Multiproduct single-machine production system with stochastic scrapped production rate, partial backordering and service level constraint

Authors:
Ata Allah Taleizadeh;Seyed Taghi Akhavan Niaki;Amir Abbas Najafi
Affiliations:
Department of Industrial Engineering, Iranian University of Science and Technology, Tehran, Iran;Department of Industrial Engineering, Sharif University, Tehran, Iran;Department of Industrial Engineering, Qazvin Islamic Azad University, Qazvin, Iran
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

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Abstract

In this paper, a multiproduct single-machine production system under economic production quantity (EPQ) model is studied in which the existence of only one machine causes a limited production capacity for the common cycle length of all products, the production defective rates are random variables, shortages are allowed and take a combination of backorder and lost sale, and there is a service rate constraint for the company. The aim of this research is to determine the optimal production quantity, the allowable shortage level, and the period length of each product such that the expected total cost, including holding, shortage, production, setup and defective items costs, is minimized. The mathematical model of the problem is derived for which the objective function is proved to be convex. Then, a derivative approach is utilized to obtain the optimal solution. Finally, two numerical examples in each of which a sensitivity analysis is performed on the model parameters, are provided to illustrate the practical usage of the proposed methodology.