Route Planning Software and Hybrid Genetic Algorithm Design of a DSS to solve the routing problem in a Courier Service

Ph. D. Walter Vaca Arellano (EPN)

Ing. James Tomalá Robles

(UTE Universidad Tecnológica Equinoccial)

Ing. Johnny Pincay Villa (ESPOL)

EcuadorALIO-INFORMS meeting Buenos Aires

2010

Instituto de Ciencias Matemáticas-ESPOL

Motivation

In Ecuador, there are approximately 800 courier agencies, and all of them use empirical methods to

plan their routes

It directly affects the two objectives of integrated

logistics

Problem: the absence of a decision support system applying heuristic procedures for the transport operations planning of a courier company

Objectives1. Obtain a model

for courier delivery problem.

2. Design and develop a Metaheuristic based on genetic algorithm.

3. Propose a DSS design that uses the developed metaheuristic.

Mathematic formulationCapacitated Vehicle Routing Problem with smooth Time windows

Visitar todos los clientes una sola vez.

Todos los vehículos salen del depósito.

Mathematic formulation

Cada ruta es realizada por un solo vehículo.

La demanda no puede superar la capacidad del vehículo.

Se respeta la atención más temprana del cliente y se permite atraso.

Continuidad del tiempo y eliminación de subtours. Miller, Tucker y Zemlin [2].

Var. Binaria y positivos

GA for CVRPTW

Evolutionary Strategy

local search heuristics

Restrictions of time windows

GA for CVRPTW

Thangiagh [16], Bonrostro, Zhu[17], Homberger y Gehring [23]

On a review of GA publications, we may be concluded that GA requires modification of the classic genetic operators such as:

a) Redesign of the mutation and crossover operators.b) Inclusion of local search to improve solutions.c)And considerations of time constrains

Generation of population

Reproductive And

improving stage

BEGIN /* Hybrid Genetic Algorithm*/

Cargar_datos() //reads data from a filet←0

Po←generacion_poblacion_incial()

WHILE (t ≤ NUM_ITERACIONES) DO

/* Produce new generation*/

evaluacion_poblacion(Pt)

Pt<-mutacion_padres(Pt)

Pt← generar_hijos(Pt) // Produce new individuals with strategy (µ, λ )-EA t←t+1

END

END

Half - insertion heuristicHalf- Ramdomly

improving routesunifies routes

Replace if the child is better than one parent

The metaheuristic

chromosome representation

• chromosome:

1

0Dep

7

3

5

8

4

6

2

2

34

3

11

1

2

2

1

2

 2 8  3  9  7  4  6 10  5  1

It adopts the permutation representation of integers, where the routes separator is a number greater than n, where n is the number of clients

evaluation , Fitness, Selection

• cost of the route:

• Penalty for delay :

• Cost of the solution (Fitness):

• Selection:

ordering the individuals in the population according to their fitness, that is, lowest to highest cost, and randomly selects among which are located below from 40th percentile.

Mutation

improve routes

unify routes

For i=1 ; i<= MOV_MUT

Select a local search operator{2-Opt *, relocation , exchange }Operator is applied

It tries to delete a route

Based on Homberger y Gehring [16].

combination operator

fatherBest routes

motherBest routes

Child

Inherit

The best

Based on uniform Crossover (UC) Áslaug Sóley Bjarnadóttir [11]

The combination strategy selects the best routes from the parents and insert them to the child provided it’s not conflict.

Proposal DSS

BD: Orders,demand

the TMS (Transportation  managemen system)

WEB APPLICATION:DSS

planningmodule

APIGoogle Maps

component that calculates the distances  between each pair of 

customersInternet Hybrid GA

(Metaheurística )

Road and georeferential 

DATA

Test results of solomon

optimum our solution

InstanceNumber of routes

Cost Number of routes

Cost

C101 10 827.30 10 828.94C102 10 827.30 10 828.94R104 10 982.010 10 1174.84R111 12 1048.70 11 1316.00RC103 11 1258.0 11 1424.34

The developed strategy to solve the problem requires less computational effort when data is grouped by area, it was found that in these cases, the number of iterations needed to reach a good solution is less than 40. On the other hand, we must increase the number of iterations when customers are completely randomly distributed in a geographical region.

Results – Study Case

RUT

A ORDEN DE VISITAS

CLIENTE

S

1

0-5-33-66-39-20-45-26-32-48-61-34-17-9-21-27-10-56-4-

12-29-0 20

2

0-7-38-37-23-57-24-35-52-25-54-65-51-60-43-62-36-63-

55-15-49-0 20

3 0-14-44-18-47-22-13-16-53-40-31-30-59-3-46-6-58-0 16

4 0-1-50-19-28-11-8-42-41-2-64-0 10RUTAS T ESPERA T ATRASO T SERVICIO T RUTA TOTAL

1 0:22:12 0:00:00 2:31:48 2:10:12 5:04:12

2 0:10:48 0:00:36 2:11:24 1:57:36 4:20:24

3 0:00:00 0:00:00 1:54:00 1:12:00 3:06:00

4 0:00:00 0:00:00 1:58:12 1:16:48 3:15:00

TOTAL 0:33:00 0:00:36 8:35:24 6:36:36 15:45:36

The developed Metaheuristic increases the level of service to 98.46%

According to company data, the average

service level of the first quarter of 2009, was 69.35%, ie, 20 clients were not treated on

time.

Example prototype using the Google Maps API

• available: www.ecualogistic.com/ruteo.php

The example prototype shows the solution of the case study.Each client has been located on the map according to their geographical location , additionally displays data such as order of visit, time of arrival and departure time. it was developed using javascript and dynamic language php.

Muchas gracias por su atención

James Tomalájtomala@ecualogistic.com

www.ecualogistic.com