Genetic algorithm for obstacle location-allocation problems with customer priorities

Ashkan Ayough; Farbod Farhadi; Mostafa Zandieh; Parisa Rastkhadiv

doi:10.3934/jimo.2020044

Article Contents

2021, Volume 17, Issue 4: 1753-1769. Doi: 10.3934/jimo.2020044

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Genetic algorithm for obstacle location-allocation problems with customer priorities

1.
Department of Industrial Management, School of Management and Accounting, Shahid Beheshti University, G.C., Tehran, Iran
2.
Mario J. Gabelli School of Business, Roger Williams University, 1 Old Ferry Road, Bristol, RI 02809, USA
3.
Kar Higher Education Institute, Tehran, Iran

Corresponding author: Mostafa Zandieh
Corresponding author: Mostafa Zandieh

Received: July 31, 2018

Revised: May 31, 2019

Early access: March 2020

Published: July 2021

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Abstract

In this paper we propose a metaheuristic approach to solve a customer priority based location-allocation problem in presence of obstacles and location-dependent supplier capacities. In many network optimization problems presence of obstacles prohibits feasibility of a regular network design. This includes a wide range of applications including disaster relief and pandemic disease containment problems in healthcare management. We focus on this application since fast and efficient allocation of suppliers to demand nodes is a critical process that impacts the results of the containment strategy. In this study, we propose an integrated mixed-integer program with location-based capacity decisions that considers customer priorities in the network design. We propose an efficient multi-stage genetic algorithm that solves the problem in continuous space. The computational findings show the best allocation strategies derived from proposed algorithms.

Keywords:

Capacitated Obstacle Location-allocation,
Emergency Management,
Disease Outbreak,
Facility Location,
Visibility Graph,
Customer Priority,
Genetic Algorithm.

Mathematics Subject Classification: Primary: 90B10, 90C11; Secondary: 90C59.

Citation:

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Figure 1. Obstacle and the marginal area

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Figure 2. Alternative connecting paths around an obstacle

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Figure 3. Visibility graph method around the obstacles

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Figure 4. Type two chromosome crossover

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Figure 5. Supplier and demand network in the sample

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Figure 6. Convergence of GCOLAP1 and GCOLAP2 on the sample

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Table 1. Sample instance from randomly generated instances

Parameter	Value
Number of customers	17
Number of distribution centers	3
Number of forbidden areas	1
The radius of margin	15
The coordinates of margin center	(50, 30)
Number of corners of each of regions	5

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Table 2. Summary of computational results on randomly generated instances

			Objective Function
Instance	m	n	R-SCOLAP	SCOLAP	GCOLAP1	GCOLAP2	MIP gap	GA gap
1	2	8	0.0435	19.41	25.44	26.96	0	0.31
2	2	10	0.0443	30.56	36.57	34.21	0	0.2
3	2	12	0.0424	33.26	39.18	47.41	0	0.18
4	2	15	0.0493	65.52	80.89	77.46	0	0.23
5	3	17	0.0443	65.5	87.34	105.68	0	0.33
6	3	20	0.0542	138.12	177.07	139.72	0.00009	0.28
7	3	25	0.0677	163.25	209.29	214.77	0.0001	0.28
8	3	30	0.0723	273.86	329.96	277.23	0.00254	0.2
9	4	35	0.0738	-	249.24	501.61	-	-
10	4	40	0.0881	-	387.83	500.64	-	-
11	4	44	0.0733	-	618.62	645.86	-	-
12	5	47	0.077	-	721.32	941.63	-	-
13	5	50	0.138	-	835.72	1122.76	-	-
14	5	55	0.0971	-	854.85	1025.11	-	-
15	6	60	0.1343	-	1542.82	1825.43	-	-
16	6	65	0.1067	-	1382.88	1738.93	-	-
17	7	70	0.1536	-	1699.78	2836.1	-	-
18	7	74	0.1206	-	2021.15	2590.2	-	-
19	8	78	0.1088	-	2145.16	3079.13	-	-
20	8	82	0.1156	-	3210.13	3450.84	-	-

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