Title: An optimal inventory control in hybrid manufacturing/remanufacturing system with deteriorating and defective items

Authors: Ali Khaleel Dhaiban; Md. Azizul Baten; Nazrina Aziz

Addresses: The University of Mustansiriyah, Baghdad, Iraq; School of Quantitative Science, University Utara Malaysia, Malaysia ' School of Quantitative Sciences, University Utara Malaysia, Malaysia ' School of Quantitative Sciences, University Utara Malaysia, Malaysia

Abstract: An optimal control model in a manufacturing/remanufacturing-inventory system, with defective, deteriorating, returned and disposed items was developed. In this model, the time of deterioration, and the percentages of defective, returned and disposed items were assumed random variables that follow the gamma distribution, beta rectangular, four-parameter generalised beta (FPGB) and Kumaraswamy distributions, respectively. The total of returned items from customers and defective items divided into the remanufacturing and disposed items. An optimality conditions were derived from the dynamic of the manufacturing/remanufacturing inventory level. The explicit solution under continuous-review policy was achieved by using the Pontryagin maximum principle. Also, simulation and sensitivity analysis results were illustrated numerically. The numerical results suggested that the model can help firms to maintain a balance between the manufacturing and remanufacturing rates to hedge demand and inventory levels. Also, the manufacturing rate was positively related to the disposal rate.

Keywords: optimal control; inventory system; deteriorating items; defective items; Pontryagin maximum principle; demand function.

DOI: 10.1504/IJMOR.2018.088575

International Journal of Mathematics in Operational Research, 2018 Vol.12 No.1, pp.66 - 90

Received: 12 May 2016
Accepted: 20 Jun 2016
Published online: 12 Dec 2017 *

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