Analytic inventory model with a mixture of back orders and lost sales (original) (raw)

Journal of Information and Optimization Sciences, 2005

Abstract

ABSTRACT A precise approach is used to extend and analyze the article published by G. Padmanabhan and P. Vrat, Int. J. Syst. Sci. 21, No. 8, 1721–1726 (1990; Zbl 0715.90038). Utilizing this approach, we develop a criterion for existence and uniqueness of the optimal solution of the total cost function. If the criterion cannot be satisfied, this model degenerate to an inventory model with one cycle. In such case, the article shows that a longer stock shortage time would lower the total cost. Therefore, we evaluate the cost variation under different allotted times to provide decision-makers with strategies to balance the time and cost. We present illustrations to demonstrate the exactness of this process.

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