1. NETWORK ANALYSIS

2. definition
A network is a line coverage, which is topology-based and has the appropriate attributes for the flow of objects such as traffic (Chang, 2002 p.306).
The network model is essentially adaptation of the vector data model. The vector network model is made up of the same arc (line segments) and node elements as any other vector data model but with the addition of special attributes, e.g. impedance which can be time, distance, fuel used, traffic volume, etc.(Heywood et al., 2002 p.63-64).
Network analysis is a special type of line analysis involving a set of interconnected lines. Network analysis can be used to answer at least four types of questions which are address geocoding, optimum routing, finding closest facilities, and resource allocation (Verbyla, 2002 p.59).

3. Shortest Path Problem
Evans and Minieka (1992) explained is supposed that we are given a graph G in which each arc (x, y) has associated with it a number a(x, y) that represents the length of the arc.
In some applications, the length may actually represent cost or some other value (impedance).
The length of a path is defined as the sum of the lengths of the individual arcs comprising the path.
For any two vertices, s and t in G, it is possible that there exist several paths from s to t.
The shortest-path problem involves finding a path from s to t that has the smallest possible length. 2 1 3 4
Arc
G = (V,A)
V(G) = {A,B,C,D,E}
A(G) = {3(A,B), 2(A,D),
1(D,E), 4(E,C)}

4. Dijkstra’s Algorithm
Step1: Initially, only node s is permanently labeled, d(s) = 0. Assign tentative distances d(x) = ∞ for all x ≠ s. Let y = s.
Step2: Recomputed tentative distances for the unlabeled nodes in forward star of y as follows:
If d(x) = ∞ for all unlabeled vertices x, then stop because no path exists from s to any unlabeled vertex. Otherwise, label the unlabeled vertex x with the smallest value of d(x). Also label the arc directed into vertex x from a labeled vertex that determined the value of d(x) in the above minimization. Let y = x.
Step3: If vertex t has been labeled then stop, since a shortest path from s to t has been discovered. If vertex t has not been labeled yet, repeat step 2.

5. Fig. 1 shortest-path example network.
Dijkstra’s Algorithm
Let us perform the Dijkstra’s shortest-path algorithm to find a shortest path from node s to node t in the graph in Fig. 1.
Example 1 s 1 2 3 4 t 7
Fig. 1 shortest-path example network.

6. Dijkstra’s Algorithm s 1 2 3 4 t Example 1 7 s loop Process Graph 1
Step1: Initially, only node s is permanently labeled, d(s) = 0. Assign tentative distances d(x) =∞ for all x ≠ s. Let y = s.
Step2: Recomputed tentative distances for the unlabeled nodes in forward star of y as follows:
d(1) = min{d(1), d(s) + a(s,1)} = min{∞, 0 + 4} = 4
d(2) = min{d(2), d(s) + a(s,2)} = min{∞, 0 + 7} = 7
d(3) = min{d(3), d(s) + a(s,3)} = min{∞, 0 + 3} = 3
Since the minimum distance on any unlabeled node is d(3) = 3, we label node 3 and arc (s, 3). The current shortest-path arborescence consists of arc (s, 3). Let y = 3.
Step3: Vertex t has not been labeled, so return to step 2. 2
Step2:
d(4) = min{d(4), d(3) + a(3,4)} = min{∞, 3 + 3} = 6
The minimum tentative distance on the unlabeled node is d(1) = 4. Label node 1 and arc (s, 1), which determined d(1). The current shortest-path arborescence consists of arcs (s, 3) and (s, 1). Let y = 1. s s 1 2 3 4 7 s 3 s 1 2 3 4 7 6 s 1 3 4

7. Dijkstra’s Algorithm s 1 2 3 4 t Example 1 7 loop Process Graph 3
Step2:
d(2) = min{d(2), d(1) + a(1,2)} = min{7, 4 + 3} = 7
d(4) = min{d(4), d(1) + a(1,4)} = min{6, 4 + 2} = 6
The minimum tentative distance on the unlabeled node is d(4) = 6. Label node 4 and arc (1, 4) or (3, 4), since both determined d(4). Let us arbitrarily select arc (3, 4). Hence the current shortest-path arborescence becomes arcs (s, 3), (s, 1) and (3, 4). Let y = 4.
Step3: Vertex t has not been labeled, so return to step 2. 4
d(t) = min{d(t), d(4) + a(4,t)} = min{∞, 6 + 2} = 8
The minimum tentative distance label is d(2) = 7. Label node 2 and arc (s, 2), which determined d(2) . The current shortest-path arborescence consists of arcs (s, 3), (s, 1), (3, 4) and (s, 2). Let y = 2. s 1 2 3 4 7 6 s 1 3 4 6 s 1 2 3 4 7 6 t 8

8. Dijkstra’s Algorithm s 1 2 3 4 t Example 17
Dijkstra’s Algorithm
Example 1
loop
Process
Graph 5
Step2:
d(t) = min{d(t), d(2) + a(2,t)} = min{8, 7 + 2} = 9
Thus, vertex t has been labeled at last. Also, arc (4, t), which determined d(t), is labeled. The final shortest-path arborescence consists of arcs (s, 3), (s, 1), (3, 4), (s, 2) and (4, t).
Step3: Vertex t has been labeled then stop s 1 2 3 4 7 6 t 8 9
A shortest path from node s to t consists of arcs (s, 3), (3, 4), and (4, t) with a length of = 8.

9. การสร้างข้อมูลโครงข่าย(Network dataset)1 2

10. การสร้างข้อมูลโครงข่าย(Network dataset)3 4 5 6 7

11. การสร้างข้อมูลโครงข่าย(Network dataset)8 9 10 11

12. การสร้างข้อมูลโครงข่าย(Network dataset)

13. การวิเคราะห์ข้อมูลโครงข่ายในArcMap
การวิเคราะห์ข้อมูลโครงข่ายของ Network Analyst Extension ใน ArcMap นั้นสามารถทำได้โดย Enable Network Analyst Extension ก่อน จากแถบ Tools->Extensions จากนั้นคลิก ขวาที่แถบเครื่องด้านบนแล้วเลือก Network Analyst จะปรากฎ แถบเครื่องมือ Network Analyst ดังรูป
ทั้งนี้การระบุตําแหน่งที่ใช่ในการวิเคราะห์โครงข่ายและการ กําหนดคุณสมบัติในการวิเคราะห์จะกระทําผ่านหน้าต่าง Network Analyst ซึ่งสามารถเปิดได้โดยคลิกที่ปุ่ม โดย หน้าต่างจะมีลักษณะดังรูป

14. Types of network analyses
Finding the best route
Finding the closest facility
Finding service areas
Creating an OD cost matrix
Solving a vehicle routing problem

15. 1. Finding the best route
ArcGIS Network Analyst can find the best way to get from one location to another or the best way to visit several locations.
The locations can be specified interactively by placing points on the screen, by entering an address, or by using points in an existing feature class or feature layer.
The best route can be determined for the order of locations as specified by the user.
Alternatively, ArcGIS Network Analyst can determine the best sequence to visit the locations.

16. 1. Finding the best route
Whether finding a simple route between two locations or one that visits several locations, people usually try to take the best route. But best route can mean different things in different situations.
The best route can be the quickest, shortest, or most scenic route, depending on the impedance chosen.
If the impedance is time, then the best route is the quickest route.
Hence, the best route can be defined as the route that has the lowest impedance, where the impedance is chosen by the user.
Any valid network cost attribute can be used as the impedance when determining the best route.

17. 1. Finding the best route
There are 2 ways to add stops: from a point feature class or by adding points to the display.
In the Network Analyst Window, right-click Stops and click Load Locations.
On the Network Analyst toolbar, click the Create Network Location tool
Click the Solve button on the Network Analyst toolbar.
Stops are locations among which a least-cost route is calculated in a route analysis. You can preset their order or the route solver can set them in a way that minimizes total cost. Furthermore, a start and end stop can be set and the solver will determine the best order for all the other stops.
Barriers are locations where the analysis should not traverse. Barriers can be used to represent locations where the analysis can't pass through; for instance, a blocked intersection. You can model road closures or accident sites as barriers if you want the route to avoid that point.
Routes are routes output from analysis.

18. 1. Finding the best route
In the example below, the first case uses time as an impedance. The quickest path is shown in blue and has a total length of 4.5 miles, which takes 8 minutes to traverse.
In the next case, distance is chosen as the impedance. Consequently, the length of the shortest path is 4.4 miles, which takes 9 minutes to traverse.

19. 1. Finding the best route
Along with the best route, ArcGIS Network Analyst provides directions with turn-by-turn maps that can be printed.

20. 2. Finding the closest facility
Finding the closest hospital to an accident, the closest police cars to a crime scene, and the closest store to a customer's address are all examples of closest facility problems.
When finding closest facilities, you can specify how many to find and whether the direction of travel is toward or away from them.
Once you've found the closest facilities, you can display the best route to or from them, return the travel cost for each route, and display directions to each facility.
Additionally, you can specify an impedance cutoff beyond which ArcGIS Network Analyst should not search for a facility.

21. 2. Finding the closest facility
There are 2 ways to add facilities: from a point feature class or by adding points to the display.
On the Network Analyst Window, right-click Facilities and click Load Locations.
On the Network Analyst toolbar, click the Create Network Location tool
Click the Solve button on the Network Analyst toolbar.
Facilities are locations used in closest facility and service area analyses. In closest facility analysis, you search for the closest set of locations (facilities) from other locations (incidents).
Incidents are used in closest facility analysis and represent the locations for which the nearest facility is sought.
Routes layer stores the resultant paths of the closest facility analysis.
Barriers are locations where the analysis should not traverse. Barriers can be used to represent locations where the analysis can't pass through; for instance, a blocked intersection. You can model road closures or accident sites as barriers if you want the route to avoid that point.

22. 2. Finding the closest facility
For instance, you can set up a closest facility problem to search for hospitals within 15 minutes' drive time of the site of an accident. Any hospitals that take longer than 15 minutes to reach will not be included in the results.
The hospitals are referred to as facilities, and the accident is referred to as an incident.
ArcGIS Network Analyst allows you to perform multiple closest facility analyses simultaneously.
This means you can have multiple incidents and find the closest facility or facilities to each incident.

23. 3. Finding service areas
With Network Analyst, you can find service areas around any location on a network.
A network service area is a region that encompasses all accessible streets, that is, streets that lie within a specified impedance.
For instance, the 10-minute service area for a facility includes all the streets that can be reached within ten minutes from that facility.

24. 3. Finding service areas What is accessibility?
Accessibility refers to how easy it is to go to a site.
In ArcGIS Network Analyst, accessibility can be measured in terms of travel time, distance, or any other impedance on the network.
Evaluating accessibility helps answer basic questions, such as, "How many people live within a 10-minute drive from a movie theater?" or "How many customers live within a half-kilometer walking distance from a convenience store?"
Examining accessibility can help you determine how suitable a site is for a new business. It can also help you identify what is near an existing business to help you make other marketing decisions.

25. 3. Finding service areas
There are 2 ways to add facilities: from a point feature class or by adding points to the display.
On the Network Analyst Window, right-click Facilities and click Load Locations.
On the Network Analyst toolbar, click the Create Network Location tool
Click the Solve button on the Network Analyst toolbar.
Facilities are locations used in closest facility and service area analyses. In service area analysis, the location for which the service area is being calculated is the facility.
Barriers are locations where the analysis should not traverse. Barriers can be used to represent locations where the analysis can't pass through; for instance, a blocked intersection. You can model road closures or accident sites as barriers if you want the route to avoid that point.
Service Area Polygons stores the resultant polygons of service area analysis.
Service Area Lines can be symbolized in the same manner as other line feature layers. While performing service area analysis, service area lines are not generated by default. You have to set the parameter to generate Lines on the Service Area Analysis Layer Properties dialog box.

26. 3. Finding service areas Evaluating accessibility
One simple way to evaluate accessibility is by a buffer distance around a point.
For example, find out how many customers live within a 5-kilometer radius of a site using a simple circle.
However, considering people travel by road, this method won't reflect the actual accessibility to the site.
Service networks computed by ArcGIS Network Analyst can overcome this limitation by identifying the accessible streets within five kilometers of a site via the road network.
Once created, you can use service networks to see what is alongside the accessible streets, for example, find competing businesses within a 5-minute drive.

27. 3. Finding service areas Evaluating accessibility
Multiple concentric service areas show how accessibility changes with an increase in impedance.
It can be used, for example, to show how many hospitals are within 5-, 10-, and 15- minute drive times of schools.

28. 4. Creating an OD cost matrix
With ArcGIS Network Analyst, you can create an origin–destination (OD) cost matrix from multiple origins to multiple destinations.
An OD cost matrix is a table that contains the network impedance from each origin to each destination.
Additionally, it ranks the destinations that each origin connects to in ascending order based on the minimum network impedance required to travel from that origin to each destination.

29. 4. Creating an OD cost matrix
There are 2 ways to add origins: from a point feature class or by adding points to the display.
On the Network Analyst Window, right-click Origins and click Load Locations.
On the Network Analyst toolbar, click the Create Network Location tool
Click the Solve button on the Network Analyst toolbar.
Origins are used in an origin-destination (OD) cost matrix as starting locations from where the route costs to destinations are calculated.
Destinations are network locations that are used in an OD cost matrix analysis to generate lines. An OD cost matrix is a table of route costs from origins to destinations.
Lines stores the resultant paths of OD cost matrix analysis.
Barriers are locations where the analysis should not traverse. Barriers can be used to represent locations where the analysis can't pass through; for instance, a blocked intersection. You can model road closures or accident sites as barriers if you want the route to avoid that point.

30. 4. Creating an OD cost matrix
The best network path is discovered for each origin-destination pair, and the cost is stored in the attribute table of the output lines, which are straight lines.
The graphic shows the results of an OD cost matrix analysis that was set to find the cost to reach the four closest destinations from each origin.

31. 4. Creating an OD cost matrix
The closest facility and OD cost matrix solvers perform very similar analyses; the main difference, however, is in the output and the computation speed.
The OD cost matrix solver is designed for quickly solving large MxN problems and as a result does not internally contain information that can be used to generate true shapes of routes and driving directions.
If you need driving directions or true shapes of routes, use the closest facility solver, otherwise use the OD cost matrix solver to reduce the computation time.

32. 5. Solving a vehicle routing problem
A dispatcher managing a fleet of vehicles is often required to make decisions about vehicle routing.
One such decision involves how to best assign a group of customers to a fleet of vehicles and to sequence and schedule their visits.
The objectives in solving such vehicle routing problems (VRP) are to provide a high level of customer service by honoring any time windows while keeping the overall operating and investment costs for each route as low as possible.
The constraints are to complete the routes with available resources and within the time limits imposed by driver work shifts, driving speeds, and customer commitments.

33. 5. Solving a vehicle routing problem
Orders are network locations that are used in vehicle routing problem analysis to represent customers that require some kind of on-site service such as a delivery, pickup, or inspection visit.
Depots are network locations that are used in vehicle routing problem analysis to represent starting, ending, or renewal locations for each route that is part of the analysis.
Routes This feature layer stores routes that are part of a given vehicle routing problem analysis layer. A route specifies the vehicle and driver characteristics as well as represents the traversal between depots, orders, and breaks. In ArcGIS Network Analyst, vehicles, routes, and drivers are synonymous, and the term "route" is used to encompass all three.
Depot Visits contains information on the depots visited for each route in a vehicle routing problem analysis layer. It provides information about the visit type at a depot such as starting depot, ending depot, or renewal depot; total quantities loaded and unloaded at the depot; and additional information that is useful in interpreting a vehicle routing problem solution. This feature layer is an output-only network analysis class and contains features that are generated by the solver during the solve operation.
Breaks are stores breaks that are part of a given vehicle routing problem analysis layer. A break specifies a rest period for a route. It has a duration and a time window in which it must begin. A break can be taken after completing an order, en route to an order, or prior to servicing an order. Each route can have at most one break.

34. 5. Solving a vehicle routing problem
Route Zones are stores route zones that are part of a given vehicle routing problem analysis layer. Route zones specify a work territory for a given route. A route zone is a polygon feature and is used to constrain routes to servicing only those orders that fall within or near a certain area.
Route seed points are used to specify point-based clustering for the routes. Typically the closer an order is to a route's seed point, the more likely the order is to be assigned to that route—as long as other criteria are met, such as specialties and capacities.
Route Renewals are used to specify the routes to which the renewals apply and the depots in the Depots feature layer that can act as renewal locations.
Specialties table are stores route specialties that are part of a given vehicle routing problem analysis layer. An order may require a technician with a certain skill set or a vehicle with certain capabilities. This is modeled by specifying a set of specialties needed by the order and by associating specialties to each route (or vehicle). A route can service an order only if it has all the specialties required for that order.
OrderPairs are stores order pairs that are part of a given vehicle routing problem analysis layer. Sometimes it is required that the pickup and delivery for orders be paired. The OrderPairs table is used to pair delivery and pickup orders in a vehicle routing problem analysis.
Barriers can be used to represent locations where the analysis can't pass through

35. 5. Solving a vehicle routing problem
Consider an example of delivering goods to grocery stores from a central warehouse location.