Intelligent pipeline control - a simulation study in the automotive sector

Automotive producers are aiming to make their order fulfilment processes more flexible. Opening the pipeline of planned products for dynamic allocation to dealers/ customers is a significant step to be more flexible but the behaviour of such Virtual-Build-To-Order systems are complex to predict and their performance varies significantly as product variety levels change. This study investigates the potential for intelligent control of the pipeline feed, taking into account the current status of inventory (level and mix) and of the volume and mix of unsold products in the planning pipeline, as well as the demand profile. Five ‘intelligent’ methods for selecting the next product to be planned into the production pipeline are analysed using a discrete event simulation model and compared to the unintelligent random feed. The methods are tested under two conditions, firstly when customers must be fulfilled with the exact product they request, and secondly when customers trade-off a shorter waiting time for compromise in specification. The two forms of customer behaviour have a substantial impact on the performance of the methods and there are also significant differences between the methods themselves. When the producer has an accurate model of customer demand, methods that attempt to harmonise the mix in the system to the demand distribution are superior.

Towards a predictive model of Ca²⁺ puffs

We investigate key characteristics of Ca²⁺ puffs in deterministic and stochastic frameworks that all incorporate the cellular morphology of IP[subscript]3 receptor channel clusters. In a first step, we numerically study Ca²⁺ liberation in a three dimensional representation of a cluster environment with reaction-diffusion dynamics in both the cytosol and the lumen. These simulations reveal that Ca²⁺ concentrations at a releasing cluster range from 80 µM to 170 µM and equilibrate almost instantaneously on the time scale of the release duration. These highly elevated Ca²⁺ concentrations eliminate Ca²⁺ oscillations in a deterministic model of an IP[subscript]3R channel cluster at physiological parameter values as revealed by a linear stability analysis. The reason lies in the saturation of all feedback processes in the IP[subscript]3R gating dynamics, so that only fluctuations can restore experimentally observed Ca²⁺ oscillations. In this spirit, we derive master equations that allow us to analytically quantify the onset of Ca²⁺ puffs and hence the stochastic time scale of intracellular Ca²⁺ dynamics. Moving up the spatial scale, we suggest to formulate cellular dynamics in terms of waiting time distribution functions. This approach prevents the state space explosion that is typical for the description of cellular dynamics based on channel states and still contains information on molecular fluctuations. We illustrate this method by studying global Ca²⁺ oscillations.