The bounding discrete phase-type method
(2006) MAM 2006 : Markov Anniversary Meeting — ISBN: [978-1932482348], p. 257-269, published
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- Abstract
- Models of production systems have always been essential. They are needed at a strategic level in order to guide the design of production systems but also at an operational level when, for example, the daily load and staffing have to be chosen. Models can be classified into three categories: analytical, simulative and approximate. In this paper, we propose an approximation approach that works as follows. Each arrival or service distribution is discretized using the same time step. The evolution of the production system can then be described by a Markov chain. The performances of the production system can then be estimated from the analysis of the Markov chain. The way the discretization is carried on determines the properties of the results. In this paper, we investigate the ``grouping at the end'' discretization method and, in order to fix ideas, in the context of production lines. In this case, upper and lower bounds on the throughput can be derived. Furthermore, the distance between these bounds is proved to be related to the time step used in the discretization. They are thus refinable and their precision can be evaluated a priori. All these results are proved using the concept of critical path of a production run. Beside the conceptual contribution of this paper, the method has been successfully applied to a line with three stations in which three buffer spaces have to be allocated. Nevertheless, the complexity and solution aspects will require further attention before making the method eligible for real large scale problems.
- Affiliations
Louvain School of Management Operations and Information FUCaM Sciences de gestion
Citations
Tancrez, J.-S., & Semal, P. (2006). The bounding discrete phase-type method. In Langville Amy N., Stewart William J. (eds.) (ed.), MAM 2006 : Markov Anniversary Meeting (p. p. 257-269). Boson Books. https://hdl.handle.net/2078.5/139323