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Dynamic supply chain scheduling

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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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Abbreviations

SC:

Supply Chain

OPC:

Optimal Program Control

OR:

Operations Research

MP:

Mathematical Programming

CT:

Control Theory

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Authors and Affiliations

  1. Faculty of Economics and Business Administration, Department of Production Economics and Industrial Organization, Chemnitz University of Technology, 09107, Chemnitz, Germany

    D. Ivanov

  2. Saint Petersburg Institute for Informatics and Automation of the Russian Academy of Science, Saint-Petersburg, Russia

    B. Sokolov

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  1. D. Ivanov
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  2. B. Sokolov
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Correspondence to D. Ivanov.

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Ivanov, D., Sokolov, B. Dynamic supply chain scheduling. J Sched 15, 201–216 (2012). https://doi.org/10.1007/s10951-010-0189-6

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  • DOI: https://doi.org/10.1007/s10951-010-0189-6

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