Title: Robust control of pricing and inventory in a two-level supply network with competing retailers and delays in decision

Authors: Azeddine Zemzam; Jamila El Alami; Nourddine El Alami

Addresses: LASTIMI Laboratory, Mohammedia School of Engineers (EMI) and High School of Technology (EST), Mohammed V University in Rabat, Rabat 765, Morocco ' LASTIMI Laboratory, High School of Technology (EST), Mohammed V University in Rabat, Salé 227, Morocco ' Mohammedia School of Engineers (EMI), Mohammed V University in Rabat, Rabat 765, Morocco

Abstract: In this paper, we construct a type of dynamic joint pricing and inventory supply model with switching time-varying delays and weights in pricing, scarcity effect in inventory and the uncertainties of parameters and customer's demand. This model is consisted of one distributor and two retailers under stock and price-dependent demand. Based on the rule of bounded rationality, the uncertain switched nonlinear system is approximated by the Takagi-Sugeno fuzzy model. Meanwhile, the fuzzy robust control method is introduced to minimise the bullwhip effect (BE), and a sufficient condition for the stability is presented utilising switched and delayed H-infinity state-feedback controller. The parallel distributed compensation is used to design the controller for the overall T-S fuzzy model. Finally, a simulation example is provided to investigate the influence of the different parameters as well as their relative uncertainties on the complex dynamic characteristics of the system and to illustrate the effectiveness of the proposed method. Moreover, the influence of the competition/partnership interactions on the dynamics and robustness is examined.

Keywords: robust control; switched fuzzy systems; bullwhip effect; competition; partnership; stock and price dependent demand.

DOI: 10.1504/IJMOR.2021.120101

International Journal of Mathematics in Operational Research, 2021 Vol.20 No.4, pp.453 - 505

Received: 13 Feb 2020
Accepted: 25 Jun 2020
Published online: 07 Jan 2022 *

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