Problem with a model for Assembly Line Balancing

[Marian Gröger]

Dear Google-Group,

in the context of an acedemic project, me and my project team need to implement an Assembly Line Balancing Problem for multiple variants with variant-specific processing times (MALBP) into AIMMS.

The optimization models task is to assign work steps for different variants of a certain product to a given amount of stations within a flow production system. Therefor exist precedence relations of the worksteps and a maximum cycle time which should not be exceeded by the processing times of the worksteps in total. If so, there will be cycle time violations. These cycle time violations are included in the objective function and should be minimized.

The implementation itself is not the problem since all the information about sets, parameters, variables and constraints are given (please find the attachment 'MALBP-var1' and 'MALBP-var2' with its reference: Bock, S., 2000). The implemented model is attached as well ('MALBP.zip').

First of all, we had a problem with an error that stopped the programme since it is a mixed integer nonlinear programming problem (MINLP). This failure could be solved by an outer approximation module which we had found here: http://techblog.aimms.com/2012/02/27/solving-minlp-problems-with-aimms-outer-approximation/

Afterwards, the model seemed to work but all worksteps will always be assigned to the first station. Because this can not be the correct solution of the problem (this would cause the highest possible cycle time violation in total), there has to be a mistake within the model which we do not see.

I hope that I described the problem sufficiently since this is my first entry to a google group and about an AIMMS problem. Please feel free to give feedback no matter which aspect it concerns and ask questions if there are uncertainties.

Thank you very much in advance,

Marian

[Marcel Hunting]

Hi,

The precedence relation constraints look strange to me, but as I do not have access to the reference I cannot tell what is wrong.

Note: You can linearize CycleTimeViolations and its definition in which case you end up with a linear model. That is a nice exercise.

Best regards,

Marcel Hunting

AIMMS Optimization Specialist

[Frederik]

Hey,

I am also in the project team. 

In the picture is a mistake in the precedence relation. It must be k instead of j. 

What do you mean by linearizing the CycleTimeViolations ? 

Thank you and best regards, 

Frederik Günther

[Frederik]

Hey, 

I got it working. We had to add a restriction in the Index Domain field for the PrecedenceRelations. 

It must be (i,j) | (PrecedenceGraph(i,j) = 1)

Best regards,

Frederik