Correlation among tardiness-based measures for scheduling using priority dispatching rules

Abstract

One of the most commonly used methods to schedule manufacturing systems is to use priority dispatching rules (pdrs). It is frequently desired to distinguish the behaviour of pdrs with regard to tardiness-based performance measures. However, the relation among these performance measures is generally not obvious even for simple scheduling strategies such as pdrs. In this paper, we first focus on the maximum tardiness, which is a very interesting performance measure for the decision-maker on the shop floor. However, because of its singularity, it is not trivial to assess. We conducted a simulation study on a benchmark model of a dynamic job-shop system to evaluate the relative performance of a set of pdrs chosen either because they are used extensively or because they exhibit very good performance. Based upon the distribution of the maximum tardiness of these benchmark pdrs, we identify two sub-sets of pdrs. From this, we conducted experiments on the root-mean-square tardiness, which is used to distinguish a system with a few very tardy jobs from a system with a lot of less tardy jobs. The experiments show a positive correlation between maximum tardiness and root-mean-square tardiness. Because of the fact that the root-mean-square tardiness is an aggregate measure, it is much easier to assess than the maximum tardiness. This provides an opportunity to predict the relative performance of pdrs with regard to the maximum tardiness as well as the width of the tardiness by evaluating the root-mean-square tardiness only.

Keywords:

• scheduling
• simulation
• job shop
• stochastic models
• tardiness
• priority dispatching