An explicit analysis of the lead time syndrome: stability condition and performance evaluation

Abstract

Updating planned lead times in response to changing workload levels leads to erratic ordering behaviour, resulting in even larger variability in the workload levels and flow times. This phenomenon is called lead time syndrome, and describes the cyclic interaction between adaptive planned lead times and order sizes. Although it has been conceptually defined and intuitively accepted, formal analysis with analytical evaluation of the phenomenon has not been conducted. The objective of this paper is to provide a stronger understanding of the lead time syndrome, and to give new insights into the effects of frequently updating planned lead times. We develop a two-dimensional Markov process to model a single-item production process with orders released sensitive to the planned lead time. Using matrix-geometric methods, analytical results on the utilization level and the variability in the system are presented in relation to the frequency of updating the planned lead time. Although the average utilization level is always retained, the lead time syndrome causes an increase in the average workload level and the actual flow times of the completed orders. The variability of the planned lead time increases with the update frequency except at the utilization boundaries, where the relative effect of the update frequency diminishes.

Keywords:

• lead time setting
• order release
• quasi-birth-and-death processes
• matrix-geometric methods