### Burak Buke (University of Edinburgh)

#### Fluid networks with parameter uncertainty

*Wednesday 11 November 2009 at 15.30, JCMB 6206*

##### Abstract

The makespan of a fluid network is defined as the time to drain the
system, when there is fluid present in the buffers initially. In this
presentation, our main focus is minimizing makespan when the problem
parameters are uncertain. Assuming distributional information about
parameters is available, the decision maker's goal is to optimally
allocate the capacity in order to minimize the expected value of the
makespan. We consider two decision making schemes. In the first scheme,
the controller sets the allocations before observing the parameters.
After the initial allocations are set, they cannot be changed. In the
second scheme, the controller is allowed a recourse action after a data
collection process. It is shown that both schemes differ considerably
from the deterministic version of the problem. We formulate both schemes
as stochastic programs. The first scheme is easier to solve since the
resulting model is convex. Unfortunately, under the second decision
scheme, the objective function is non-convex. We develop a
branch-and-bound methodology to solve the resulting stochastic
non-convex program.

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