Predictive Scheduling with Markov Chains and ARIMA Models

Abstract

Production scheduling is attracting considerable scientific interest. Effective scheduling of production jobs is a critical element of smooth organization of the work in an enterprise and, therefore, a key issue in production. The investigations focus on improving job scheduling effectiveness and methodology. Due to simplifying assumptions, most of the current solutions are not fit for industrial applications. Disruptions are inherent elements of the production process and yet, for reasons of simplicity, they tend to be rarely considered in the current scheduling models. This work presents the framework of a predictive job scheduling technique for application in the job-shop environment under the machine failure constraint. The prediction methods implemented in our work examine the nature of the machine failure uncertainty factor. The first section of this paper presents robust scheduling of production processes and reviews current solutions in the field of technological machine failure analysis. Next, elements of the Markov processes theory and ARIMA (auto-regressive integrated moving average) models are introduced to describe the parameters of machine failures. The effectiveness of our solutions is verified against real production data. The data derived from the strategic machine failure prediction model, employed at the preliminary stage, serve to develop the robust schedules using selected dispatching rules. The key stage of the verification process concerns the simulation testing that allows us to assess the execution of the production schedules obtained from the proposed model.