Solving an EPQ Model with Rework and Service Level Constraint

Yuan-Shyi Chiu,Hong-Dar Lin,Singa Chiu

doi:10.3390/mca11010075

Abstract

This paper examines an economic production quantity (EPQ) model with rework and service level constraint. First, we prove that the expected overall costs for an imperfect EPQ model with backlogging permitted is less than or equal to that of the one without backlogging. Secondly, the relationship between “imputed backorder cost” and maximal shortage level is derived for decision-making on whether the required service level is achievable. Then an equation for calculating the intangible backorder cost is proposed for situation when the required service level is not attainable. By including this intangible backorder cost in mathematical analysis, one can derive a new optimal lot-size policy that minimizes expected total costs as well as satisfies the maximal shortage level constraint for the EPQ model with rework. Numerical example is provided to demonstrate its practical usage.

Highlights

In manufacturing sector, when items are produced internally instead of being obtained from an outside supplier, the economic production quantity (EPQ) model is often employed to determine the optimal production lot-size that minimizes overall production/inventory costs
The complexity of a resulting EPQ model depends on the assumptions one makes about various parameters of the inventory system
This paper examines the optimal lot-size decision for an EPQ model with rework and service level constraint

Summary

INTRODUCTION

In manufacturing sector, when items are produced internally instead of being obtained from an outside supplier, the EPQ model is often employed to determine the optimal production lot-size that minimizes overall production/inventory costs. The complexity of a resulting EPQ model depends on the assumptions one makes about various parameters of the inventory system Among these features are demand types, actions for excess demand, production rates, treatment for imperfect quality items, minimal service level constraint, various cost parameters, and issuing policies when items are perishable. This paper examines the optimal lot-size decision for an EPQ model with rework and service level constraint. This paper extends the work of Hayek and Salameh [7] and Chiu [4], studies the effect of service level constraint on the optimal lot-size decision of an EPQ model with rework

NOTATIONS AND ASSUMPTIONS

MATHEMATICAL MODELLING AND ANALYSIS

Formulation of the EPQ Model with Rework and Shortage Not Permitted

The Effects of Backlogging and Shortage Level Constraint on the Model

NUMERICAL EXAMPLE AND DISCUSSION