Application of Chebyshev Inequality in Stochastic Inventory Model with Controllable Lead Time and Backorder Discount

Abstract

Many researchers have recognized the importance of lead time reduction in stochastic inventory model, as it helps the firm to improve service level, manufacturing schedule and low safety stock. A good amount of work has been published in this context. Most of the authors have assumed that demand during the lead time either follows a normal known distribution or an unknown distribution. For an unknown distribution, authors have obtained the results using Minimax approach usually. In this paper a continuous review inventory model is developed with controllable lead time and backorder discount where lead time demand distribution is unknown. The solution is obtained by using Chebyshev inequality. The comparative analysis of all the three approaches viz. Chebyshev inequality, Minimax and Normal is also presented.