A Model for the Analysis of Inventory Systems and Lead Times Using the Cumulative Curve

Abstract

Cumulative curve is an analytic technique that is used for the improvement of production processes and planning in manufacturing. For example, the cumulative curve can be expressed by accumulated generating operation of input and output data in a manufacturing system. Here, the lead time is shown as a horizontal interval between the input and output curve. The inventory is shown as a vertical interval between the input and output curve. We have already proposed that the cumulative curve can be expressed as GM(1,1) and GM(1,2) models. In this paper, we suggest a method to solve the lead time and inventory between arbitrary processes with GM(1,1) and GM(1,2) models. The equation to compute the lead time and inventory can be proved mathematically with the GM(1,1) and GM(1,2) models. We prove this with numerical experiments. As a result, lead times and inventory can be solved with coefficients of GM(1,1) and GM(1,2) models of cumulative curve and the initial value of time series data. Cumulative curve can be expressed as a transfer function. The models discussed are illustrated with numerical examples.