An EPQ Model with Unit Production Cost and Set-Up Cost as Functions of Production Rate

Behrouz Afshar-Nadjafi

doi:10.1155/2013/727685

Behrouz Afshar-Nadjafi

Open Access

https://doi.org/10.1155/2013/727685

Copy DOI

Abstract

Extensive research has been devoted to economic production quantity (EPQ) problem. However, no attention has been paid to problems where unit production and set-up costs must be considered as functions of production rate. In this paper, we address the problem of determining the optimal production quantity and rate of production in which unit production and set-up costs are assumed to be continuous functions of production rate. Based on the traditional economic production quantity (EPQ) formula, the cost function associated with this model is proved to be nonconvex and a procedure is proposed to solve this problem. Finally, utility of the model is presented using some numerical examples and the results are analyzed.

Highlights

The economic production quantity (EPQ) model has been widely used in practice because of its simplicity
The results indicate that the loss due to using the classical EPQ model increases with ε
The results show that the economic production quantity increases as ψ increases; lot size is inflated when ψ approaches unity from below

Summary

Introduction

The economic production quantity (EPQ) model has been widely used in practice because of its simplicity. Darwish generalized the EPQ model by considering a relationship between the set-up cost and the production run length [3]. Freimer et al studied the effect of imperfect yield on EPQ decisions They considered set-up cost reductions and process quality improvements as types of investments in the production processes [7]. Jaber et al applied first and second laws of thermodynamics on inventory management problem They showed that their approach yields higher profit than that of the classical EPQ model [11]. Hou considered an EPQ model with imperfect production processes, in which the set-up cost and process quality are functions of capital expenditure [12]. The classical EPQ model is extended by considering unit production cost and set-up cost as continuous functions of production rate.

Assumptions and Notation

Model Development

Numerical Example and Discussion

Conclusions