7,446 research outputs found
Stochastic bias in multi-dimensional excursion set approaches
We describe a simple fully analytic model of the excursion set approach
associated with two Gaussian random walks: the first walk represents the
initial overdensity around a protohalo, and the second is a crude way of
allowing for other factors which might influence halo formation. This model is
richer than that based on a single walk, because it yields a distribution of
heights at first crossing. We provide explicit expressions for the
unconditional first crossing distribution which is usually used to model the
halo mass function, the progenitor distributions, and the conditional
distributions from which correlations with environment are usually estimated.
These latter exhibit perhaps the simplest form of what is often called nonlocal
bias, and which we prefer to call stochastic bias, since the new bias effects
arise from `hidden-variables' other than density, but these may still be
defined locally. We provide explicit expressions for these new bias factors. We
also provide formulae for the distribution of heights at first crossing in the
unconditional and conditional cases. In contrast to the first crossing
distribution, these are exact, even for moving barriers, and for walks with
correlated steps. The conditional distributions yield predictions for the
distribution of halo concentrations at fixed mass and formation redshift. They
also exhibit assembly bias like effects, even when the steps in the walks
themselves are uncorrelated. Finally, we show how the predictions are modified
if we add the requirement that halos form around peaks: these depend on whether
the peaks constraint is applied to a combination of the overdensity and the
other variable, or to the overdensity alone. Our results demonstrate the power
of requiring models to reproduce not just halo counts but the distribution of
overdensities at fixed protohalo mass as well.Comment: 9 pages, 5 figures, submitted to MNRA
Modeling Stochastic Lead Times in Multi-Echelon Systems
In many multi-echelon inventory systems, the lead times are random variables. A common and reasonable assumption in most models is that replenishment orders do not cross, which implies that successive lead times are correlated. However, the process that generates such lead times is usually not well defined, which is especially a problem for simulation modeling. In this paper, we use results from queuing theory to define a set of simple lead time processes guaranteeing that (a) orders do not cross and (b) prespecified means and variances of all lead times in the multiechelon system are attained
Mixed-model Sequencing with Reinsertion of Failed Vehicles: A Case Study for Automobile Industry
In the automotive industry, some vehicles, failed vehicles, cannot be
produced according to the planned schedule due to some reasons such as material
shortage, paint failure, etc. These vehicles are pulled out of the sequence,
potentially resulting in an increased work overload. On the other hand, the
reinsertion of failed vehicles is executed dynamically as suitable positions
occur. In case such positions do not occur enough, either the vehicles waiting
for reinsertion accumulate or reinsertions are made to worse positions by
sacrificing production efficiency.
This study proposes a bi-objective two-stage stochastic program and
formulation improvements for a mixed-model sequencing problem with stochastic
product failures and integrated reinsertion process. Moreover, an evolutionary
optimization algorithm, a two-stage local search algorithm, and a hybrid
approach are developed. Numerical experiments over a case study show that while
the hybrid algorithm better explores the Pareto front representation, the local
search algorithm provides more reliable solutions regarding work overload
objective. Finally, the results of the dynamic reinsertion simulations show
that we can decrease the work overload by ~20\% while significantly decreasing
the waiting time of the failed vehicles by considering vehicle failures and
integrating the reinsertion process into the mixed-model sequencing problem.Comment: 26 pages, 6 figures, 5 table
Discrete Time Analysis of Multi-Server Queueing Systems in Material Handling and Service
In this doctoral thesis, performance parameters of multi-server queueing systems are estimated under general stochastic assumptions. We present an exact calculation method for the discrete time distribution of the number of customers in the queueing system at the arrival moment of an arbitrary customer. The waiting time distribution and the sojourn time distribution are estimated exactly, as well. For the calculation of the inter departure time distribution, we present an approximation method
- …