Modeling the resilient supplier selection and optimal order Allocation considering the vehicle routing and disruption risk assessment based on the Bayesian network

Mohammad Khosroabadi; Jafar Gheidar-Kheljani; Mohammad Hosein Karimi-Gavareshki

doi:10.3934/jimo.2025021

Article Contents

2025, Volume 21, Issue 5: 3500-3540. Doi: 10.3934/jimo.2025021

This issue Previous Article Asset-liability management under uncertain economic environment Next Article Nonconvex regularizer and homotopy-based sparse optimization: Convergent algorithms and applications

Modeling the resilient supplier selection and optimal order Allocation considering the vehicle routing and disruption risk assessment based on the Bayesian network

1.
Department of Management & Industrial Engineering, Malek-Ashtar University of Technology, Tehran, Iran

^*Corresponding author: Jafar Gheidar-Kheljani
^*Corresponding author: Jafar Gheidar-Kheljani

Received: April 2024

Revised: November 2024

Early access: February 2025

Published: May 2025

Abstract / Introduction Full Text(HTML) Figure(21) / Table(12) Related Papers Cited by

Abstract

This study develops a novel framework for designing resilient supply chain networks under uncertainty and disruption. The framework integrates supplier selection, order allocation, and vehicle routing, considering factors like supplier resilience, transportation costs, and demand variability. The Traveling Purchaser Problem (TPP) has been used to model the resilient supplier selection and determine the optimal order allocation. A key contribution is the incorporation of a Bayesian network to model the cascading effects of disruptions, enabling a more comprehensive understanding of supply chain risks. The proposed model also considers the impact of inflation on demand and the trade-off between cost and resilience. The findings indicate a positive correlation between the penalty for unmet demand and the level of customer service. This research has achieved a resilient supply chain and reduced overall costs by making informed decisions regarding supplier's proposed price, resilience cost, distance, and optimal supply route. Moreover, the proposed model offers a practical solution for supply chain managers facing unexpected disruptions. By utilizing linear programming, alternative suppliers or routes can be quickly identified in the event of natural disasters.

The effectiveness of the model is demonstrated through a case study and sensitivity analysis, highlighting its potential to improve supply chain resilience and performance. The Fuzzy C-Means (FCM) clustering technique and Cross Impact Balance (CIB) Analysis are used for scenario reduction. This model makes manufacturers ready for better decision-making and planning when dealing with future risks and uncertainties.

Keywords:

Mathematics Subject Classification: Primary: 90B06, 90C05, 90C11, 90Bxx, 90B05; Secondary: 90C29, 90C23, 90B50, 90-10.

Citation:

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Figure 1. Searched word cloud

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Figure 2. Famous authors of resilient supplier

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Figure 3. Famous authors of traveling purchaser

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Figure 4. Framework of study and implementation of the mathematical model

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Figure 5. Structural model of risks in previous studies

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Figure 6. Studied structural model

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Figure 7. Minimum distance between suppliers

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Figure 8. Probabilistic modeling of disruption occurring for a supplier under the effect of two disrupting incidents

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Figure 9. Three final scenarios through ScenarioWizard

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Figure 10. Normality tests of Iran's inflation rate

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Figure 11. Approximate location of suppliers on Iran's Map

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Figure 12. Optimal Pareto solutions for scenario 1

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Figure 13. Optimal Pareto solutions for scenario 2

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Figure 14. Optimal Pareto solutions for scenario 3

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Figure 15. Service level for six problems in scenario 1

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Figure 16. Service level for six problems in scenario 2

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Figure 17. Total cost of three problems

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Figure 18. Cost of penalty for not satisfying demand

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Figure 19. Cost of penalty for not satisfying demand in each period

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Figure 20. Total transportation cost

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Figure 21. Transportation cost of each problem during the programming period

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Table 1. Computation of disruption probability of supplier under the effect of two disruption incidents

Network	States	$ P(H_1\| u_i) $	$ P(u_i) $
	$ \mathrm{U}_1 = \{\sim e_1, \sim e_2\} $	$ \alpha_{H_1} = 10\% $	$ (1 - \alpha_1)(1 - \alpha2) = 0.81 $
	$ \mathrm{U}_2 = \{\sim e_1, e_2\} $	$ 1-(1-\alpha_{H_1})(1-\beta_{H_1 \|e_2})=0.37 $	$ (1-\alpha_1)\alpha_2=0.09 $
	$ \mathrm{U}_3 = \{e_1, \sim e_2\} $	$ 1-(1-\alpha_{H_1})(1-\beta_{H_1 \|e_1})=0.37 $	$ \alpha_1(1-\alpha_2)=0.09 $
	$ \mathrm{U}_4 = \{e_1, e_2\} $	$ 1-(1-\alpha_{H_1})(1-\beta_{H_1 \|e_2})(1-\beta_{H_1 \|e_1})=0.559 $	$ \alpha_1\alpha_2=.01 $
$ F_{H_{1}} = \sum_{\forall u_{i}} P(H_1\| u_i)P(u_i) \approx .15319 $

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Table 2. Distance between nodes

distance between nodes ($ m $)
Supp No.		Depot	Rasht	Ghazvin	Esfehan	kashan	Tehran
0	Depot	0	298000	130000	435000	240000	50000
1	Rasht	298000	0	168000	733000	538000	278000
2	Ghazvin	130000	168000	0	565000	370000	110000
3	Esfehan	435000	733000	565000	0	195000	445000
4	kashan	240000	538000	370000	195000	0	250000
5	Tehran	50000	278000	110000	445000	250000	0

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Table 3. Transportation cost

$ tr(i, j) $ (Toman)
	Depot	Rasht	Ghazvin	Esfehan	kashan	Tehran
Depot		1490000	650000	2175000	1200000	250000
Rasht	1490000	0	840000	3665000	2690000	1390000
Ghazvin	650000	840000	0	2825000	1850000	550000
Esfehan	2175000	3665000	2825000	0	975000	2225000
kashan	1200000	2690000	1850000	975000	0	1250000
Tehran	250000	1390000	550000	2225000	1250000	0

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Table 4. Random generation of the data

$ \varpi $	100000	$ \nabla_{v} $	3000000	$ \Theta_{v} $	400
$ \Gamma $	700000	$ \theta_{j} $	900000	$ \psi_{t} $	100
$ h_{t} $	35000	$ \delta $	$ \mathrm{Uniform}[.1, .9] $	$ \phi_{i} $	$ 10^7 $
$ \nu_{0} $	N(21.44, 1.726)	$ \tau_{it}^{E} $	$ \mathrm{Uniform}[.7, .9] $	$ cap_{it} $	620

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Table 5. Pareto optimal solution associated with three scenarios

S	low		medium		high
	TC	GS	TC	GS	TC	GS
1	12613390074	4755000	12971790074	4755000	13330890074	4755000
2	12608890074	4200000	12967290074	4200000	13326390074	4227000
3	12608890074	3570000	12967290074	3635000	13326390075	4032000
4	12608890074	3039000	12967290075	3327000	13326390074	2929000
5	12607990075	2678000	12966390074	2418000	13325490075	2483000
6	12607990074	1743000	12966390075	2223000	13325490074	1778000

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Table 6. Service level in different scenarios

Low						Medium						High
t1	s1	0.20	t4	s1	0.20	t1	s1	0.20	t4	s1	0.20	t1	s1	0.19	t4	s1	0.19
t1	s2	0.21	t4	s2	0.21	t1	s2	0.20	t4	s2	0.20	t1	s2	0.19	t4	s2	0.19
t2	s1	0.61	t5	s1	0.87	t2	s1	0.59	t5	s1	0.84	t2	s1	0.57	t5	s1	0.82
t2	s2	0.62	t5	s2	0.89	t2	s2	0.59	t5	s2	0.85	t2	s2	0.57	t5	s2	0.82
t3	s1	0.28	t6	s1	0.61	t3	s1	0.27	t6	s1	0.59	t3	s1	0.26	t6	s1	0.57
t3	s2	0.28	t6	s2	0.62	t3	s2	0.27	t6	s2	0.59	t3	s2	0.26	t6	s2	0.57

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Table 7. Vehicle routing for medium scenario

$ X_{ijvt}^s $
i0	i1	v1	t2	s1	1	i1	i2	v1	t2	s1	1	i2	i0	v1	t2	s1	1
i0	i1	v1	t3	s1	1	i1	i0	v1	t3	s1	1
i0	i1	v2	t1	s1	1	i1	i2	v2	t1	s1	1	i2	i0	v2	t1	s1	1
i0	i1	v2	t4	s1	1	i1	i2	v2	t4	s1	1	i2	i0	v2	t4	s1	1
i0	i1	v2	t6	s1	1	i1	i0	v2	t6	s1	1
i0	i2	v1	t6	s1	1	i2	i0	v1	t6	s1	1
i0	i2	v2	t2	s1	1	i2	i0	v2	t2	s1	1
i0	i2	v2	t5	s1	1	i2	i0	v2	t5	s1	1
i0	i3	v1	t1	s1	1	i3	i0	v1	t1	s1	1
i0	i3	v1	t4	s1	1	i3	i4	v1	t4	s1	1	i4	i0	v1	t4	s1	1
i0	i3	v2	t3	s1	1	i3	i0	v2	t3	s1	1
i0	i3	v3	t1	s1	1	i3	i0	v3	t1	s1	1
i0	i3	v3	t2	s1	1	i3	i4	v3	t2	s1	1	i4	i0	v3	t2	s1	1
i0	i3	v3	t3	s1	1	i3	i4	v3	t3	s1	1	i4	i0	v3	t3	s1	1
i0	i3	v3	t4	s1	1	i3	i4	v3	t4	s1	1	i4	i0	v3	t4	s1	1
i0	i3	v3	t5	s1	1	i3	i4	v3	t5	s1	1	i4	i0	v3	t5	s1	1
i0	i3	v3	t6	s1	1	i3	i4	v3	t6	s1	1	i4	i0	v3	t6	s1	1
i0	i4	v1	t5	s1	1	i4	i0	v1	t5	s1	1

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Table 8. Service level based on the $\Gamma$ increase

	Prob.1		Prob.2		Prob.3		Prob.4		Prob.5		Prob.6
$ \Gamma $	50000		500000		1000000		2000000		2500000		3500000
	s1	s2	s1	s2	s1	s2	s1	s2	s1	s2	s1	s2
t1	0.41	0.42	0.42	0.42	0.42	0.42	0.93	0.94	0.93	0.94	0.93	0.94
t2	0.62	0.63	0.63	0.64	0.63	0.64	1	1	1	1	1	1
t3	0.43	0.43	0.46	0.46	0.46	0.46	1	1	1	1	1	1
t4	0.41	0.42	0.42	0.42	0.42	0.42	0.93	0.94	0.93	0.94	0.93	0.94
t5	0.84	0.85	0.84	0.85	0.84	0.85	0.84	0.85	1	0.85	1	1
t6	0.62	0.63	0.63	0.64	0.63	0.64	1	1	1	1	1	1

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Table 9. Service level changing

	Prob.1	Prob.2	Prob.3	Prob.4	Prob.5	Prob.6
Resilience Level(m)	35	35	35	60	65	70

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Table 10. Objective functions and service levels for three new problems

problem 1				problem 2				problem 3
S	TC	s1	s2	S	TC	s1	s2	S	TC	s1	s2
4755*$ 10^3 $	190212*$ 10^5 $	0.42	0.43	4755*$ 10^3 $	190172*$ 10^5 $	0.31	0.32	4755*$ 10^3 $	190276*$ 10^5 $	0.29	0.3
		0.42	0.43			0.63	0.64			0.33	0.34
		0.42	0.43			0.31	0.32			0.39	0.4
		0.42	0.43			0.63	0.64			0.46	0.47
		0.42	0.43			0.31	0.32			0.56	0.57
		0.42	0.43			0.63	0.64			0.72	0.73
Total		2.52	2.58	Total		2.82	2.88	Total		2.75	2.81

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Table 11. Comparison of costs before and after losing route

Medium		Medium-distruption
Transportation cost	Total cost	Transportation cost	Total cost
120700000	1.306*$ 10^{10} $	108300000	1.3111*$ 10^{10} $

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Table 12. New routing after losing route of first supplier

$ X^{s}_{ijvt} $
i0	i2	v2	t1	s1	1	i2	i0	v2	t1	s1	1
i0	i2	v2	t3	s1	1	i2	i0	v2	t3	s1	1
i0	i2	v3	t2	s1	1	i2	i0	v3	t2	s1	1
i0	i2	v3	t4	s1	1	i2	i0	v3	t4	s1	1
i0	i2	v3	t5	s1	1	i2	i0	v3	t5	s1	1
i0	i2	v3	t6	s1	1	i2	i0	v3	t6	s1	1
i0	i3	v1	t1	s1	1	i3	i4	v1	t1	s1	1	i4	i0	v1	t1	s1	1
i0	i3	v1	t2	s1	1	i3	i4	v1	t2	s1	1	i4	i0	v1	t2	s1	1
i0	i3	v1	t3	s1	1	i3	i4	v1	t3	s1	1	i4	i0	v1	t3	s1	1
i0	i3	v1	t4	s1	1	i3	i4	v1	t4	s1	1	i4	i0	v1	t4	s1	1
i0	i3	v1	t5	s1	1	i3	i0	v1	t5	s1	1
i0	i3	v2	t4	s1	1	i3	i4	v2	t4	s1	1	i4	i0	v2	t4	s1	1
i0	i3	v2	t6	s1	1	i3	i4	v2	t6	s1	1	i4	i0	v2	t6	s1	1
i0	i3	v3	t1	s1	1	i3	i4	v3	t1	s1	1	i4	i0	v3	t1	s1	1
i0	i3	v3	t3	s1	1	i3	i4	v3	t3	s1	1	i4	i0	v3	t3	s1	1
i0	i4	v1	t6	s1	1	i4	i0	v1	t6	s1	1
i0	i4	v2	t2	s1	1	i4	i0	v2	t2	s1	1
i0	i4	v2	t5	s1	1	i4	i0	v2	t5	s1	1

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