2,686 research outputs found
A comparison between the order and the volume fill rates for a base-stock inventory control system under a compound renewal demand process
The order fill rate is less commonly used than the volume fill rate (most often just denoted fill rate) as a performance measure for inventory control systems. However, in settings where the focus is on filling customer orders rather than total quantities, the order fill rate should be the preferred measure. In this paper we consider a continuous review, base-stock policy, where all replenishment orders have the same constant lead time and all unfilled demands are backordered. We develop exact mathematical expressions for the two fill-rate measures when demand follows a compound renewal process. We also elaborate on when the order fill rate can be interpreted as the (extended) ready rate. Furthermore, for the case when customer orders are generated by a negative binomial distribution, we show that it is the size of the shape parameter of this distribution that determines the relative magnitude of the two fill rates. In particular, we show that when customer orders are generated by a geometric distribution, the order fill rate and the volume fill rate are equal (though not equivalent when considering sample paths). For the case when customer inter-arrival times follow an Erlang distribution, we show how to compute the two fill rates.Backordering; continuous review; compound renewal process; inventory control; negative binomial distribution; service levels
Reconstruction of annular bi-layered media in cylindrical waveguide section
A radial transverse resonance model for two cylindrical concentric layers
with different complex dielectric constants is presented. An inverse problem
with four unknowns - 3 physical material parameters and one dimensional
dielectric layer thickness parameter- is solved by employing TE110 and TE210
modes with different radial field distribution. First a Newton-Raphson
algorithm is used to solve a least square problem with a Lorentzian function
(as resonance model and "measured" data generator). Then found resonance
frequencies and quality factors are used in a second inverse Newton-Raphson
algorithm that solves four transverse resonance equations in order to get four
unknown parameters. The use of TE110 and TE210 models offers one dimensional
radial tomographic capability. An open ended coax quarter-wave resonator is
added to the sensor topology, and the effect on the convergence is
investigated
Weighted Branching Simulation Distance for Parametric Weighted Kripke Structures
This paper concerns branching simulation for weighted Kripke structures with
parametric weights. Concretely, we consider a weighted extension of branching
simulation where a single transitions can be matched by a sequence of
transitions while preserving the branching behavior. We relax this notion to
allow for a small degree of deviation in the matching of weights, inducing a
directed distance on states. The distance between two states can be used
directly to relate properties of the states within a sub-fragment of weighted
CTL. The problem of relating systems thus changes to minimizing the distance
which, in the general parametric case, corresponds to finding suitable
parameter valuations such that one system can approximately simulate another.
Although the distance considers a potentially infinite set of transition
sequences we demonstrate that there exists an upper bound on the length of
relevant sequences, thereby establishing the computability of the distance.Comment: In Proceedings Cassting'16/SynCoP'16, arXiv:1608.0017
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