An Economic Production Quantity model with shortages, a variable lead time and a variable holding cost

Abstract

Nwakobi, Micheal Nnamdi

An economic production quantity model with shortages, a variable lead time and a variable holding cost represents a common real-life observation. It provides quantitative insight into a serious practical problem where costs are amplified due to production delay. Previous models incorporating variable lead time assume that the holding cost is constant for the entire inventory cycle. A mathematical model has been developed for determining the optimal production quantity and the optimal cycle time. The holding cost is considered as an increasing function of the ordering cycle length. Differential calculus is used for finding the optimal solution. A numerical example is used to validate the proposed model.