The processing facility location-allocation problem for tunnel slag during tunnel construction

Guohua Zhou; Wanting Du

doi:10.3934/jimo.2024006

Article Contents

2024, Volume 20, Issue 7: 2376-2404. Doi: 10.3934/jimo.2024006

This issue Previous Article Homocentric quadratic surfaces and maximum margin approach for imbalanced data classification Next Article Multiple-attribute decision-making for selection of medical robotic engineering based on logarithmic square root neutrosophic normal approach

The processing facility location-allocation problem for tunnel slag during tunnel construction

Guohua Zhou^, and
Wanting Du

South West Jiaotong University, China

^*Corresponding author: Guohua Zhou
^*Corresponding author: Guohua Zhou

Received: August 2022

Revised: March 2023

Early access: January 18, 2024

Published online: January 18, 2024

The first author is supported by Natural Science Foundation of China (No. 71942006) and China State Railway Group Co., Ltd (Project No. N2020G039).

Abstract / Introduction Full Text(HTML) Figure(8) / Table(12) Related Papers Cited by

Abstract

In this paper, we consider the process of resource utilization of tunnel slag, and propose a "regional self-balanced" reverse logistics network. We propose a location-allocation model that takes the uncertainty of availability, various types of output, various types of demand, and various types of facilities into account when solving the location-allocation problem for facilities in the network. According to our research, we obtain a feasible model and algorithm for use in the engineering field, and we find that the logistics cost can be decreased by appropriately increasing the number of facilities and choosing the locations of facilities based on scientific principles, thereby lowering the total cost. We determined the parameters of the algorithm by Taguchi's analysis and verified the effectiveness of the algorithm by comparing it with the exact algorithm and other heuristic algorithms. By analyzing the impact of the availability of tunnel slag on the site selection of facilities, we obtain policy recommendations on the number of facilities.

Keywords:

Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

Citation:

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Figure 1. Comparison of utilization methods of "recycling type" and "regional self-balancing type"

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Figure 2. "Regional self-balancing" reverse logistics network for tunnel slag utilization

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Figure 3. Schematic diagram of the simple model of beetle

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Figure 4. Algorithm flowchart

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Figure 5. Chromosome coding diagram

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Figure 6. Algorithm convergence graph

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Figure 7. Distribution map of tunnel slag utilization in the second construction unit

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Figure 8. Confidence level change analysi

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Table 1. Classification of reverse logistics network

Types of reverse logistics networks	Characteristic	Applicable industries
Repair type	This applies to a single type of item that has been repaired and returned to the forward supply chain or into a remanufacturing process.	Refrigerator repair, etc.
Reuse type	This applies to a single type of item that is returned to the forward supply chain after a simple cleaning, disinfection, etc.	Plastic bottles, etc.
Remanufacture type	This applies to a single type of item that is remanufactured in whole or in part.	Telephone, mobile phone, etc.
Recycling type	It is suitable for a single type of item, and the processing time of this item is long, and the item at the output point cannot directly supply the demand at the demand point. The output point and the demand point have an intersecting relationship.	Construction waste, waste paper, etc.
Regional self-balancing type	It is suitable for a multi-type item. The processing time of the item is short, which can meet the needs of the demand point, and the output point and the demand point have an inclusive relationship.	Tunnel slag

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Table 2. Taguchi design analysis – GA

$ popsize $	$ p_c $	$ p_m $	Run1	Run2	Run3	Run4	Run5	$ S/N $
60	0.06	0.6	4319	4506	4465	4218	4506	-72.88
60	0.08	0.7	4465	4319	4218	4319	4506	-72.80
60	0.1	0.8	4218	4203	4506	4319	4465	-72.76
60	0.12	0.9	4218	4465	4177	4203	4319	-72.62
80	0.06	0.7	4177	4319	4218	4177	4465	-72.61
80	0.08	0.6	3993	4177	4319	4042	3964	-72.26
80	0.1	0.9	3964	3993	4042	3964	4042	-72.04
80	0.12	0.8	4042	4203	4177	3993	4177	-72.30
100	0.06	0.8	4319	4177	4218	4306	4203	-72.56
100	0.08	0.9	3993	4042	4203	4177	3964	-72.21
100	0.1	0.6	4465	4319	4306	4203	4306	-72.71
100	0.12	0.7	3993	4218	4203	4465	4203	-72.50
120	0.06	0.9	4177	3993	4042	3964	4218	-72.21
120	0.08	0.8	4203	4177	4203	3993	4042	-72.31
120	0.1	0.7	4203	4218	4218	4306	4042	-72.46
120	0.12	0.6	4506	4042	4319	4177	4319	-72.62

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Table 3. Taguchi design analysis-BAS

$ k $	$ \delta $	$ d $	Run1	Run2	Run3	Run4	Run5	$ S/N $
10	1300	1300	4734	4465	4678	4203	4902	-73.26
10	1500	1700	4465	4734	4306	4465	4902	-73.22
10	1700	1500	4678	4319	4899	4465	4734	-73.30
20	1300	1700	4306	4203	4902	4899	4319	-73.13
20	1500	1500	4203	4306	4319	4306	4465	-72.71
20	1700	1300	4902	4899	4734	4465	4319	-73.39
30	1300	1500	4734	4465	4899	4203	4203	-73.08
30	1500	1300	4899	4203	4465	4734	4899	-73.35
30	1700	1700	4734	4902	4678	4678	4465	-73.43

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Table 4. Taguchi design analysis - BAS-IGA

$ elite ratio $	$ N_c $	$ \zeta $	Run1	Run2	Run3	Run4	Run5	$ S/N $
0.1	20	2	3458	3458	3461	3458	3461	-70.78
0.1	40	4	3570	3660	3660	3697	3746	-71.29
0.1	60	6	3684	3993	3589	3922	3570	-71.49
0.1	80	8	3660	3964	4042	3627	3964	-71.72
0.2	20	4	3589	3589	3746	3689	3697	-71.28
0.2	40	2	3660	3746	3697	3993	3697	-71.50
0.2	60	8	3993	3964	4042	3684	3993	-71.90
0.2	80	6	3697	3993	4177	3922	3964	-71.94
0.3	20	6	4042	3922	3964	3964	3993	-71.99
0.3	40	8	3697	3964	3993	3689	3689	-71.62
0.3	60	2	3922	3689	4042	3746	3660	-71.63
0.3	80	4	3993	3697	4177	3964	3922	-71.94
0.4	20	8	3964	4177	3964	3993	4042	-72.10
0.4	40	6	3922	3964	3746	4042	3993	-71.90
0.4	60	4	3922	4177	3697	3964	3922	-71.91
0.4	80	2	3746	3922	3993	3697	4177	-71.85
0.1	20	2	3458	3458	3461	3458	3461	-70.78
0.1	40	4	3570	3660	3660	3697	3746	-71.29

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Table 5. Algorithm parameter value

Algorithm	Parameter
BAS-IGA	$ T_{Maxgen}=100 $, $ popsize=80 $, $ p_c=0.9 $, $ p_m=0.1 $, $N_c=20$, $\zeta=2$, $k=20$, $\delta=1500$, $d=1500$
BAS-GA	$T_{Maxgen}=100$, $popsize=80$, $p_c=0.9$, $p_m=0.1$
IGA	$ T_{Maxgen}=100 $, $ popsize=80 $, $ p_c=0.9 $, $ p_m=0.1 $, $ \zeta=2 $, $ N_c=20 $
GA	$ T_{Maxgen}=100 $, $ popsize=80 $, $ p_c=0.9 $, $ p_m=0.1 $

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Table 6. Algorithm performance comparison

Scale	Num	Gurobi		BAS-IGA		BAS-GA		IGA		GA		GAP1(%)	GAP2(%)	GAP3(%)	GAP4(%)
		OV	CT	OV	CT	OV	CT	OV	CT	OV	CT
Scale 1	1	976	0.1	976	0.5	976	0.4	976	0.43	976	0.4	0	0	0	0
	2	979	0.1	979	0.5	979	0.4	979	0.43	979	0.4	0	0	0	0
	3	974	0.1	974	0.5	974	0.4	974	0.43	974	0.4	0	0	0	0
	4	978	0.1	978	0.5	978	0.4	978	0.43	978	0.4	0	0	0	0
	5	976	0.1	976	0.5	976	0.4	976	0.43	976	0.4	0	0	0	0
Scale 2	1	1222	0.5	1222	1.3	1225	1	1222	1	1222	0.8	0	0.2	0	0
	2	1217	0.4	1217	1.1	1220	0.8	1217	0.8	1217	0.7	0	0.2	0	0
	3	1226	0.4	1226	1.3	1229	0.8	1226	1	1226	0.8	0	0.2	0	0
	4	1279	0.5	1279	1.3	1282	0.9	1279	0.9	1279	0.8	0	0.2	0	0
	5	1227	0.4	1227	1.2	1230	0.8	1227	0.9	1227	0.8	0	0.2	0	0
Scale 3	1	1462	5.6	1462	7.9	1469	6.8	1462	8.6	1465	7.9	0	0.5	0	0.2
	2	1481	5.6	1481	8.2	1489	6.7	1481	8.4	1484	8	0	0.5	0	0.2
	3	1449	5.3	1449	7.7	1455	6.9	1449	8.2	1454	8	0	0.4	0	0.3
	4	1459	5.3	1459	7.9	1467	6.8	1459	8.4	1463	8.3	0	0.5	0	0.3
	5	1476	5.6	1476	8	1482	6.8	1476	8.4	1480	8	0	0.4	0	0.3
Scale 4	1	2691	1265	2699	115	2711	101	2814	115.7	2850	112.3	0.3	0.7	4.6	5.9
	2	2699	1266	2705	116.1	2719	105.1	2827	116.8	2870	113	0.2	0.7	4.7	6.3
	3	2692	1265	2701	114.2	2712	102.9	2823	117.1	2830	112.9	0.3	0.7	4.9	5.1
	4	2680	1263	2684	115.2	2699	102.1	2798	116	2812	111.3	0.1	0.7	4.4	4.9
	5	2671	1261	2679	114.2	2695	102.1	2781	116.8	2809	111.3	0.3	0.9	4.1	5.2
Scale 5	1	3859*	> 3600	3855	675.7	3966	457	4149	688.4	4222	624.9	-0.1	2.8	7.5	9.4
	2	3876*	> 3600	3864	676.1	3973	456.9	4154	689.1	4231	632.1	-0.3	2.5	7.2	9.2
	3	3856*	> 3600	3851	675.7	3961	456.9	4137	688.4	4217	625.9	-0.1	2.7	7.3	9.4
	4	3827*	> 3600	3820	674	3942	454.2	4103	687.6	4183	625	-0.2	3.0	7.2	9.3
	5	3852*	> 3600	3841	675.7	3959	456.9	4125	688.4	4198	624.9	-0.3	2.8	7.1	9.0
T test						-3.095711629		-3.512948236		-3.504924076
P value						0.002469032		0.000892134		0.000910028

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Table 7. Scheme cost comparison table

Cost name	Scheme
Cost name	Scheme 1 ($\times 10^4$ RMB)	Scheme 2 ($\times 10^4$ RMB)	Scheme 3 ($\times 10^4$ RMB)
Construction cost	960	1260	1470.2
Transportation cost	\	1038.8	305.7
Processing cost	4440.99 (Including shipping and miscellaneous charges)	1591.2	1591.2
Environmental cost	2468	0	0
Total cost	7868	3890	3367.1

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Table 8. Scheme comparison table

Name		Scheme
Name		Scheme 1	Scheme 2	Scheme 3
Type 1 processing plant	Mileage	\	DK429+210	DK406+956.5, DK413+463, DK431+713.4
Type 1 processing plant	Land size	\	\	4500m2, 4500 m2, 10367m2
Type 1 mixing plant	Mileage	DK409+105, DK422+250, DK425+600, DK434+526	DK409+105, DK422+250, DK425+600, DK434+526	DK406+956.5, DK412+836, DK413+463, DK421+651 DK422+376.5, DK424+118, DK431+713.4
Type 1 mixing plant	Specifications	180 +120, 2×180 2×120, 2×120	180+120, 2×180 2×120, 2×120	90,120 120, 2×120+90 90, 90,120
Type2 mixing plant	Mileage	DK409+105	DK409+105	DK421+651, DK424+118
Type2 mixing plant	model	medium	medium	medium, medium

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Table 9. Site selection schemes for processing plants

The available amount of tunnel slag (10,000 m3)	Proportion	Number of processing plants	Processing plants location
121.09	1	3	DK406+956.5, DK413+463, DK431+713.4
113.825	0. 94	3	DK406+956.5, DK413+463, DK431+713.4
112.614-8.476	0.93-0.07	2	DK406+956.5, DK431+713.4
7.264	0.06	1	DK428+797.85
6.055	0.05	1	DK426.5+580.7
3.633	0.03	1	DK423+ 294.2
1.211	0.01	1	DK416+ 564.8
1.090	0.009	\

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Table 10. Location and schedule

Name	Starting mileage	Ending mileage	Start time	End time
Roadbed 1	DK404+867.00	DK404+977.00	2018/11/1	2019/11/1
Tunnel 1	DK404+977.00	DK408+936.00	2018/11/1	2020/6/3
Roadbed 2	DK408+936.00	DK408+953.52	2018/11/1	2020/4/1
Bridge 1	DK408+953.52	DK409+349.48	2018/12/1	2020/5/20
Roadbed 3	DK409+349.48	DK409+585.00	2018/11/1	2019/11/1
Tunnel 2	DK409+585.00	DK411+319.00	2018/11/1	2020/1/4
Roadbed 4	DK411+319.00	DK411+406.11	2018/11/1	2020/4/1
Bridge 2	DK411+406.11	DK412+276.87	2018/12/1	2020/7/1
Roadbed 5	DK412+276.87	DK412+561.00	2018/11/1	2020/4/1
Tunnel 3	DK412+561.00	DK412+812.00	2019/7/14	2020/1/31
Roadbed 6	DK412+810.00	DK412+862.12	2018/11/1	2020/4/1
Bridge 3	DK412+862.12	DK413+094.53	2019/7/1	2020/4/13
Roadbed 7	DK413+094.53	DK413+106.00	2018/11/1	2020/4/1
Tunnel 4	DK413+106.00	DK413+820.00	2018/11/1	2019/12/11
Roadbed 8	DK413+820.00	DK413+834.37	2018/11/1	2020/4/1
Bridge 4	DK413+834.37	DK414+058.76	2019/3/1	2020/4/7
Tunnel 5	DK414+058.76	DK415+125.00	2018/11/1	2020/1/24
Roadbed 9	DK415+125.00	DK415+210.09	2018/11/1	2020/4/1
Bridge 5	DK415+210.09	DK417+495.22	2019/1/1	2020/5/25
Roadbed 10	DK417+495.22	DK417+634.39	2018/11/1	2020/4/1
Bridge 6	DK417+634.39	DK420+508.68	2018/11/1	2020/4/10
Roadbed 11	DK420+508.68	DK420+925.66	2018/12/1	2020/4/1
Bridge 7	DK420+925.66	DK422+376.50	2018/12/1	2020/1/24
Roadbed 12	DK422+376.50	DK422+487.87	2018/11/1	2020/4/1
Bridge 8	DK422+487.87	DK424+100.56	2018/12/1	2020/6/29
Roadbed 13	DK424+100.56	DK424+118.00	2018/11/1	2020/4/1
Tunnel 6	DK424+118.00	DK424+350.00	2019/8/29	2020/3/20
Roadbed 14	DK424+350.00	DK424+646.37	2018/11/1	2019/11/1
Bridge 9	DK424+646.37	DK424+813.39	2019/2/5	2020/5/28
Roadbed 15	DK424+813.39	DK425+140.71	2018/6/1	2020/4/1
Bridge 10	DK425+140.71	DK425+526.86	2019/5/15	2020/6/29
Roadbed 16	DK425+526.86	DK425+565.78	2018/12/1	2019/11/1
Bridge 11	DK425+565.78	DK428+595.705	2018/11/1	2020/7/30
Tunne l7	DK428+595.705	DK429+000.00	2018/12/1	2019/9/27
bridge12	DK429+000.00	DK429+124.54	2019/11/22	2020/7/10
Roadbed 17	DK429+124.54	DK429+210.00	2018/11/1	2020/4/1
Tunnel 8	DK429+210.00	DK429+337.37	2018/11/1	2019/4/30
Bridge 13	DK429+337.37	DK429+373.43	2019/2/10	2020/6/30
Tunnel 9	DK429+373.43	DK432+903.00	2018/12/1	2020/6/13
Tunnel 10	DK430+467.52	DK432+959.27	2018/12/1	2020/3/15
Tunnel 11	DK431+171.24	DK433+150.70	2018/12/1	2020/6/13

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Table 11. Quantity of tunnel slag

Name	Quantity of tunnel slag (m3)
Tunnel 1	800000
Tunnel 2	350000
Tunnel 3	133600
Tunnel 4	148800
Tunnel 5	40600
Tunnel 6	64000
Tunnel 7	31800

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Table 12. Demand

Name	Sand and gravel demand(kg/m)
Roadbed	51442
Bridge	84227
Tunnel	131818

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