Linear Operations

1
Linear Operations

• Dynamic Segmentation
• Geocoding
• Routing
• Network Analysis

2
Dynamic Segmentation

• Dynamic segmentation associates multiple sets of
  attributes to any portion of a linear feature
• Dynamic segmentation models linear features using
  routes and events
• A route represents a linear feature, such as a
  street, highway or stream
• Events are attributes associated with a route

3
What is Dynamic Segmentation

• Dynamic segmentation models linear features using
  routes and events
• Routes represent linear features (track
  centerline, stream, road)
• Routes contain measures which describe distance
  along them
• Events model data along routes

4
Where Dynamic Segmentation is Used

• Collecting data along such linear features as
  roads, rivers and railways
• Managing pavement quality
• Managing public transit
• Managing railroad track quality
• Managing rivers and streams
• Modeling shorelines
• Modeling pipelines
• Analyzing oil and gas exploration

5
5-Year Frequency Analyses Maps from TC - 81
6
(No Transcript)
7
Dynamic Segmentation of TC-81 Data
8
Example of Routes, Measures, and Events

• Routes
• Measures
• Events

286
50
100
150
200
250
0
286
92
115
42
0
180
225
9
Source ESRI
10
Shapes

• ArcView has traditionally represented shapes
  with one or more coordinate pairs (e.g.
  Lat/Long)

Source ESRI
11
Measured Shapes

• Measured shapes store a calibration or measure
  (m) value at each coordinate
• A measured shape is made up of one or more
  coordinates

Source ESRI
12
Dynamic Segmentation Commands

• Example of Dynamic Segmentation

13

• Routing and Scheduling

14
What is routing

• Once you find where your clients are, the next
  thing you have to do is figure out how to get to
  them.
• But, if you want to stay in business, you better
  figure out how to get to them better than your
  competitor.
• This concept will focus on routing and
  scheduling, which is a fast growing area of
  geospatial analysis, used by businesses to
  enhance their competitive edge.
• Routing is a computing method for finding a
  shortest or least-cost path in which to visit
  locations in a street network. The cost doesnt
  have to be just money. It could represent time
  (which in business is money ? ), or it could be
  distance, or even danger.

15
Routing terms

• Weve just thrown a couple buzz words at you
  network, and least-cost.
• When we talk about "networks" we are really
  talking about a branch of mathematics called
  graph theory. In mathematics, a "graph"
  represents the mathematical description of a
  series of nodes that are often joined by links.
  You can think of the links as lines connecting
  the nodes.
• For clarification, we will not be using the term
  lines because routing is focused on graph theory,
  or networks, and mathematicians use the term
  links instead. So to separate the differences
  between network analysis and basic GIS we will
  use the term link.

16
Routing terms

• Links are termed either directed or undirected.
  A directed link is like a one-way street it
  starts at one node and ends at another node. In
  the case of a directed link, one assumes the
  travel paths have directionality, and are often
  called directed networks. Structuring a network
  with directed links would prevent a path from
  driving the wrong way on a one way link.
• An undirected link has no implied direction.
  Therefore, you can traverse in any direction.
  So, if a two lane road was represented in a GIS
  by a single centerline, the network
  representation would be an undirected link.
  Networks that have only undirected links are
  called undirected networks.
• Transportation systems used in business
  geographics usually are usually a combination of
  both directed and undirected networks

Directed network
Un-Directed network
17
Routing terms

• We also introduced the term least-cost. Links
  and nodes in networks may also have weights
  associated with them. Weights are values
  assigned to the link or node that represents a
  potential constraint on the object such as the
  flow capacity, the length of the link, the speed
  limit, the average travel time, or the number of
  delivery points along the link. Nodes can also
  have weights that might represent a penalty for a
  left hand turn, or the delay for stopping at an
  intersection.
• Graphs or networks that have weights associated
  with them are termed weighted graphs

18
Routing terms

• A directed route is a represented in a graph
  where all the edges in the route from the first
  node to the last node are oriented in the correct
  way to allow a continuous path from the beginning
  to the end.
• Path was another term we used. A path is
  essentially a minimum cost route through a
  network between targeted locations. Paths are
  usually visited in a specified order that are
  known beforehand. For instance, a repairman
  might have appointments that he must keep
  throughout the day, so he looks for the least
  cost path between appointments.
• A tour represents situation where we dont know
  the order. So, we have to find both the order to
  visit the stops and the shortest path between the
  stops. Therefore, a tour orders the stops and
  then finds the least-cost path among them.
• Well see more of this shortly.

19
Side Note

• Graph theory is very useful for decision making.
  In fact, the links dont even have to represent
  geography. They can represent different paths to
  get to a solution. For example, you chose to
  take this course, hoping it would improve your
  understanding of business geographics. That was
  a decision you made. So, we could create a
  theoretical graph of your life
• Go to college / Not go to college - impact on
  available income
• Get married / Dont get married - impact on
  available time
• Have children / Dont have children - greater
  impact on time
• All of these decision have impact. And, if we
  were to structure it in a graph, we could
  determine say, the best opportunity for pursuing
  the hobby of surfing ? That is, we want to
  maximize free time, and possibly maximize money
  (to take those trips to Hawaii). But, that is
  somewhat off our subject of routing. Just
  realize that graphs arent only for road networks
  in a GIS.

20
UNIQUE ISSUES INROUTING
Marriage of State-of-the-Art

• Routing in a GIS is actually the marriage of two
  powerful state of the art sciences namely,
  integrating geographic information systems with
  mathematical graph theory.

GIS Technologies
Advanced Routing Algorithms based on graph theory
21

• For most people, routing is typically thought of
  as the method for getting from one place to
  another. Similar to this Mapquest web page.
• It is certainly true that what Mapquest is doing
  through their web page is routing. However, we
  will see that routing can be a whole lot more,
  and a whole lot more beneficial to a business.

22
CLASSIFICATION OF ROUTING AND SCHEDULING PROBLEMS

• Routing and scheduling problems can be broken
  down into many different sub categories. We will
  look at the following
• Shortest Path Problem
• Traveling Salesman Problem (TSP)
• M-TSP
• Single Depot, Multiple Vehicle Routing
• Multiple Depot, Multiple Vehicle
• Single Depot, Mult. Vehicle w/ Demands
• Capacitated Arc Routing Problem

23
Shortest Path

• The shortest path problem is the most basic
  routing solution. Essentially, we are interested
  in finding the least cost method to get from
  point A to point B on a connected graph.
• The problem is generally very easy to solve from
  a mathematical standpoint. In fact, most
  Sophomore or Junior college students obtaining a
  degree in operations research are often required
  write a shortest path algorithm as a class
  project.
• The following examples show a shortest path route
  in an example graph, and one on a real street
  network.
• This is an example of a simple path.

24
(No Transcript)
25
Shortest Path
3
1

• Just because you have a GIS that can compute
  shortest path doesnt mean you are doing routing.
  Hardly, as you will see, it gets more complex,
  way more complex.
• For example, if we added three more stops (1,
  2, 3) and just ran a shortest path algorithm,
  are answer would be less than ideal.
• By just coming up with shortest paths from 1 - 2
  - 3 and then back home, is not the best
  solution.
• What we really want is the best overall tour
  through a graph

2
3
1
2
26
(No Transcript)
27
(No Transcript)
28
Traveling Salesman Problem

• You can see that our second example actually
  created a tour, rather than multiple paths. This
  is often referred to as the traveling salesman
  problem.
• In theory, a salesman must find the most
  efficient way to visit all of the appointments in
  his territory. And, he doesnt want to go back
  to an appointment he already made.
• In reality, once you add more than a few links
  and a few appointments (nodes) the problem is
  impossible to solve. The true optimal solution
  requires too many calculations, even with modern
  computers.
• Therefore, a heuristic (a fancy word for an
  educated guess) finds an approximate best tour,
  and for the most part is usually very close to
  the optimal solution.
• So, you can see that this is quite more
  complicated than a shortest path hang on, were
  not out of the woods yet

29
Multiple Traveling Salesman Problem

• We just modified our shortest path problem to
  create a tour for a single salesman. But, how
  many companies do you know that have only one
  salesman?
• The reality is, just because the GIS software you
  are thinking of buying can solve the traveling
  salesman problem, doesnt mean its going to meet
  your need.
• That adds to the complexity alittle more, doesnt
  it.
• The example on the right determines the least
  cost tour for two salesmen and five delivery
  points.

30
Multiple Traveling Salesman Balanced workloads

• You might be happy with our solution, IF YOU WERE
  THE RED SALESMAN!!!
• Obviously just finding the least cost tour is not
  enough here. One salesman is working four times
  harder than the other one.
• This is a classic example of what happens in the
  sanitation or meter reading industries. One crew
  may be able to finish really early and go home
  (with pay), while the other crew has to work
  overtime (with time and a half pay). This
  amounts to a lot of money wasted on
  inefficiencies.
• The important consideration is to not just solve
  an optimal tour, but also meet a new constraint
  Cw (worktime) . That is, trying to get everyone
  to nominally work an 8 hour day.

31
Single Depot, Multiple Vehicle Routing

• This is a takeoff on the last example. But here,
  there is a single depot that the workers start
  at, and a single depot where they drop their
  truck off. This is a fairly typical scenario for
  a company that has delivery trucks housed at
  their warehouse.
• We up-the-anty on this scenario by adding
  multiple depots and multiple salesmen.
• Each one of these scenarios, though having their
  basis in the shortest path, shortest tour,
  actually have some significant additions that you
  may not find in GIS software.

32
Adding some demands fixed capacity vehicles

• Any college road-trip with 7 people trying to fit
  into a VW Bug will tell you that there is a
  finite amount of room in a vehicle. This same
  reality applies to routing.
• Whether you are delivering pizza, washing
  machines, or flowers, there is only so much space
  available within a truck. Also, if you are
  picking up things like garbage, there is only so
  much available space before you have to unload
  the truck.
• So here, one of the pickup locations has more
  merchandise. So, the routes may not be as short
  as we would like, but we need to satisfy our
  additional constraint of a fixed capacity
  vehicle.
• And remember, we may still have to meet our other
  constraints nominal 8 hour days, multiple
  vehicles, single depot

33
Adding some demands time windows

• If you have ever ordered an appliance, you
  understand the problem a customer faces when they
  are told the delivery truck will be there
  sometime on Tuesday. Or, to be real helpful,
  they may tell you Tuesday afternoon. This is an
  unacceptable requirement for some customers.
  And, if you want to stay ahead of your
  competition you have to provide better
  information like
• Our delivery truck is scheduled to be at your
  house between 300 and 400 in the afternoon.
• This just becomes another constraint within the
  routing solution. Here we need to find the best
  tour, while satisfying the condition of being at
  a particular location during a specific time, or
  not being at a location during a specific
  timeframe.
• A good example of avoiding an area at a certain
  time is for sanitation pickup. At restaurants you
  want to avoid stopping there during lunch or
  dinner times.

34
Adding some demands side of street

• Just because you route to a street where a
  location exists, doesnt mean that you are
  meeting all your criteria.
• Sometimes it makes sense to specify the side of
  the street you want to drive up.
• For example, the bus should pull up on the
  correct side of the road so that riders dont
  have to cross the street to get on the bus.
  There is no magic to make that happen, right hand
  side of the road pickup must be programmed into
  the software.

35
Neighborhood Routing

• Its one thing to find the shortest paths to
  individual delivery points, its another if your
  business visits all the locations on a street.
• Businesses like sanitation companies, the US
  Postal Service, and electric and gas utilities
  often have to visit every house on a block.
  Therefore, instead of 200 delivery points, there
  are possibly 100,000 or more delivery points, and
  you might have to visit every street in a
  neighborhood.
• So, the problem we are trying to answer is
• Given an undirected network with demands for each
  link which must be satisfied by one or more
  vehicles, each of capacity W, find the vehicle
  tours that satisfy all demands at a minimal total
  cost

36
Considerations when building routes

• Weve certainly come a long way from our
  assumption that routing is simply finding the
  shortest path from point A to point B. Here are
  a few other considerations when performing
  routing. Think about these points when you
  evaluate routing software and ask the question
  does the software support this kind of
  functionality

37
Considerations when building routes

• Number and types of vehicles available can you
  change the number of vehicles in the fleet.
  Also, can to assign different types of vehicles
  such as a large truck or small truck.
• Vehicle costs can each of the vehicles in the
  fleet be assigned different costs (some vehicles
  get better gas mileage than others)
• Number and geographic location of stops to
  service can you assign the geographic location
  for multiple stops, or does the software only
  support a shortest path between two points?
• Frequency of collection does the software allow
  you to assign the frequency of collection or
  delivery for individual stops (for example, in a
  nursing agency, does Mrs. Jones get visited on
  M,W,F, while Mrs. Smith only gets visited on T,R,
  and Mrs. Park has to be checked in both the AM
  and PM on W and F).

38
Considerations when building routes

• Volume variability Does the software allow you
  to change the amount of volume per site. If you
  are collecting garbage, some on restaurant have
  more garbage than others. Or, on Valentines Day,
  you certainly deliver more flowers than on other
  days. Also, funeral parlors typically get more
  flowers than residential customers.
• Crew availability and costs Does the software
  allow you to assign different crews or skill-sets
  to a vehicle. For instance, do you have less
  people available on Mondays to work. Or, if you
  do construction, are your electricians available
  on M and W, and your plumbers are only available
  on M.
• Geography (terrain, barriers to travel) Does
  the software allow you to consider the terrain in
  assigning costs. That is, if you collect
  garbage, do you want to avoid areas with hills at
  the end of the day since the truck will be more
  full.

39
Considerations when building routes

• Transportation network (one way streets,
  seasonality) does the software use a single
  street centerline, or can you modify the
  centerlines to account for some streets being
  closed in the winter?
• Disposal sites (location, queuing and dump time)
  Can the software allow you to specify multiple
  pick up locations, or do you have to stick with
  one. For example, if you work for a retailer,
  delivering furniture, can you pick up furniture
  in a warehouse on the east end of town, and later
  in the day, pick up addition furniture in the
  west end warehouse. Also, can you program in the
  amount of time it takes to drop off the furniture
  at a location (for example, maybe a TV takes 30
  minutes, but a dining room table takes 2 hours
  because the company offers set-up).

40
Two Approaches to Solving Routing Problems

• POINT TO POINT ROUTING
• Service Required at Individual Locations
• Low Density of Points to be Serviced

• NEIGHBORHOOD ROUTING
• Service Required on Most Street Segments
• Higher Density of Points to be Serviced

41
Two Approaches to Solving Routing Problems

• Point to Point Routing
• Easier to perform than neighborhood routing
• However, becomes difficult if you try to
  represent very high density of customers as
  points

• Neighborhood Routing
• Much more difficult to perform than point to
  point routing
• Represents reality better than point to point
  routing when considering high density of customers

42
Point-to-Point RoutingKey Considerations

• When you perform point-to-point routing, you have
  to consider the following
• Create route that go to the actual customer
  address
• Create routes that Restriction the time of
  service
• Control the number and duration of routes
• Support the insertion of new customers and and
  the ability to swap routes (give route A to a
  different person

43
Neighborhood RoutingKey Considerations

• When you perform point-to-point routing, you have
  to consider the following
• Generate routes based on the length of the day,
  number of routes, or a combination of both
• Create routes that can be walked, driven, or a
  combination of both. Like the example shown, a
  meter reader might drive a car to a subdivision,
  and then get out and walk the rest of the route.
  The question then is
• Where is the most efficient place to park the car
  and then walk

44
What to Look for In Routing Solutions

• You want to make sure that you accurately models
  real life constraints as we discussed in this
  concept.
• You want to make sure that the software can
  balance and optimize workload.
• The system supports what-if scenarios (closed
  streets, people calling in sick so you have a
  smaller crew
• Solutions can be output in both text direction
  and map formats

45
Benefits of Good Routing Solutions

• Studies in routing solutions show that here is
  often anywhere from 10 to 23 reduction in fleet
  costs when using routing and optimization
  software
• Crew cost savings
• Mileage reduction
• Vehicle cost savings
• Reduction in Route Planning Efforts
• City of Charlotte, NC estimates a savings in
  excess of 2,800 person hours in route planning
• Improved Customer Service
• Reliable scheduling
• Meet time window demands of your customers
• And, as they say on the VISA commercial
• Staying ahead of your competition - PRICELESS

46
Conclusion

• We have covered a lot of ground, and have really
  expanded the notion of shortest path to some real
  life routing solutions.
• You should be able to appreciate the kinds of
  complexities that routing solutions can offer,
  and also articulate the kinds of things you need
  a routing solution to do for you.