Title: Modelling and performance evaluation in the (R, s, l_nQ) inventory system

Authors: Nedjma Aiane; Fazia Rahmoune; Djamil Aïssani

Addresses: Research Unit LaMOS (Modeling and Optimization of Systems), Faculty of Exact Sciences, University of Bejaia, Bejaia, 06000, Algeria ' Research Unit LaMOS (Modeling and Optimization of Systems), Faculty of Exact Sciences, University of Bejaia, Bejaia, 06000, Algeria ' Research Unit LaMOS (Modeling and Optimization of Systems), Faculty of Exact Sciences, University of Bejaia, Bejaia, 06000, Algeria

Abstract: In this work, we propose to analyse a periodic review inventory model with an (R, s, l_nQ) policy and an instant replenishment via a discrete Markov chain approach. Then, we adopt the strong stability method to evaluate the characteristics of the considered model in the case of the perturbation of some of its parameters (demand rate and demand law). Thus, we find the approximation bounds of the stationary distribution, with an exact computation of the constants, to evaluate the error generated by this approximation. Finally, we study numerically the effect of the perturbation of the arrival rate and the demand law respectively on the average stock and the total cost of the considered inventory model. Several numerical examples have been performed to illustrate the performance of this approach.

Keywords: inventory control; (R, s, l_nQ) policy; Markov chains; transition kernel; strong stability; stability inequalities; stationary distributions; relative error; the error on the average stock; total cost.

DOI: 10.1504/IJMOR.2022.124139

International Journal of Mathematics in Operational Research, 2022 Vol.22 No.3, pp.363 - 402

Received: 18 Jan 2021
Accepted: 25 May 2021
Published online: 14 Jul 2022 *

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