Computing idle times in fuzzy flexible job shop scheduling

Abstract

The flexible job shop scheduling problem is relevant in many different areas. However, the usual deterministic approach sees its usefulness limited, as uncertainty plays a paramount role in real-world processes. Considering processing times in the form of fuzzy numbers is a computationally affordable way to model uncertainty that enhances the applicability of obtained solutions. Unfortunately, fuzzy processing times add an extra layer of complexity to otherwise straightforward operations. For example, in energy-aware environments, measuring the idle times of resources is of the utmost importance, but it goes from a trivial calculation in the deterministic setting to a critical modelling decision in fuzzy scenarios, where different approaches are possible. In this paper, we analyse the drawbacks of the existing translation of the deterministic approach to a fuzzy context and propose two alternative ways of computing the idle times in a schedule. We show that, unlike in the deterministic setting, the different definitions are not equivalent when fuzzy processing times are considered, and results are directly affected, depending on which one is used. We conclude that the new ways of computing idle times under uncertainty provide more reliable values and, hence, better schedules.