title: Clearing function in the context of the invariant manifold method
metadata.name: dc.contributor.author
metadata.value: Mustafin, Almaz T.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Kantarbayeva, Aliya K.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2023-08-22T16:59:41Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2023-08-22T16:59:41Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2023-06
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Mustafin A. T., Kantarbayeva A. K. Clearing function in the context of the invariant manifold method. Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 2023, vol. 19, iss. 2, pp. 185–198.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/11701/spbu10.2023.205
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/43827
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: Clearing functions (CFs), which express a mathematical relationship between the expected throughput of a production facility in a planning period and its workload (or work-inprogress, WIP) in that period have shown considerable promise for modeling WIP-dependent cycle times in production planning. While steady-state queueing models are commonly used to derive analytic expressions for CFs, the finite length of planning periods calls their validity into question. We apply a different approach to propose a mechanistic model for one-resource, one-product factory shop based on the analogy between the operation of machine and enzyme molecule. The model is reduced to a singularly perturbed system of two differential equations for slow (WIP) and fast (busy machines) variables, respectively. The analysis of this slow-fast system finds that CF is nothing but a result of the asymptotic expansion of the slow invariant manifold. The validity of CF is ultimately determined by how small is the parameter multiplying the derivative of the fast variable. It is shown that sufficiently small characteristic ratio ’working machines: WIP’ guarantees the applicability of CF approximation in unsteady-state operation.
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Applied Mathematics. Computer Science. Control Processes;Volume 19; Issue 2
metadata.lang: -
metadata.name: dc.subject
metadata.value: work in progress
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: production model
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: quasi-steady-state approximation
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: singular perturbation
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: enzyme catalysis
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Clearing function in the context of the invariant manifold method
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 05.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/43827/1/05.pdf
resources.format: Adobe PDF
resources.size: 467,4 kB