# An Economic Production Quantity Model with Imperfect Quality Raw Material and Backorders

### Noura Yassine, Christine Markarian, Raed El-Khalil

#### 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 probability 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.

Download#### Paper Citation

#### in Harvard Style

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 - Volume 1: ICORES,* ISBN 978-989-758-396-4, pages 202-211. DOI: 10.5220/0008980302020211

#### in Bibtex Style

@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 - Volume 1: ICORES,},

year={2020},

pages={202-211},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0008980302020211},

isbn={978-989-758-396-4},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 9th International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,

TI - An Economic Production Quantity Model with Imperfect Quality Raw Material and Backorders

SN - 978-989-758-396-4

AU - Yassine N.

AU - Markarian C.

AU - El-Khalil R.

PY - 2020

SP - 202

EP - 211

DO - 10.5220/0008980302020211