An optimal solution of a general lot size inventory model with deteriorated and imperfect products, taking into account inflation and time value of money

Zaid T. Balkhi

54 citations0/0 files storedInternational Journal of Systems Science

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Supply Chain and Inventory Management Sustainable Supply Chain Management Optimization and Mathematical Programming

Abstract

This paper considers a general production lot size inventory model with deteriorated and imperfect products taking into account inflation and time value of money. The production, demand, and deterioration rates are known, continuous, and differentiable functions of time. Shortages are allowed, but only a fraction of the stock out is backordered, and the rest is lost. Under these general assumptions, the inventory model is formulated, and a closed form of the total relevant costs of the underlying inventory system is obtained. Sufficient conditions which lead to a minimal solution of the considered problem are derived. Then, a rigorous mathematical analysis is used to prove that such a minimal solution is unique and global-optimal. A numerical verification of the proposed model is also given.

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References

2001Recent trends in modeling of deteriorating inventory 2000Economic production quantity model for items with imperfect quality 1991An Economic Order Quantity Model with Demand-Dependent Unit Production Cost and Imperfect Production Processes 1995An EOQ Model for Deteriorating Items with Linear Time-dependent Demand Rate and Shortages under Inflation and Time Discounting 1991Effects of inflation and time-value of money on an inventory model with linear time-dependent demand rate and shortages 2000Observation on: “Economic production quantity model for items with imperfect quality” [Int. J. Production Economics 64 (2000) 59–64]1985The effects of inflation and the time value of money on some inventory systems 1999Economic production lot size for deteriorating items taking account of the time-value of money

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