Comparison of discrete- and continuous-time models for scheduling waste wood processing facilities

With the growing significance of environmental awareness, the role of renewable materials and their reuse and recycling possibilities have become increasingly important. Wood is one of the best examples for this, as it is a material that has a variety of primary uses, while also being a prime candidate for reuse and recycling. An important phase in most waste wood value chains is the processing of bulk waste from various sources, usually by means of shredding. This paper presents methods for scheduling the machines in such a waste wood processing facility, where incoming deliveries of different types of wood are processed by a series of treatment and transformation steps to produce shredded wood. Two mathematical models are developed for the problem that both allow overlaps between consecutive steps to optimize resource flow through the system. One of these is a more traditional discrete-time model, while the other is precedence-based and uses continuous-time variables for the timing of the various tasks. Both modeling techniques have their advantages and shortcomings with regard to the ease of integration of further problem-specific parameters and requirements. Next to providing a sound approach for the identified problem class, another aim is to evaluate, which technique suits better for this problem class, and should be used as a basis for extended and integrated cases in the future. Thus, the performance of these models is compared on instances that were randomly generated based on real-world distributions from the literature.