How to Cook a Gourmet Meal with Limited Resources using Conservation Laws
Abstract
We will discuss aspects of the generic scheduling problem,
how to optimally process N 'products' which have to pass
through M 'machines' in a certain sequence. This problem
has a wide variety of quite different applications,
ranging from organizing the production process on a
factory floor to scheduling patients in a large hospital,
to cooking a five course meal when you only have three
pots and two hot-plates. After giving an overview over
standard simulation techniques, such as deterministic and
Monte Carlo type discrete event simulators and so called
fluid models, we will focus on models based on hyperbolic
conservation laws. The goal of the presented work is to
derive these models from the equivalent of first
principles (i.e. Little's Law). Numerical comparisons with
discrete event simulations will be presented and the
implementation of scheduling policies such as FIFO (First
In First Out) and frequency domain policies will be
discussed. Finally, we will discuss the issues involved in
deriving a 'master equation' for a complex system through
homogenization techniques. (Joint work with D. Armbruster
and D. Marthaler)
