difficult scheduling problem

[Bela.Patkai@pe.tut.fi]

Hello,

The scheduling problem I have to solve involves a factory with
reconfigurable assembly lines. We know how many lines can be formed - for
technical reasons - from the assembly machines, but there is nearly no
constraints on how we combine them and how long we run the chosen
configuration. So we have to produce a schedule that tells how we
configure and when we reconfigure the assembly lines and which products do
we assemble on them. A further complication is that the assembly procedure
can have several stages, because in case we have 10 assembly steps of a
product (we may have dozens of different products) we could do 5 on one
line, later do 3 on another and then the rest on another. If we remove a
machine from one line and put it in another then the two involved lines
are idle for a certain amount of time.

I have solved the problem by a genetic algorithm, with a mixed
representation: the assembly lines are a matrix with the number of
machines from a certain type (e.g. assembly line-1 is: 2-3-1-0-1), the
time this configuration is valid is another real variable, and a discrete
priority list tells the schedule builder in which order to schedule the
assemblies or subassemblies on the time-dependent combination of assembly
lines. This objective function is non-smooth and surely non-optimal,
because the schedule-builder uses only simple heuristic dispatching.

My questions:

Does it seem like a problem that can be solved by mixed-integer
programmig?

Can you point me to similar problems on the web or give advice for
improvements? (I searched and havent found much that would help).

Thanks for any comments,

Bela