Modelling Dynamics of a Log-Yard through Discrete-Event Mathematics

This article deals with the topic of modelling the log-yard of one of our industry partners. To this end, our framework is based on discrete-events modelling (DEM), as consequence that many stages of the process run as a sequence of events. The sequence starts when trucks, trains or ships arrive loaded with logs to the log-yard. A machine unloads these logs and accumulates them in different storage areas. Consequently, a machine transports logs from these areas to the pulp mill, thus finishing the process. As using probability density functions is the core concept of DEM, the necessary process data to build these PDFs have been partly provided by the company. Other necessary data have been acquired through time studies, and by defining operational requirements. The company data tell when trucks, trains, or ships arrive to the log-yard, and the amount of volume they carry. The objective is to develop the necessary formulations, model calibration techniques, and software, such that computer simulations reproduce the quantities observed in these data. To this end, this work suggests two alternatives to analyse the data itself. These two alternatives lead to two different models: (1) The first being a hybrid model, in the sense that it involves the events in the process, and the logic decisions taken by machine operators for handling the incoming load, and (2) the second containing only the main mathematical essence of the process. After running 100 simulations, both mathematical models show that the simulated values for input and output, in terms of transport units and their volume, differ only by less than 3% compared to company data. The first model has also shown the ability to replicate the decision making that a machine operator undergoes for driving the logs to the storage areas, and from there to the mill. Therefore, the framework adopted provides the necessary mathematical tools and data analysis to model the log-yard and obtain highly reliable results via simulations.