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Authors: Noura Yassine 1 ; Christine Markarian 2 and Raed El-Khalil 3

Affiliations: 1 Department of Mathematics and Computer Science, Beirut Arab University, Beirut, Lebanon ; 2 Faculty of Mathematical Sciences, Haigazian University, Beirut, Lebanon ; 3 Information Technology and Operations Management Department, Lebanese American University, Beirut, Lebanon

Keyword(s): Inventory, Economic Production Model, Imperfect Quality Raw Material, Shortages, Backorder, Maximum of Independent Random Variables.

Abstract: In this paper the classical EPQ model is extended to account for the cost and quality of the raw material used in the production process and to incorporate the effects of shortages into the model. A production process that uses n different types of raw material is considered. The various types of raw material acquired in batches from the suppliers are assumed to contain a percentage of imperfect quality items of raw material. The proportion of imperfect quality raw material found in a batch is a random variable having a known probability distribution. A mathematical model describing the inventory/production situation is formulated and used to derive a system of equations whose solution is the optimal production and shortage quantities that minimizes the total cost. It is shown that the total cost function depends on the determination of the maximum of a set of n independent random variables obtained from the proportions of imperfect quality raw material. A process for obtaining the p robability function of the maximum along with its expected value is described. Expressions for the probability density function and the expected value of the maximum are developed for the case when the random variables are uniformly distributed. A numerical example illustrating the determination of the optimal policy is presented. (More)

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Paper citation in several formats:
Yassine, N.; Markarian, C. and El-Khalil, R. (2020). An Economic Production Quantity Model with Imperfect Quality Raw Material and Backorders. In Proceedings of the 9th International Conference on Operations Research and Enterprise Systems - ICORES; ISBN 978-989-758-396-4; ISSN 2184-4372, SciTePress, pages 202-211. DOI: 10.5220/0008980302020211

@conference{icores20,
author={Noura Yassine. and Christine Markarian. and Raed El{-}Khalil.},
title={An Economic Production Quantity Model with Imperfect Quality Raw Material and Backorders},
booktitle={Proceedings of the 9th International Conference on Operations Research and Enterprise Systems - ICORES},
year={2020},
pages={202-211},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0008980302020211},
isbn={978-989-758-396-4},
issn={2184-4372},
}

TY - CONF

JO - Proceedings of the 9th International Conference on Operations Research and Enterprise Systems - ICORES
TI - An Economic Production Quantity Model with Imperfect Quality Raw Material and Backorders
SN - 978-989-758-396-4
IS - 2184-4372
AU - Yassine, N.
AU - Markarian, C.
AU - El-Khalil, R.
PY - 2020
SP - 202
EP - 211
DO - 10.5220/0008980302020211
PB - SciTePress

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