# pgRouting Manual (3.0-rc1)

## pgr_pickDeliverEuclidean - Experimental

`pgr_pickDeliverEuclidean` - Pickup and delivery Vehicle Routing Problem

Warning

Possible server crash

- These functions might create a server crash

Warning

Experimental functions

- They are not officially of the current release.
- They likely will not be officially be part of the next release:
  - The functions might not make use of ANY-INTEGER and ANY-NUMERICAL
  - Name might change.
  - Signature might change.
  - Functionality might change.
  - pgTap tests might be missing.
  - Might need c/c++ coding.
  - May lack documentation.
  - Documentation if any might need to be rewritten.
  - Documentation examples might need to be automatically generated.
  - Might need a lot of feedback from the comunity.
  - Might depend on a proposed function of pgRouting
  - Might depend on a deprecated function of pgRouting

Availability

- Version 3.0.0
  - Replaces `pgr_gsoc_vrppdtw`
  - New experimental function

Support

- Supported versions: current(3.0)
- Unsupported versions: 2.6 2.5 2.4 2.3 2.2 2.1

## Synopsis

Problem: Distribute and optimize the pickup-delivery pairs into a fleet of vehicles.

- Optimization problem is NP-hard.
- Pickup and Delivery:
  - capacitated
  - with time windows.
- The vehicles
  - have (x, y) start and ending locations.
  - have a start and ending service times.
  - have opening and closing times for the start and ending locations.
- An order is for doing a pickup and a a deliver.
  - has (x, y) pickup and delivery locations.
  - has opening and closing times for the pickup and delivery locations.
  - has a pickup and deliver service times.
- There is a customer where to deliver a pickup.
  - travel time between customers is distance / speed
  - pickup and delivery pair is done with the same vehicle.
  - A pickup is done before the delivery.

## Characteristics

- No multiple time windows for a location.
- Less vehicle used is considered better.
- Less total duration is better.
- Less wait time is better.
- Six different optional different initial solutions
  - the best solution found will be result

## Signature

    pgr_pickDeliverEuclidean(orders_sql, vehicles_sql [,factor, max_cycles, initial_sol])
    RETURNS SET OF (seq, vehicle_seq, vehicle_id, stop_seq, stop_type, order_id,
        cargo, travel_time, arrival_time, wait_time, service_time, departure_time)

### Parameters

The parameters are:

    orders_sql, vehicles_sql [,factor, max_cycles, initial_sol]

Where:

Column | Type | Default | Description
--- | --- | --- | ---
orders_sql | `TEXT` |  | Pick & Deliver Orders SQL query containing the orders to be processed.
vehicles_sql | `TEXT` |  | Pick & Deliver Vehicles SQL query containing the vehicles to be used.
factor | `NUMERIC` | 1 | (Optional) Travel time multiplier. See Factor Handling
max_cycles | `INTEGER` | 10 | (Optional) Maximum number of cycles to perform on the optimization.

initial_sol

`INTEGER`

4

(Optional) Initial solution to be used.

- `1` One order per truck
- `2` Push front order.
- `3` Push back order.
- `4` Optimize insert.
- `5` Push back order that allows more orders to be inserted at the back
- `6` Push front order that allows more orders to be inserted at the front

### Pick & Deliver Orders SQL

A SELECT statement that returns the following columns:

    id, demand
    p_x, p_y, p_open, p_close, [p_service, ]
    d_x, d_y, d_open, d_close, [d_service, ]

Where:

Column | Type | Default | Description
--- | --- | --- | ---
id | ANY-INTEGER |  | Identifier of the pick-delivery order pair.
demand | ANY-NUMERICAL |  | Number of units in the order
p_open | ANY-NUMERICAL |  | The time, relative to 0, when the pickup location opens.
p_close | ANY-NUMERICAL |  | The time, relative to 0, when the pickup location closes.
d_service | ANY-NUMERICAL | 0 | The duration of the loading at the pickup location.
d_open | ANY-NUMERICAL |  | The time, relative to 0, when the delivery location opens.
d_close | ANY-NUMERICAL |  | The time, relative to 0, when the delivery location closes.
d_service | ANY-NUMERICAL | 0 | The duration of the loading at the delivery location.

For the euclidean implementation, pick up and delivery \((x,y)\) locations are needed:

Column | Type | Description
--- | --- | ---
p_x | ANY-NUMERICAL | \(x\) value of the pick up location
p_y | ANY-NUMERICAL | \(y\) value of the pick up location
d_x | ANY-NUMERICAL | \(x\) value of the delivery location
d_y | ANY-NUMERICAL | \(y\) value of the delivery location

### Pick & Deliver Vehicles SQL

A SELECT statement that returns the following columns:

    id, capacity
    start_x, start_y, start_open, start_close [, start_service, ]
    [ end_x, end_y, end_open, end_close, end_service ]

where:

Column | Type | Default | Description
--- | --- | --- | ---
id | ANY-INTEGER |  | Identifier of the pick-delivery order pair.
capacity | ANY-NUMERICAL |  | Number of units in the order
speed | ANY-NUMERICAL | 1 | Average speed of the vehicle.
start_open | ANY-NUMERICAL |  | The time, relative to 0, when the starting location opens.
start_close | ANY-NUMERICAL |  | The time, relative to 0, when the starting location closes.
start_service | ANY-NUMERICAL | 0 | The duration of the loading at the starting location.
end_open | ANY-NUMERICAL | start_open | The time, relative to 0, when the ending location opens.
end_close | ANY-NUMERICAL | start_close | The time, relative to 0, when the ending location closes.
end_service | ANY-NUMERICAL | start_service | The duration of the loading at the ending location.

For the euclidean implementation, starting and ending \((x,y)\) locations are needed:

Column | Type | Default | Description
--- | --- | --- | ---
start_x | ANY-NUMERICAL |  | \(x\) value of the coordinate of the starting location.
start_y | ANY-NUMERICAL |  | \(y\) value of the coordinate of the starting location.
end_x | ANY-NUMERICAL | start_x | \(x\) value of the coordinate of the ending location.
end_y | ANY-NUMERICAL | start_y | \(y\) value of the coordinate of the ending location.

### Description of the result (TODO Disussion: Euclidean & Matrix)

    RETURNS SET OF
        (seq, vehicle_seq, vehicle_id, stop_seq, stop_type,
            travel_time, arrival_time, wait_time, service_time,  departure_time)
        UNION
        (summary row)

Column | Type | Description
--- | --- | ---
seq | INTEGER | Sequential value starting from 1.
vehicle_seq | INTEGER | Sequential value starting from 1 for current vehicles. The \(n_{th}\) vehicle in the solution.
vehicle_id | BIGINT | Current vehicle identifier.
stop_seq | INTEGER | Sequential value starting from 1 for the stops made by the current vehicle. The \(m_{th}\) stop of the current vehicle.

stop_type

INTEGER

Kind of stop location the vehicle is at:

- `1`: Starting location
- `2`: Pickup location
- `3`: Delivery location
- `6`: Ending location

order_id

BIGINT

Pickup-Delivery order pair identifier.

- `-1`: When no order is involved on the current stop location.

cargo | FLOAT | Cargo units of the vehicle when leaving the stop.

travel_time

FLOAT

Travel time from previous `stop_seq` to current `stop_seq`.

- `0` When `stop_type = 1`

arrival_time | FLOAT | Previous `departure_time` plus current `travel_time`.
wait_time | FLOAT | Time spent waiting for current location to open.
service_time | FLOAT | Service time at current location.

departure_time

FLOAT

\(arrival\_time + wait\_time + service\_time\).

- When `stop_type = 6` has the total_time used for the current vehicle.

Summary Row

Warning

TODO: Review the summary

Column | Type | Description
--- | --- | ---
seq | INTEGER | Continues the Sequential value
vehicle_seq | INTEGER | `-2` to indicate is a summary row
vehicle_id | BIGINT | Total Capacity Violations in the solution.
stop_seq | INTEGER | Total Time Window Violations in the solution.
stop_type | INTEGER | `-1`
order_id | BIGINT | `-1`
cargo | FLOAT | `-1`
travel_time | FLOAT | total_travel_time The sum of all the travel_time
arrival_time | FLOAT | `-1`
wait_time | FLOAT | total_waiting_time The sum of all the wait_time
service_time | FLOAT | total_service_time The sum of all the service_time
departure_time | FLOAT | total_solution_time = \(total\_travel\_time + total\_wait\_time + total\_service\_time\).

Where:

ANY-INTEGER: | SMALLINT, INTEGER, BIGINT
ANY-NUMERICAL: | SMALLINT, INTEGER, BIGINT, REAL, FLOAT

## Example

This example use the following data: TODO put link

    SELECT * FROM pgr_pickDeliverEuclidean(
        'SELECT * FROM orders ORDER BY id',
        'SELECT * from vehicles'
    );
     seq | vehicle_seq | vehicle_id | stop_seq | stop_type | order_id | cargo |   travel_time    |   arrival_time   | wait_time | service_time |  departure_time
    -----+-------------+------------+----------+-----------+----------+-------+------------------+------------------+-----------+--------------+------------------
       1 |           1 |          1 |        1 |         1 |       -1 |     0 |                0 |                0 |         0 |            0 |                0
       2 |           1 |          1 |        2 |         2 |        3 |    30 |                1 |                1 |         1 |            3 |                5
       3 |           1 |          1 |        3 |         3 |        3 |     0 |  1.4142135623731 | 6.41421356237309 |         0 |            3 |  9.4142135623731
       4 |           1 |          1 |        4 |         2 |        2 |    20 |  1.4142135623731 | 10.8284271247462 |         0 |            2 | 12.8284271247462
       5 |           1 |          1 |        5 |         3 |        2 |     0 |                1 | 13.8284271247462 |         0 |            3 | 16.8284271247462
       6 |           1 |          1 |        6 |         6 |       -1 |     0 |  1.4142135623731 | 18.2426406871193 |         0 |            0 | 18.2426406871193
       7 |           2 |          1 |        1 |         1 |       -1 |     0 |                0 |                0 |         0 |            0 |                0
       8 |           2 |          1 |        2 |         2 |        1 |    10 |                1 |                1 |         1 |            3 |                5
       9 |           2 |          1 |        3 |         3 |        1 |     0 | 2.23606797749979 | 7.23606797749979 |         0 |            3 | 10.2360679774998
      10 |           2 |          1 |        4 |         6 |       -1 |     0 |                2 | 12.2360679774998 |         0 |            0 | 12.2360679774998
      11 |          -2 |          0 |        0 |        -1 |       -1 |    -1 | 11.4787086646191 |               -1 |         2 |           17 | 30.4787086646191
    (11 rows)

## See Also

- Vehicle Routing Functions - Category (Experimental)
- The queries use the Sample Data network.

Indices and tables

- Index
- Search Page