Cyclic multi-hoist scheduling with fuzzy processing times in flexible manufacturing lines

Abstract

This work addresses the problem of scheduling multiple hoists (robots), which arises on real automated electroplating lines. Several hoists operate on a shared track and should not collide with each other. The processing time for each operation is preset in interval form. The problem simultaneously takes into account two criteria: maximum processing quality and maximum line productivity. To do this, we estimate the dependence of the duration of operations on the level of their quality and, in accordance with these estimates, we represent the processing times in the form of fuzzy numbers with triangular membership functions. The novelty of this study is two-fold. First, we propose a new mathematical model based on the use of fuzzy numbers and fuzzy operations on them, which is designed to deal with complex galvanic lines served by multiple hoists. The second new feature is a new combinatorial method developed for scheduling multiple hoists. For this, we modify and refine the so-called “method of prohibited intervals”, which has been actively used in scheduling theory in recent decades to solve problems, but until now was known only for the case of a single hoist. Thus, the second novelty of this work is that it is actually the first attempt to use the powerful technique of fuzzy set theory to solve a practical problem of scheduling multiple hoists. Computational experiments on real and randomly generated instances show that the new algorithm can successfully solve real problems that arise in practice.