An event-based decision and regulation strategy for the production-warehousing-selling model

Ziqi Liu; Ziqi Liu

doi:10.3934/era.2024210

Electronic Research Archive

2024, Volume 32, Issue 7: 4614-4631. doi: 10.3934/era.2024210

Previous Article Next Article

Research article Special Issues

An event-based decision and regulation strategy for the production-warehousing-selling model

Ziqi Liu ^,

College of Economics and Management, Northwest A & F University, Yangling 712100, China

Received: 13 April 2024 Revised: 16 July 2024 Accepted: 22 July 2024 Published: 26 July 2024

This paper focused on the decision and regulation for the production-warehousing-selling (P-W-S) model. A novel event-triggered mechanism (ETM) was meticulously developed to determine when to impose control, alongside the development of the corresponding impulsive strategy. By applying the input-to-state stability (ISS) theory, some quantitative relationships between system parameters and ETM were integrated into the estimation of the state of the P-W-S model. It was shown that under the designed ETM and impulsive strategy, the warehouse was able to autonomously adjust inventory levels based on factory production efficiency and market selling trends, and hence the quantity of goods could be maintained within a reasonable range, avoiding excessive inventory while adequately meeting market requirements. At last, an example with numerical simulations was presented to validate our results.
- production-warehousing-selling,
- event-triggered mechanism,
- decision and regulation,
- impulsive control,
- input-to-state stability
Citation: Ziqi Liu. An event-based decision and regulation strategy for the production-warehousing-selling model[J]. Electronic Research Archive, 2024, 32(7): 4614-4631. doi: 10.3934/era.2024210

Related Papers:

Abstract

This paper focused on the decision and regulation for the production-warehousing-selling (P-W-S) model. A novel event-triggered mechanism (ETM) was meticulously developed to determine when to impose control, alongside the development of the corresponding impulsive strategy. By applying the input-to-state stability (ISS) theory, some quantitative relationships between system parameters and ETM were integrated into the estimation of the state of the P-W-S model. It was shown that under the designed ETM and impulsive strategy, the warehouse was able to autonomously adjust inventory levels based on factory production efficiency and market selling trends, and hence the quantity of goods could be maintained within a reasonable range, avoiding excessive inventory while adequately meeting market requirements. At last, an example with numerical simulations was presented to validate our results.

References

[1]	L. M. A. Chan, D. Simchi-Levi, J. Swann, Pricing, production, and inventory policies for manufacturing with stochastic demand and discretionary sales, Manuf. Serv. Oper. Manage., 8 (2006), 149–168. https://doi.org/10.1287/msom.1060.0100 doi: 10.1287/msom.1060.0100
[2]	H. Andersson, A. Hoff, M. Christiansen, G. Hasle, A. Løkketangen, Industrial aspects and literature survey: combined inventory management and routing, Comput. Oper. Res., 37 (2010), 1515–1536. https://doi.org/10.1016/j.cor.2009.11.009 doi: 10.1016/j.cor.2009.11.009
[3]	T. Cheng, S. Podolsky, Just-in-time Manufacturing: An Introduction, Springer Science & Business Media, 1996.
[4]	F. Buttle, S. Maklan, Customer Relationship Management: Concepts and Technologies, Routledge, 2019. https://doi.org/10.4324/9781351016551
[5]	H. AL-Khazraji, C. Cole, W. Guo, Optimization and simulation of dynamic performance of production–inventory systems with multivariable controls, Mathematics, 9 (2021), 568. https://doi.org/10.3390/math9050568 doi: 10.3390/math9050568
[6]	M. Çimen, C. Kirkbride, Approximate dynamic programming algorithms for multidimensional flexible production-inventory problems, Int. J. Prod. Res., 55 (2017), 2034–2050. https://doi.org/10.1080/00207543.2016.1264643 doi: 10.1080/00207543.2016.1264643
[7]	R. Li, L. Xiao, D. Yao, Dynamic pricing and production control in a two-item make-to-stock system with flexible dual sourcing and lost sales, Prod. Oper. Manage., 32 (2023), 3119–3137. https://doi.org/10.1111/poms.14026 doi: 10.1111/poms.14026
[8]	Y. S. Huang, C. C. Fang, Y. A. Lin, Inventory management in supply chains with consideration of logistics, green investment and different carbon emissions policies, Comput. Ind. Eng., 139 (2020), 106207. https://doi.org/10.1016/j.cie.2019.106207 doi: 10.1016/j.cie.2019.106207
[9]	S. Baldi, A. Papachristodoulou, E. B. Kosmatopoulos, Adaptive pulse width modulation design for power converters based on affine switched systems, Nonlinear Anal. Hybrid Syst., 30 (2018), 306–322. https://doi.org/10.1016/j.nahs.2018.07.002 doi: 10.1016/j.nahs.2018.07.002
[10]	G. Wolfowicz, J. J. Morton, Pulse techniques for quantum information processing, eMagRes, 5 (2016), 1515–1528. https://doi.org/10.1002/9780470034590.emrstm1521 doi: 10.1002/9780470034590.emrstm1521
[11]	B. Liu, L. Chen, Y. Zhang, The effects of impulsive toxicant input on a population in a polluted environment, J. Biol. Syst., 11 (2003), 265–274. https://doi.org/10.1142/S0218339003000907 doi: 10.1142/S0218339003000907
[12]	R. Korn, Portfolio optimisation with strictly positive transaction costs and impulse control, Finance Stochastics, 2 (1998), 85–114. https://doi.org/10.1007/s007800050034 doi: 10.1007/s007800050034
[13]	J. Lu, B. Jiang, W. X. Zheng, Potential impacts of delay on stability of impulsive control systems, IEEE Trans. Autom. Control, 67 (2022), 5179–5190. https://doi.org/10.1109/TAC.2021.3120672 doi: 10.1109/TAC.2021.3120672
[14]	W. H. Chen, W. Xu, W. X. Zheng, Sliding-mode-based impulsive control for a class of time-delay systems with input disturbance, Automatica, 164 (2024), 111633. https://doi.org/10.1016/j.automatica.2024.111633 doi: 10.1016/j.automatica.2024.111633
[15]	S. Yu, Z. Yu, H. Jiang, A rumor propagation model in multilingual environment with time and state dependent impulsive control, Chaos, Solitons Fractals, 182 (2024), 114779. https://doi.org/10.1016/j.chaos.2024.114779 doi: 10.1016/j.chaos.2024.114779
[16]	Z. Liu, M. Luo, J. Cheng, I. Katib, K. Shi, Security synchronization problem for stochastic complex networks via event-triggered impulsive control with actuation delays, Commun. Nonlinear Sci. Numer. Simul., 133 (2024), 107958. https://doi.org/10.1016/j.cnsns.2024.107958 doi: 10.1016/j.cnsns.2024.107958
[17]	X. Li, P. Li, Input-to-state stability of nonlinear systems: event-triggered impulsive control, IEEE Trans. Autom. Control, 67 (2022), 1460–1465. https://doi.org/10.1109/TAC.2021.3063227 doi: 10.1109/TAC.2021.3063227
[18]	B. Liu, D. J. Hill, Z. Sun, Stabilisation to input-to-state stability for continuous-time dynamical systems via event-triggered impulsive control with three levels of events, IET Control Theory Appl., 12 (2018), 1167–1179. https://doi.org/10.1049/iet-cta.2017.0820 doi: 10.1049/iet-cta.2017.0820
[19]	Z. Hu, X. Mu, Event-triggered impulsive control for stochastic networked control systems under cyber attacks, IEEE Trans. Syst. Man Cybern.: Syst., 52 (2021), 5636–5645. https://doi.org/10.1109/TSMC.2021.3130614 doi: 10.1109/TSMC.2021.3130614
[20]	K. Zhang, E. Braverman, Event-triggered impulsive control for nonlinear systems with actuation delays, IEEE Trans. Autom. Control, 68 (2022), 540–547. https://doi.org/10.1109/TAC.2022.3142127 doi: 10.1109/TAC.2022.3142127
[21]	S. Baek, H. Lee, S. Han, Communication-efficient event-triggered time-delay control and its application to robot manipulators, IEEE Trans. Ind. Electron., 69 (2021), 9288–9297. https://doi.org/10.1109/TIE.2021.3114696 doi: 10.1109/TIE.2021.3114696
[22]	Y. Zhou, Y. Guo, C. Liu, H. Peng, H. Rao, Synchronization for markovian master-slave neural networks: an event-triggered impulsive approach, Int. J. Syst. Sci., 54 (2023), 2551–2565. https://doi.org/10.1080/00207721.2022.2122904 doi: 10.1080/00207721.2022.2122904
[23]	E. Sontag, Smooth stabilization implies coprime factorization, IEEE Trans. Autom. Control, 34 (1989), 435–443. https://doi.org/10.1109/9.28018 doi: 10.1109/9.28018
[24]	H. Zhu, X. Li, S. Song, Input-to-state stability of nonlinear impulsive systems subjects to actuator saturation and external disturbance, IEEE Trans. Cybern., 53 (2023), 173–183. https://doi.org/10.1109/TCYB.2021.3090803 doi: 10.1109/TCYB.2021.3090803
[25]	G. Şahan, D. Özdemir, Uniform asymptotic and input to state stability by indefinite lyapunov functions, Eur. J. Control, 76 (2024), 100945. https://doi.org/10.1016/j.ejcon.2023.100945 doi: 10.1016/j.ejcon.2023.100945
[26]	R. Heydari, M. Farrokhi, Robust event-triggered model predictive control of polytopic lpv systems: an input-to-state stability approach, Syst. Control Lett., 163 (2022), 105202. https://doi.org/10.1016/j.sysconle.2022.105202 doi: 10.1016/j.sysconle.2022.105202
[27]	S. Dashkovskiy, V. Slynko, Dwell-time stability conditions for infinite dimensional impulsive systems, Automatica, 147 (2023), 110695. https://doi.org/10.1016/j.automatica.2022.110695 doi: 10.1016/j.automatica.2022.110695
[28]	P. Bachmann, N. Bajcinca, Average dwell-time conditions for input-to-state stability of impulsive systems, IFAC-PapersOnLine, 53 (2020), 1980–1985. https://doi.org/10.1016/j.ifacol.2020.12.2564 doi: 10.1016/j.ifacol.2020.12.2564
[29]	S. Dashkovskiy, P. Feketa, Input-to-state stability of impulsive systems and their networks, Nonlinear Anal. Hybrid Syst., 26 (2017), 190–200. https://doi.org/10.1016/j.nahs.2017.06.004 doi: 10.1016/j.nahs.2017.06.004
[30]	H. Zhu, J. Lu, J. Lou, Y. Liu, Saturated control for uncertain nonlinear impulsive systems with non-uniformly distributed packet loss, Nonlinear Anal. Hybrid Syst., 51 (2024), 101438. https://doi.org/10.1016/j.nahs.2023.101438 doi: 10.1016/j.nahs.2023.101438
[31]	X. Li, H. Zhu, S. Song, Input-to-state stability of nonlinear systems using observer-based event-triggered impulsive control, IEEE Trans. Syst. Man Cybern.: Syst., 51 (2020), 6892–6900. https://doi.org/10.1109/TSMC.2020.2964172 doi: 10.1109/TSMC.2020.2964172
[32]	H. Zhu, J. Lu, J. Lou, Event-triggered impulsive control for nonlinear systems: the control packet loss case, IEEE Trans. Circuits Syst. II Express Briefs, 69 (2022), 3204–3208. https://doi.org/10.1109/TCSII.2022.3140346 doi: 10.1109/TCSII.2022.3140346
[33]	J. P. Hespanha, D. Liberzon, A. R. Teel, Lyapunov conditions for input-to-state stability of impulsive systems, Automatica, 44 (2008), 2735–2744. https://doi.org/10.1016/j.automatica.2008.03.021 doi: 10.1016/j.automatica.2008.03.021
[34]	S. Boyd, L. El Ghaoui, E. Feron, V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, SIAM, 1994. https://doi.org/10.1137/1.9781611970777
[35]	K. Gao, J. Lu, W. X. Zheng, X. Chen, Synchronization in coupled neural networks with hybrid delayed impulses: average impulsive delay-gain method, IEEE Trans. Neural Networks Learn. Syst., (2024), 1–10. https://doi.org/10.1109/TNNLS.2024.3357515
[36]	S. Dashkovskiy, P. Feketa, Asymptotic properties of zeno solutions, Nonlinear Anal. Hybrid Syst., 30 (2018), 256–265. https://doi.org/10.1016/j.nahs.2018.06.005 doi: 10.1016/j.nahs.2018.06.005

Reader Comments

Your name:*

Email:*
© 2024 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)