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We review the literature about shop scheduling problems in manufacturing systems, revealing the concepts and methodologies that most impact the usage of scheduling theory in manufacturing environments. We focus our attention on the job shop and flow shop problems and their variants. We emphasize the interactions between the scheduling functions and manufacturing paradigms such as Industry 4.0, Computer Integrated Manufacturing, Computer‐Aided Process Planning, Advanced Planning and Scheduling, and Integrated Process Planning and Scheduling. We describe the main components and characteristics of the scheduling ecosystem, and we discuss how the scheduling interacts with the components that make it up and how it is affected by them. The metadata collected from the digital libraries on which the review was based (ScienceDirect, Scopus, and Elsevier) made it possible to characterize the historical evolution of the main concepts of the scheduling ecosystem in terms of scientific publications and research trends in the period 2000–2020. [ABSTRACT FROM AUTHOR]

In this paper, we propose the notions of the max-plus algebra of the interval tensors, which can be used for the extension of interval linear systems to interval multi-linear systems in the max-plus algebra. Some properties and basic results of interval multi-linear systems in max-plus algebra are derived. An algorithm is developed for computing a solution of the multi-linear systems in the max-plus algebra. Necessary and suficient conditions for the interval multi-linear systems for weak solvability over max-plus algebra are obtained as well. Also, some examples are given for illustrating the obtained results. Moreover, we briey sketch how our results can be used in the max-plus algebraic system theory for synchronized discrete event systems. [ABSTRACT FROM AUTHOR]