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Routing and Logistics with TransCAD. Network Flow Models. Introduction.

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## Routing and Logistics with TransCAD

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### Routing and Logistics with TransCAD

Network Flow Models

Introduction

- You need to ship an inventory of goods from 15 warehouses to 100 retail centers, each with a given demand, and you want to determine which warehouses should service which retail centers to minimize the total transportation cost.
- You need to route empty rail cars from their current locations to locations where they are required for new loads, taking into account rail traffic density by link.

Introduction

- You need to assign 100 employees to 100 projects, to minimize the total time spent or to produce work of the highest quality
- You need to assign jobs to machines such that the total process time is minimized
- As a production manager, you need to schedule production of a product at several different plants, given a certain geographic pattern of demand, to minimize the overall production and transportation cost

Types of Network Flow Models

- The Minimal Spanning Tree Problem
- The Bipartite and Non-Bipartite Weighted Matching Problems
- The Transportation Problem
- The Minimum Cost Flow Problem

Solving Weighted Matching Problem

- The Bipartite Weighted Matching Problem is the problem of finding the best (the least cost or the maximal benefit) one-to-one matching between two groups of objects.
- Assign employees to projects, so as to minimize the total length of time required to complete all the projects
- Assign tenants to apartments, so as to maximize the level of satisfaction
- Assign medical school graduates to a set of available internships, so as to maximize the exposure of graduates to appropriate medical procedures

Solving Weighted Matching Problem

- The Non-Bipartite Weighted Matching Problem is the problem of dividing a group of objects into pairs, such that the total cost is minimized or the total benefit is maximized.

Preparing Data for the Weighted Matching Procedures (Bipartite)

- A point or area layer containing the origins and destinations, or one layer for the origins and another for the destinations
- If the origins and destinations are in the same layer, a selection set of origins and a selection set of destinations (that contain the same number of features)
- A cost or benefit matrix indicating the cost or benefit of assigning each origin to each destination

Preparing Data for the Weighted Matching Procedures (non-Bipartite)

- Just need one point or area layer, a selection set in the layer, and the cost matrix
- Each row of the matrix represents an origin, and each column a destination.
- A missing value indicates that a particular origin and destination cannot be assigned to each other.

Solving the Transportation Problem

- The Transportation Problem involves identifying the most efficient way to service a set of destinations from a set of origins.
- A simple example is a company that needs to deliver goods to retail stores from two or move warehouses.
- Each warehouse has some supply of product, and each store requires that a certain volume of product be delivered.

Preparing Data

- A point layer containing the origins and destinations, or one layer for the origins and another for the destinations.
- If the origins and destinations zare in the same layer, a selection set of origins and a selection set of destinations
- A cost matrix indicating the cost of shipping a unit of product from each origin to each destination

Preparing Data

- Origin layer
- Supply (integer)
- Destination layer
- Demand (integer)
- If you are using a network-base cost matrix, you must also include the following field for both the origins and destinations:
- NodeID (integer)

To Solve the Transportation Problem(TRNSPORT.WRK)

If you have not alreasy done so, open or create a map containing the origin and destination layers, create any necessary selection sets, then open or create the cost matrix

Minimum Cost Flow Problem

- The Minimum Cost Flow Problem is a more general version of the Transportation Problem that takes link capacities into account.
- A simple case of the Minimum Cost Flow Problem is a requirement to ship some quantity of product from a single origin to a single destination, where capacity constraints make it impossible to utilize the shortest path for the entire shipment.
- In another common example, goods must be shipped from several origins to several destinations, but there are bottlenecks such as bridges or tunnels that limit the volume of flow.

Preparing Data for the Minimum Cost Flow Procedure

- A point layer containing the origins and destinations, or one layer for the origins and another for the destinations
- If the origins and destinations are in the same layer, a selection set of origins and a selection set of destinations
- A link layer containing cost and capacity data for each link
- A network, created from the line layer, that includes the cost and capacity data

Origin layer

Supply (integer)

Destination layer

Demand (integer)

The link layer must have the following fields:

Capacity (integer)

Cost (numeric)

If the origins or destinations are not part of the network (that is, if they come from and area or point layer that is separate from the line layer used to create the network), then you must also include the following field:

NodeID (integer)

Preparing Data for the Minimum Cost Flow ProcedureTo Solve the Minimum Cost Flow Problem

If you have not already done so, open or create a map containing the origin and destination layer(s) and the line layer from which the network is built, and open or create a network file.

Error Conditions

- The minimum cost flow procedure exits with an error message if any of the following conditions occurs:
- The total demand is not equal to the total supply
- A demand or supply quantity has negative or missing values
- A node ID is not found in the network

Building a Network or Straight-Line Based Cost Matrix

- The Cost Matrix procedure is a utility that helps you construct a matrix file of network or straight-line distance or time between features in one or two map layers.
- You can compute a matrix in which the origins and destinations are from different layers.
- You can use a network to compute the cost of travel between features even if they are not explicitly part of the network. Ex: you can estimate the network distance or travel time between customer locations using a street network, even if the customers are not nodes in the network.

Building a Network or Straight-Line Based Cost Matrix

- To Create a cost matrix you must choose the following:
- The origins you want to include
- The destinations you want to include
- The method you want to use to measure the shortest path costs

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