Optimal control of a continuous review production inventory system with Gamma distributed deterioration

Article type: Research Article

Authors: Baten, Md. Azizul | Khalid, Ruzelan

Affiliations: School of Quantitative Sciences, Universiti Utara Malaysia, Kedah Darul Aman, Malaysia

Note: [] Corresponding author. Md. Azizul Baten, School of Quantitative Sciences, Universiti Utara Malaysia, 06010 UUM Sintok, Kedah Darul Aman, Malaysia. Tel.: +60 49286425; Fax: +60 49286309; E-mail: [email protected]; [email protected] (Ruzelan Khalid).

Abstract: This paper develops the production inventory models with and without Gamma distributed deteriorating items. The production system with inventory level dependent demand is considered here and the Pontryagin maximum principle is used to determine the optimal control, which is the production rate that minimizes the optimal inventory control model, while satisfying the system dynamics. The necessary optimality conditions associated with and without Gamma distributed deteriorating items are derived from the Hamiltonian functions. The optimal inventory levels and the optimal production rates are derived and numerical simulations are used to illustrate the theoretical results.

Keywords: Inventory systems, production control, Gamma distribution, deterioration item, optimal control, Pontryagin maximum principle, continuous review policy

DOI: 10.3233/IFS-141253

Journal: Journal of Intelligent & Fuzzy Systems, vol. 27, no. 6, pp. 2937-2948, 2014