

depot

6,[9-12]

nearest insertion no time windows
Nearest Insertion - No Time Windows

Insert nearest customer to route in best location.

3

3

1

2

1

2

4

4

5

5

depot

depot

6

6

nearest insertion no time windows18
Nearest Insertion - No Time Windows

Insert nearest customer to route in best location.

3

3

1

2

1

2

4

4

5

5

depot

depot

6

6

nearest insertion no time windows19
Nearest Insertion - No Time Windows

Insert nearest customer to route in best location.

3

3

1

2

1

2

4

4

5

5

depot

depot

6

6

nearest insertion with time windows
Nearest Insertion with Time Windows

One hour travel time between any two customers.

Half hour delivery time at each customer.

Leave depot: 8:00 - 11:00

Arrive at 1: 9:00 - 12:00

Leave 1: 9:30 - 12:30

3,[2-4]

1, [9-12]

2,[1-3]

4,[10-2]

5,[8-11]

depot

6,[9-12]

depot-1

nearest insertion with time windows21
Nearest Insertion with Time Windows

One hour travel time between any two customers.

Half hour delivery time at each customer.

Leave depot: 10:30

Arrive at 1: 11:30

Leave 1: 12:00

Arrive at 2: 1:00

Leave 2: 1:30

3,[2-4]

1, [9-12]

2,[1-3]

4,[10-2]

5,[8-11]

depot

6,[9-12]

depot-1-2

nearest insertion with time windows22
Nearest Insertion with Time Windows

One hour travel time between any two customers.

Half hour delivery time at each customer.

Leave depot: 9:00

Arrive at 1: 10:00

Leave 1: 10:30

Arrive at 4: 11:30

Leave 4: 12:00 Arrive at 2: 1:00

Leave 2: 1:30

3,[2-4]

1, [9-12]

2,[1-3]

4,[10-2]

5,[8-11]

depot

6,[9-12]

depot-1-4-2

nearest insertion with time windows one option
Nearest Insertion with Time Windows - one option

One hour travel time between any two customers.

Half hour delivery time at each customer.

Leave depot: 8:00

Arrive at 1: 9:00

Leave 1: 9:30 Arrive at 5: 10:30

Leave 5: 11:00

Arrive at 4: 12:00

Leave 4: 12:30 Arrive at 2: 1:30

Leave 2: 2:00

3,[2-4]

1, [9-12]

2,[1-3]

4,[10-2]

5,[8-11]

depot

6,[9-12]

depot-1-5-4-2

nearest insertion with time windows a better option
Nearest Insertion with Time Windows - a better option

One hour travel time between any two customers.

Half hour delivery time at each customer.

Leave depot: 7:30

Arrive at 5: 8:30

Leave 5: 9:00

Arrive at 4: 10:00

Leave 4: 10:30 Arrive at 1: 11:30

Leave 1: 12:00

Arrive at 2: 1:00

Leave 2: 1:30

3,[2-4]

1, [9-12]

2,[1-3]

4,[10-2]

5,[8-11]

depot

6,[9-12]

depot-5-4-1-2

nearest insertion with time windows25
Nearest Insertion with Time Windows

One hour travel time between any two customers.

Half hour delivery time at each customer.

Leave depot: 7:30

Arrive at 5: 8:30

Leave 5: 9:00

Arrive at 4: 10:00

Leave 4: 10:30 Arrive at 1: 11:30

Leave 1: 12:00

Arrive at 2: 1:00

Leave 2: 1:30

Arrive at 3: 2:30

Leave 3: 3:30

3,[2-4]

1, [9-12]

2,[1-3]

4,[10-2]

5,[8-11]

depot

6,[9-12]

depot-5-4-1-2-3

nearest insertion with time windows26
Nearest Insertion with Time Windows

One hour travel time between any two customers.

Half hour delivery time at each customer.

Leave depot: 7:00

Arrive at 5: 8:00

Leave 5: 8:30

Arrive at 6: 9:30

Leave 6: 10:00

Arrive at 1: 11:00

Leave 1: 11:30 Arrive at 4: 12:30

Leave 4: 1:00

Arrive at 2: 2:00

Leave 2: 2:30

Arrive at 3: 3:30

3,[2-4]

1, [9-12]

2,[1-3]

4,[10-2]

5,[8-11]

depot

6,[9-12]

depot-5-6-1-4-2-3

routing with time windows
Routing with Time Windows

Route must be built with both time windows & geography in mind!

3,[2-4]

1, [9-12]

2,[1-3]

4,[10-2]

5,[8-11]

depot

6,[9-12]

clustering and time windows
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]

clustering and time windows29
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]

arclogistics route solution technique
ArcLogistics Route Solution Technique
  • Construct travel time (distance) matrix.
    • Shortest paths on actual (GIS) road network.
  • Build initial routes by inserting orders on routes.
    • Can not exceed vehicle capacities, precedence rules, skill set constraints (specialties).
    • Can violate time windows and route duration.
  • Improve routes.
    • Within route improvements.
    • Between route improvements.
arclogistics route insertions
ArcLogistics Route Insertions
  • Objective: Minimize weighted sum of:
    • travel times (t),
    • time window violations (v), and
    • free (waiting) time (w).

1tr + 2vr + 3wr

  • User sets weights 1, 2 ,3 via slider bar in “Rate the importance of meeting time windows”.
    • Lowest value = 0 is for lowest cost
    • Highest value = 10 is for most importance on meeting time windows.

r

arclogistics route improvements
ArcLogistics Route Improvements
  • Within route (intra-route) improvements.
    • Maintain stops on each route.
    • Consider each route separately.
    • Find best position for each stop on each route.
  • Between route (inter-route) improvements.
    • Transfer or switch: Move one stop from one route to another.
    • Exchange: Exchange two stops between two routes.
improvement heuristics33

Intra-route

improvement

Inter-route

improvement

depot

“Improved” routes

Improvement Heuristics

depot

Starting routes

modeling details
Modeling Details
  • Road network.
    • How detailed is the road network?
    • Affects distance and cost calculations.
  • Geocoding.
    • Where are addresses located?
  • Linking locations to road network.
    • How do vehicles get from locations to road nework?
road network detail
Road Network Detail
  • Models should measure travel distance, time and cost on actual road network.
  • More detailed road networks mean:
    • More accurate cost, distance and travel time.
    • Slower solutions.
    • Longer time to set up data.
    • Larger data files.
  • What is purpose?
    • Operational: To provide detailed driving directions?
    • Strategic: To estimate costs, times, and routes?
road network detail36
Road Network Detail
  • How are speeds specified?
    • Different types of roads have different speeds.
    • Hard to include time varying speeds.
  • Showing every road may be unrealistic.
    • Large trucks may not use small local roads.
  • Road network changes over time.
    • Example: new residential areas.
    • Are customers in older, established areas or newer suburbs?
geocoding
Geocoding
  • Finding geographic locations from addresses.
  • Depending on scale of problem, may geocode at various levels.
  • Zip codes.
    • Geocode to a point at center of zip code.
    • Zip codes are defined with boundaries and centroids.
  • Cities.
    • Geocode to a point representing city location.
geocoding street addresses
Geocoding - Street Addresses
  • Street addresses
    • Each road segment has associated address ranges on each side.
    • Address is interpolated between start and end of address range.
    • Assumes even spacing of addresses.
  • Example:
    • Main Street, left side: 300-498, right side 301-499
    • 420 E. Main Street is about 60% of the way down the road segment on the left side.
address matching
Address Matching
  • Can be very complicated.
  • Only part of address may match.
    • Street name, city and zip code match; address range doesn’t.
    • Street name and city match; zip code doesn’t.
  • Part of address may be incorrect.
    • Missing prefix (East).
    • Incorrect suffix (Street vs. Boulevard).
    • Name may be abbreviated in database (Ave for Avenue or Avenida).
    • Zip code may be wrong.
address matching40
Address Matching
  • Streets may have several names.
    • Highway 67 is also Lindbergh Blvd.
  • Streets change names, especially at city boundaries.
    • Lindbergh, Highway 67, Kirkwood Road.
    • Olive Boulevard, Olive Street, Olive Street Road, Old Olive Street Road.
  • New streets are added and old streets are renamed.
linking locations to road network

ArcLogistics Route assumes locations is here

Linking Locations to Road Network
  • User may specify locations not on streets.
    • User Pick in ArcLogistics Route.
  • How should this be linked to street network?
  • ArcLogistics Route forces locations not on streets to be on nearest street.
linking locations to road network42

Some packages compares these distances.

Linking Locations to Road Network
  • Other packages assume straight line travel from nearest street intersection.