# Concepts¶

## General documentation¶

Vehicle Routing Problems VRP are NP-hard optimization problem, it generalises the travelling salesman problem (TSP).

• The objective of the VRP is to minimize the total route cost.

• There are several variants of the VRP problem,

vrpRouting does not try to implement all variants.

## Characteristics¶

• Capacitated Vehicle Routing Problem CVRP where The vehicles have limited carrying capacity of the goods.

• Vehicle Routing Problem with Time Windows VRPTW where the locations have time windows within which the vehicle’s visits must be made.

• Vehicle Routing Problem with Pickup and Delivery VRPPD where a number of goods need to be moved from certain pickup locations to other delivery locations.

Limitations

• No multiple time windows for a location.

• Less vehicle used is considered better.

• Less total duration is better.

• Less wait time is better.

### Pick & Delivery¶

Problem: CVRPPDTW Capacitated Pick and Delivery Vehicle Routing problem with Time Windows

• Times are relative to 0

• The vehicles

• have start and ending service duration times.

• have opening and closing times for the start and ending locations.

• have a capacity.

• The orders

• Have pick up and delivery locations.

• Have opening and closing times for the pickup and delivery locations.

• Have pickup and delivery duration service times.

• have a demand request for moving goods from the pickup location to the delivery location.

• Time based calculations:

• Travel time between customers is $$distance / speed$$

• Pickup and delivery order pair is done by the same vehicle.

• A pickup is done before the delivery.

## Getting Started¶

This is a simple guide to walk you through the steps of getting started with vrpRouting. In this guide we will cover:

### Create a routing Database¶

The first thing we need to do is create a database and load pgrouting in the database. Typically you will create a database for each project. Once you have a database to work in, your can load your data and build your application in that database. This makes it easy to move your project later if you want to to say a production server.

For Postgresql 9.2 and later versions

createdb mydatabase
psql mydatabase -c "create extension postgis"
psql mydatabase -c "create extension pgrouting"


#### Handling Parameters¶

To define a problem, several considerations have to be done, to get consistent results. This section gives an insight of how parameters are to be considered.

### Capacity and Demand Units Handling¶

The capacity of a vehicle, can be measured in:

• Volume units like $$m^3$$.

• Area units like $$m^2$$ (when no stacking is allowed).

• Weight units like $$kg$$.

• Number of boxes that fit in the vehicle.

• Number of seats in the vehicle

The demand request of the pickup-deliver orders must use the same units as the units used in the vehicle’s capacity.

To handle problems like: 10 (equal dimension) boxes of apples and 5 kg of feathers that are to be transported (not packed in boxes).

If the vehicle’s capacity is measured by boxes, a conversion of kg of feathers to equivalent number of boxes is needed. If the vehicle’s capacity is measured by kg, a conversion of box of apples to equivalent number of kg is needed.

Showing how the 2 possible conversions can be done

Let: - $$f_boxes$$: number of boxes that would be used for 1 kg of feathers. - $$a_weight$$: weight of 1 box of apples.

Capacity Units

apples

feathers

boxes

10

$$5 * f\_boxes$$

kg

$$10 * a\_weight$$

5

#### Locations¶

• When using the Euclidean signatures:

• The vehicles have $$(x, y)$$ pairs for start and ending locations.

• The orders Have $$(x, y)$$ pairs for pickup and delivery locations.

• When using a matrix:

• The vehicles have identifiers for the start and ending locations.

• The orders have identifiers for the pickup and delivery locations.

• All the identifiers are indices to the given matrix.

### Time Handling¶

The times are relative to 0

Suppose that a vehicle’s driver starts the shift at 9:00 am and ends the shift at 4:30 pm and the service time duration is 10 minutes with 30 seconds.

All time units have to be converted

Meaning of 0

time units

9:00 am

4:30 pm

10 min 30 secs

0:00 am

hours

9

16.5

$$10.5 / 60 = 0.175$$

9:00 am

hours

0

7.5

$$10.5 / 60 = 0.175$$

0:00 am

minutes

$$9*60 = 54$$

$$16.5*60 = 990$$

10.5

9:00 am

minutes

0

$$7.5*60 = 540$$

10.5

TBD

TBD

TBD

TBD

TBD

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