Classification of Cumulative Curve from Initial Inventory and Relationship between Inventory Quantity and Lead Time

Abstract

Cumulative curve is a method that is used for the analysis and improvement of production systems. The cumulative curve consists of accumulated input curve and output curve. Inventory is shown as a vertical interval between the input and output curve. And lead time is shown as a horizontal interval between the input and output curve. The number of research papers on mathematical analytic technique of the cumulative curve are very few. The mathematical analysis of the cumulative curve needs information about the start time to measure time series data. So, this paper proposes a method for classifying the expression of cumulative curves from information on inventory quantity and production quantity in measurement of the start time. Production conditions analyzed here are the case in which the production is newly started and the case in which the production is carried out under conditions that were continued as is. This classification is helpful to analyze cumulative curves mathematically using a gray theory. A Gray theory developed by Deng Ju Long in China and has been targeted for the field of automatic control. The theory uses a GM model with accumulated value of time series. The CM model is used to show and predict time series with parameters of a differential equation model. So, next is shown the method to accumulate time series for a gray theory by the classifications. And, an average lead time can be shown as an accumulated value of daily inventory divided by an accumulated value of daily output. Until now, mathematical proof of this theory has not been produced. So, finally, in this paper the mathematical proof is given by the classifications.