Data-driven control of a production system by using marking-dependent threshold policy

Abstract

As increasingly more shop-floor data becomes available, the performance of a production system can be improved by developing effective data-driven control methods that utilize this information. We focus on the following research questions: how can the decision to produce or not to produce at any time be given depending on the real-time information about a production system?; how can the collected data be used directly in optimizing the policy parameters?; and what is the effect of using different information sources on the performance of the system? In order to answer these questions, a production/inventory system that consists of a production stage that produces to stock to meet random demand is considered. The system is not fully observable but partial production and demand information, referred to as markings is available. We propose using the marking-dependent threshold policy to decide whether to produce or not based on the observed markings in addition to the inventory and production status at any given time. An analytical method that uses a matrix geometric approach is developed to analyze a production system controlled with the marking-dependent threshold policy when the production, demand, and information arrivals are modeled as Marked Markovian Arrival Processes. A mixed integer programming formulation is presented to determine the optimal thresholds. Then a mathematical programming formulation that uses the real-time shop floor data for joint simulation and optimization (JSO) of the system is presented. Using numerical experiments, we compare the performance of the JSO approach to the analytical solutions. We show that using the marking-dependent control policy where the policy parameters are determined from the data works effectively as a data-driven control method for manufacturing.