Dynamic analysis of supply chain robustness and adaptation with the help of attainable sets and positional optimization

Dmitry Ivanov, Boris Sokolov, Inna Solovyeva, Semen Potryasaev

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


At the master planning level, economic performance is set up subject to a desired service level and maximization of net profits. The achievement of the planned economic performance at the execution level is related to control in an uncertain and perturbed environment. In this chapter, the issue of an integrated analysis of execution policies and the achievement of the planned economic performance is considered. In particular, two control theoretic tools - attainable sets and program-positional optimization are applied to. It is shown that attainable sets can be used to obtain estimations of performance attainability and consider perturbations in continuous time as constrained functions. Subsequently, the applicability of attainable sets to master planning level and robustness analysis is provided. With the presented results, it becomes possible to obtain attainable sets for interval data with no a priori information about perturbation impacts, i.e., for non-stationary perturbations. With the use of attainable sets, dynamic analysis of performance and robustness in operational system can be extended beyond existing approaches regarding multi-objective and dynamic formulations. Positional optimization can be used for adaptation of SC schedules. This allows considering robustness as a dynamic category subject to both disturbances and schedule recovery actions.

Original languageEnglish
Title of host publicationSequencing and Scheduling with Inaccurate Data
PublisherNova Science Publishers, Inc.
Number of pages28
ISBN (Electronic)9781629487229
ISBN (Print)9781629486772
StatePublished - 1 Jan 2014

Scopus subject areas

  • Mathematics(all)


  • Attainable (reachable) set
  • Economic performance
  • Master planning
  • Positional optimization
  • Robustness
  • Scheduling
  • Uncertainty


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