Abstract
An adaptive control of a reverse logistic inventory system with unknown deterioration and disposal rates is considered. An adaptive control approach with a feedback is applied to track the inventory levels toward their goal levels. Also, the updating rules of both deterioration and disposal rates are derived from the conditions of asymptotic stability of the reference model. Important characteristics of the adaptive inventory system are discussed. The adaptive controlled system is modeled by a nonlinear system of differential equations. Finally, the numerical solution of the controlled system is discussed and displayed graphically.
Highlights
Applications of optimal control theory to management science, and especially to production planning, are proving to be quite fruitful; see Sethi and Thompson 1 and El-Gohary et al 2
The aim of this paper is to introduce the mathematical model of a reverse logistic system with two different types of natural deteriorations
The motivation of this paper is to extend and generalize the reverse logistic system and applying an adaptive control approach to stabilize the system about the steady states of this system
Summary
Applications of optimal control theory to management science, and especially to production planning, are proving to be quite fruitful; see Sethi and Thompson 1 and El-Gohary et al 2. Ii El-Gohary and Elsyed 4 discussed the problem of optimal control of multi-item inventory models with different types of deterioration. They derived inventory levels which minimize the total holding cost of the system. Advances in Operations Research iii Alshamrani and El-Gohary 5 applied Pontryagin principle to a two-item inventory model with different types of deteriorating items They minimized the total cost which includes the sum of the holding costs of inventory items, the holding costs of one item due to the presence of the other, and the production cost. We apply an adaptive control technique to derive the updating rules of both of deteriorations and disposal rates from the conditions of asymptotic stability of the reference model. The motivation of this paper is to extend and generalize the reverse logistic system and applying an adaptive control approach to stabilize the system about the steady states of this system
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