A grey wolf optimizer for estimating the stochastic SIRD and optimizing a regime-switching cash flow model

Endah R. M. Putri; Julinar; Novie A. Windarko

doi:10.3934/jimo.2025024

Article Contents

2025, Volume 21, Issue 5: 3600-3617. Doi: 10.3934/jimo.2025024

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A grey wolf optimizer for estimating the stochastic SIRD and optimizing a regime-switching cash flow model

1.
Department of Mathematics, Faculty of Science and Data Analytics, Institut Teknologi Sepuluh Nopember, Indonesia
2.
Department of Electrical Engineering, Politeknik Elektronika Negeri Surabaya, Indonesia

^*Corresponding author: Endah R. M. Putri
^*Corresponding author: Endah R. M. Putri

Received: January 2024

Revised: October 2024

Early access: February 2025

Published: May 2025

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Abstract

The COVID-19 pandemic has significantly impacted various sectors, including industries. Companies have struggled with operational risks while striving to optimize their cash flows. To address the financial challenges posed by the pandemic, we propose a novel cash flow model that aims to determine the optimal profit for a company. This model operates based on two distinct states or regimes: mothballing (temporary suspension of operations) and reactivating conditions. The regime-switching is determined by the number of infected employees in the company which is estimated based on the stochastic SIRD model. Leveraging insights from the stochastic SIRD model, we employ a grey wolf optimizer to estimate key parameters in the stochastic SIRD and subsequently the cash flow model. In conclusion, our approach allows us to estimate the optimal timing for implementing mothballing or reactivating strategies accurately, taking into account the number of infected employees. By doing so, companies can make informed decisions to maximize profit while safeguarding employee well-being.

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Mathematics Subject Classification: Primary: 37N40; Secondary: 37A50.

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Figure 1. The SIRD compartment diagram with external influence

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Figure 2. A social hierarchy of the best fitness values $ \alpha, \beta, \delta, $ and $ \omega $ in the grey wolf optimizer

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Figure 3. Prediction of infected individuals of COVID-19 using the point estimation approach

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Figure 4. Prediction of infected individuals of COVID-19 using the piecewise path approach

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Figure 5. Projection of 100 paths of infected individuals with regime-switching for employee productivity $ \xi = 0 $

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Figure 6. Projection of 100 paths of infected individuals with regime-switching for employee productivity $ \xi = 0.2 $

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Figure 7. Projection of 100 paths of infected individuals with regime-switching for employee productivity $ \xi = 0.5 $

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Figure 8. Regime-switching diagram for for employee productivity $ \xi = 0 $

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Figure 9. Regime-switching diagram for for employee productivity $ \xi = 0.2 $

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Figure 10. Regime-switching diagram for for employee productivity $ \xi = 0.5 $

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Table 1. MAPE of some methods improving the grey wolf optimizer

No	Method	Number of Trial	Average MAPE
1	Repetitive trials	8	28.58225 %
2	An average of path generating	3	30, 50744 %
3	Point optimization	3	9, 987356667 %
4	Data separation	3	17, 08581833 %
5	A piecewise path	3	2, 540766667 %

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Table 2. Parameters estimation of the stochactic SIRD model using the point optimization method

No	Bounds	Parameter value
1	$ S_0 $	1, 402, 564
2	$ a $	0.05174
3	$ r $	0.02259
4	$ \kappa $	0.00117
5	$ \eta $	$ 1.35\times 10^{-6} $
6	$ \sigma_1 $	0.00028
7	$ \sigma_2 $	0.13321
8	$ \sigma_3 $	0.06669
9	$ \sigma_4 $	0.005
10	$ \sigma_5 $	0.07198

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Table 3. Cash flow model parameters

$ H $	$ VC $	$ FC $	$ E $	$ \rho $	$ M $	$ A $
$ 42.000 $	$ 14.000 $	$ 7.000.000 $	$ 14.000 $	$ 0.05 $	$ 4.200.000 $	$ 4.200.000 $

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Table 4. Comparison of the expected discounted cash flow

No	$ V $	Employee productivity rate $ \xi $
No	$ V $	$ \xi=0 $	$ \xi=0.2 $	$ \xi=0.5 $
1	$ V_{no-rs} $	408, 100, 495.980802	411, 387, 580.676322	417, 957, 373.160371
2	$ V_{with-rs} $	437, 373, 960.8549	440, 827, 318. 187527	446, 813, 557.30296

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Table 5. The transition probability of the regime-switching scheme for different productivity level

No	Bounds	Employee productivity rate $ \xi $
No	Bounds	$ \xi=0 $	$ \xi=0.2 $	$ \xi=0.5 $
1	$ p_{11} $	0.99690	0.99687	0.99691
2	$ p_{12} $	0.00310	0.00313	0.00309
3	$ p_{21} $	0.09091	0.06667	0.10000
4	$ p_{22} $	0.90909	0.93333	0.90000
5	$ p_{1} $	0.96707	0.95509	0.97006
6	$ p_{2} $	0.03293	0.04491	0.02994

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Table 6. Comparison of the upper bound ($ I_H $) and lower bound ($ I_L $) of the regime-switching scheme

No	Bounds	Employee productivity rate $ \xi $
No	Bounds	$ \xi=0 $	$ \xi=0.2 $	$ \xi=0.5 $
1	$ I_H $	36	28	32
2	$ I_L $	10	9	10

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