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


  • Nwakobi, Micheal Nnamdi University of Nigeria, Nsukka Enugu State, Nigeria


Inventory model, variable lead time, variable holding cost, shortage cost, Optimization


Communication in Physical Science, 2021, 7(2): 69-72

Received 08 April 2020/Accepted 02 May 2021

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.


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Author Biography

Nwakobi, Micheal Nnamdi, University of Nigeria, Nsukka Enugu State, Nigeria

Department Of Statistics


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