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Symmetry 2019, 11(2), 183; https://doi.org/10.3390/sym11020183

Optimal Control of Nonsmooth Production Systems with Deteriorating Items, Stock-Dependent Demand, with or without Backorders

1
Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
2
Department of Industrial Engineering, Alfaisal University, Riyadh 12714, Saudi Arabia
3
Department of Mathematics, Public Authority for Applied Education and Training, Kuwait City 13092, Kuwait
4
Department of Computer Engineering, College of Engineering, King Saud University, Riyadh 11453, Saudi Arabia
*
Author to whom correspondence should be addressed.
Received: 9 January 2019 / Revised: 22 January 2019 / Accepted: 28 January 2019 / Published: 4 February 2019
(This article belongs to the Special Issue Nonlinear, Convex, Nonsmooth, Functional Analysis in Symmetry)
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Abstract

We propose a nonsmooth dynamic system integrating production and inventory where the items may deteriorate and the demand is stock-dependent. We aim to derive the optimal production rate. In our first model, backorders are not allowed, while in the second model they are. Using optimal control, necessary optimality conditions are obtained for general forms of the cost, demand, and deterioration rates and closed form solutions are derived for specific forms of these rates. Numerical simulations are presented and sensitivity of the solutions are examined. View Full-Text
Keywords: nonsmooth production inventory systems; item deterioration; backorder; optimal control; maximum principle nonsmooth production inventory systems; item deterioration; backorder; optimal control; maximum principle
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Bounkhel, M.; Tadj, L.; Benhadid, Y.; Hedjar, R. Optimal Control of Nonsmooth Production Systems with Deteriorating Items, Stock-Dependent Demand, with or without Backorders. Symmetry 2019, 11, 183.

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