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Description
In this flow shop problem we have a set of Machines and a set of Jobs. Every job has to be processed on every machine, and the sequence of machines on which a job is processed is the same for every job. The goal is to find a schedule such that the time to process all the jobs on all the machines is as small as possible.
An optimal schedule is determined by the sequence of the jobs on the machines, that is which job is processed first on every machine, which second and so on. Besides this ordering, the start time of the job on the machines determines the optimal schedule.
This model seems rather easy, however the number of binary variables is equal to the square of the number of jobs. This means that the time the solver needs to solve this problem grows rapidly with the increase of the number of jobs.
In complex cases like this one might want to use startvalues to help find an optimal solution faster. This example will illustrate how a (MIP) variable can be initialized by assigning a value to it prior to calling the solve statement.
Keywords
CallBackNewIncumbent, Gantt chart, MIP Start Values
Industries
Model Types
Download AIMMS Example
You can download an AIMMS example dealing with this problem via the link below, and run it after installing the AIMMS software. If you don't have an AIMMS license yet, you can download a free license of AIMMS.
ftp://ftp.aimms.com/pub/Download/Examples/Flow Shop.aimmspack
Please make sure to save this file including the .aimmspack extension so that it can be opened by AIMMS.
This example application is a simplification of reality. Please do not hesitate to contact us to discuss how AIMMS enables you to build a complete optimization application that captures the full complexity of your problem.
Screenshot AIMMS Example
