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

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 | 1.41421356237 | 6.41421356237 |         0 |            3 |  9.41421356237
   4 |           1 |          1 |        4 |         2 |        2 |    20 | 1.41421356237 | 10.8284271247 |         0 |            2 |  12.8284271247
   5 |           1 |          1 |        5 |         3 |        2 |     0 |             1 | 13.8284271247 |         0 |            3 |  16.8284271247
   6 |           1 |          1 |        6 |         6 |       -1 |     0 | 1.41421356237 | 18.2426406871 |         0 |            0 |  18.2426406871
   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 |  2.2360679775 |  7.2360679775 |         0 |            3 |  10.2360679775
  10 |           2 |          1 |        4 |         6 |       -1 |     0 |             2 | 12.2360679775 |         0 |            0 |  12.2360679775
  11 |          -2 |          0 |        0 |        -1 |       -1 |    -1 | 11.4787086646 |            -1 |         2 |           17 |  30.4787086646
(11 rows)

See Also

Indices and tables