A control approach to scheduling flexibly configurable jobs with dynamic structural-logical constraints. (2nd January 2021) - Ivanov, Dmitry; Sokolov, Boris; Chen, Weiwei; Dolgui, Alexandre; Werner, Frank; Potryasaev, Semyon
Abstract: We study the problem of scheduling in manufacturing environments which are dynamically reconfigurable for supporting highly flexible individual operation compositions of the jobs. We show that such production environments yield the simultaneous process design and operation sequencing with dynamically changing hybrid structural-logical constraints. We conceptualize a model to schedule jobs in such environments when the structural-logical constraints are changing dynamically and offer a design framework of algorithmic development to obtain a tractable solution analytically within the proven axiomatic of the optimal control and mathematical optimization. We further develop an algorithm to simultaneously determine the process design and operation sequencing. The algorithm is decomposition-based and leads to an approximate solution of the underlying optimization problem that is modeled by optimal control. We theoretically analyze the algorithmic complexity and apply this approach on an illustrative example. The findings suggest that our approach can be of value for modeling problems with a simultaneous process design and operation sequencing when the structural and logical constraints are dynamic and interconnected. Utilizing the outcomes of this research could also support the analysis of processing dynamics during the operations execution.