Dynamic supply chain scheduling |
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Authors: | D Ivanov B Sokolov |
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Affiliation: | 1. Faculty of Economics and Business Administration, Department of Production Economics and Industrial Organization, Chemnitz University of Technology, 09107, Chemnitz, Germany 2. Saint Petersburg Institute for Informatics and Automation of the Russian Academy of Science, Saint-Petersburg, Russia
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Abstract: | Based on a combination of fundamental results of modern optimal program control theory and operations research, an original
approach to supply chain scheduling is developed in order to answer the challenges of dynamics, uncertainty, and adaptivity.
Both supply chain schedule generation and execution control are represented as an optimal program control problem in combination
with mathematical programming and interpreted as a dynamic process of operations control within an adaptive framework. Hence,
the problems and models of planning, scheduling, and adaptation can be consistently integrated on a unified mathematical axiomatic
of modern control theory. In addition, operations control and flow control models are integrated and applicable for both discrete
and continuous processes. The application of optimal control for supply chain scheduling becomes possible by formulating the
scheduling model as a linear non-stationary finite-dimensional controlled differential system with the convex area of admissible
control and a reconfigurable structure. For this model class, theorems of optimal control existence can be used regarding
supply chain scheduling. The essential structural property of this model are the linear right parts of differential equations.
This allows applying methods of discrete optimization for optimal control calculation. The calculation procedure is based
on applying Pontryagin’s maximum principle and the resulting essential reduction of problem dimensionality that is under solution
at each instant of time. The gained insights contribute to supply chain scheduling theory, providing advanced insights into
dynamics of the whole supply chains (and not any dyadic relations in them) and transition from a partial “one-way” schedule
optimization to the feedback loop-based dynamic and adaptive supply chain planning and scheduling. |
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Keywords: | |
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