Ambulance routing in disaster response considering variable patient condition: NSGA-II and MOPSO algorithms

Masoud Rabbani; Nastaran Oladzad-Abbasabady; Niloofar Akbarian-Saravi

doi:10.3934/jimo.2021007

Article Contents

2022, Volume 18, Issue 2: 1035-1062. Doi: 10.3934/jimo.2021007

This issue Previous Article Stabilization of 2-d Mindlin-Timoshenko plates with localized acoustic boundary feedback Next Article A unified analysis for scheduling problems with variable processing times

Ambulance routing in disaster response considering variable patient condition: NSGA-II and MOPSO algorithms

1.
School of Industrial Engineering, University of Tehran, Tehran, Iran

^* Corresponding author: Masoud Rabbani, Tel: +98 21 88335605, Email: mrabani@ut.ac.ir
^* Corresponding author: Masoud Rabbani, Tel: +98 21 88335605, Email: mrabani@ut.ac.ir

Received: May 2020

Revised: September 2020

Early access: January 2021

Published: March 2022

Abstract Full Text(HTML) Figure(20) / Table(7) Related Papers Cited by

Abstract

The shortage of relief vehicles capacity is a common issue throughout disastrous situations due to the abundance of injured people who need urgent medical aid. Hence, ambulances fleet management is highly important to save as many injured individuals as possible. In this regard, the present paper defines different patient groups based on their needs and characteristics. In order to provide the affected people with proper and timely medical aid, changes in their health status are also considered. A Mixed-integer Linear Programming (MILP) model is proposed to find the best sequence of routes for each ambulance and minimize the latest service completion time (SCT) as well as the number of patients whose condition gets worse because of receiving untimely medical services. Non-dominated Sorting Genetic Algorithm II (NSGA-II) and Multi-Objective Particle Swarm Optimization (MOPSO) are used to find high-quality solutions over a short time. In the end, Lorestan province, Iran, is considered as a case study to assess the model's performance and analyze the sensitivity of solutions with respect to the major parameters, which results in insightful managerial suggestions.

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Mathematics Subject Classification: Primary: 90C11.

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Figure 1. Requests classification and changes in patient condition

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Figure 2. The flowchart of NSGA-II

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Figure 3. An illustrative example of the decoding process

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Figure 4. An illustrative example of the classical order crossover

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Figure 5. An illustrative example of the two-point swap mutation

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Figure 6. The flowchart of MOPSO

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Figure 7. Results of NSGA-II parameter tuning based on the Taguchi method

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Figure 8. Results of MOPSO parameter tuning based on the Taguchi method

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Figure 9. Optimal Pareto front for test instance 1

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Figure 10. Pareto front approximation for test instance 10

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Figure 11. Comparison of NSGA-II and MOPSO based on CPU time

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Figure 12. Comparison of NSGA-II and MOPSO based on RNI

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Figure 13. Comparison of NSGA-II and MOPSO based on DM

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Figure 14. Comparison of NSGA-II and MOPSO based on SM

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Figure 15. Comparison of NSGA-II and MOPSO based on GD

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Figure 16. Lorestan province hospital locations and post-disaster potential locations for medical demands

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Figure 17. Alternation of OFVs according to the variation in the number of hospitals

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Figure 20. Alternation of OFVs according to the variation of travel time

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Figure 18. Alternation of OFVs according to the variation in the number of ambulances

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Figure 19. Alternation of OFVs according to the variation in the number of patients

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Table 1. Assumptions considered in the related works on emergency medical service

Authors	Objective function	Problem	Modes	Variable condition	Patient groups	Solution approach
Talarico et al. [40]	Min max response time	Routing	_	_	X	Heuristic
Jotshi et al. [26]	Max demand coverage/Min coverage cost	Routing	_	_	X	Heuristic
Schuurman et al. [37]	Max demand coverage	Locating	_	_	_	Exact
Erdemir et al. [12]	Min establishment cost/Max demand coverage	Locating	X	_	_	Heuristic
Branas et al. [7]	Min average response time	Locating	_	_	_	Heuristic
Furuta and Tanaka [14]	Min max transfer time/Min response time	Locating	X	_	_	Exact
Sasaki et al. [35]	Min transfer time	Locating	_	_	_	Exact
Berman et al. [5]	Min transfer time	Locating	_	_	_	Heuristic
Hosseinijou and Bashiri [25]	Min max distance	Locating	_	_	_	Exact: analytical/numerical
Kalantari et al. [27]	Min transfer time	Locating	_	_	_	Heuristic
Camacho et al. [8]	Min response time	Distribution	X	_	_	Exact
Tikani and Setak [41]	Min max response time	Routing	_	_	X	Heuristic
Fitzsimmons and Srikar [13]	Min max response time	Locating	_	_	_	Heuristic
Gendreau et al. [19]	Max demand coverage	Relocating	_	_	_	Heuristic
Knight et al. [28]	Max survival probability	Locating	_	_	X	Heuristic
Toro-Díaz et al. [45]	Min response time/Max demand coverage	Locating/dispatching	_	_	_	Heuristic
Andersson and Värbrand [1]	Min max transfer time	Locating/dispatching	_	_	_	Heuristic
Schmid [36]	Min average response time	Relocating/dispatching	_	_	_	Heuristic
Goldberg and Listowsky [23]	_	Routing	_	_	_	Survey
Tlili et al. [44]	Min travel cost	Routing	_	_	_	Heuristic
Bozorgi-Amiri et al. [6]	Min transfer time	Locating	X	_	_	Exact
Navazi et al. [30]	Min establishment cost/Min response time	Locating	X	_	_	Exact
This paper	Min max response time/Min number of patients	Routing	_	X	X	Heuristic

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Table 2. Employed notation for modeling the ARP

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Table 3. Adjusted parameters for NSGA-II and MOPSO

Algorithm	Parameter
Algorithm	$ N_{pop} $	$ max-it $	$ p_c $	$ p_m $	$ p_m $	$ w $	$ c_1 $	$ c_2 $
NSGA-II	75	100	0.6	0.2	_	_	_	_
MOPSO	100	125	_	_	75	0.5	1.25	1.5

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Table 4. Results of the 15 problem instances using NSGA-II and MOPSO

Problem Num.	Dimension	NSGA-II					MOPSO					Optimal
Problem Num.	Dimension	CPU time (s)	RNI	DM	SM	GD	CPU time (s)	RNI	DM	SM	GD	CPU time (s)
1	(3, 4, 4, 3)	124.23	0.31	2.1253	0.0079	0.005	136.61	0.16	1.9872	0.0098	0.005	15
2	(5, 6, 8, 6)	132.4	0.37	1.5231	0.0091	0.003	148.25	0.11	1.9865	0.0111	0.005	89
3	(8, 10, 10, 7)	139.87	0.29	3.2964	0.0082	0.003	161.2	0.2	5.2964	0.0109	0.006	236
4	(12, 15, 13, 11)	149.12	0.4	0.4374	0.011	0.004	169.59	0.33	0.1381	0.0147	0.004	894
5	(15, 17, 15, 13)	156.76	0.64	1.0964	0.0054	0.006	175.32	0.42	2.1784	0.0021	0.006	2601
6	(20, 23, 20, 18)	161.2	0.57	1.4384	0.0066	0.003	183.82	0.62	5.9824	0.0069	0.002	8732
7	(20, 24, 22, 20)	168.94	0.59	1.9842	0.0069	0.001	187.48	0.48	3.9855	0.0132	0.003	15000
8	(25, 28, 21, 20)	175.54	0.21	4.7337	0.0074	0.005	193.56	0.15	2.9156	0.0097	0.007	15000
9	(25, 27, 25, 21)	179.36	0.28	3.341	0.0043	0.002	195.7	0.27	3.4415	0.004	0.008	15000
10	(30, 32, 24, 22)	188.87	0.88	3.7609	0.0121	0.003	210.1	0.42	4.5699	0.0158	0.005	15000
11	(40, 43, 29, 25)	194.3	0.91	1.2745	0.0108	0.001	223.24	0.81	6.1801	0.0124	0.001	15000
12	(50, 55, 41, 32)	212.25	0.73	2.8954	0.0039	0.002	240.51	0.83	4.0643	0.0061	0.001	15000
13	(75, 83, 66, 45)	237.86	0.77	5.762	0.0089	0.006	271.24	0.5	5.957	0.009	0.008	15000
14	(90, 95, 70, 51)	264.22	0.86	3.8713	0.0077	0.005	284.5	0.46	3.869	0.0111	0.005	15000
15	(100, 112, 84, 62)	283.67	0.94	1.8751	0.0106	0.005	303.2	0.73	5.5147	0.0131	0.006	15000

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Table 5. The analytical results of two-sample t-test

Criteria	Optimal method	Average results		Two-sample t-test
Criteria	Optimal method	NSGA-II	MOPSO	Comparison of means	P-value
CPU time (s)	Both methods	194.5727	205.6213	$ \mu_{NSGA-II}=\mu_{MOPSO} $	0
RNI	NSGA-II	0.5833	0.4326	$ \mu_{NSGA-II}> \mu_{MOPSO} $	0.32
DM	MOPSO	2.6276	3.8711	$ \mu_{NSGA-II}< \mu_{MOPSO} $	0.212
SM	NSGA-II	0.0079	0.0098	$ \mu_{NSGA-II}< \mu_{MOPSO} $	0.901
GD	NSGA-II	0.0036	0.0048	$ \mu_{NSGA-II}< \mu_{MOPSO} $	0.625

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Table 6. Data related to the Lorestan province cities

City name	Population	% of injured people	% of GC demands	% of RC demands
Aleshtar	33, 132	30%	88%	12%
Aligudarz	89, 521	21%	49%	51%
Azna	41, 703	27%	83%	17%
Borujerd	245, 730	19%	77%	23%
Dorud	100, 979	32%	66%	34%
Khorramabad	354, 854	15%	41%	59%
Kuhdasht	111, 737	28%	58%	42%
Nur Abad	62, 195	34%	71%	29%
Pol Dokhtar	32, 590	26%	92%	8%

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Table 7. Data related to the Lorestan province hospitals

Hospital name	RC patient capacity	Number of ambulances
Ibn Sina	120	25
Imam Ali	215	30
Imam Jafar Sadegh	148	28
Imam Khomeini	270	41
Kuhdasht	132	27
Shohada-ye Ashayer	347	40
Shahid Chamran	221	36
Shohada-ye Haftom Tir	150	20

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