Problem in Calculate Makespan (P||Cmax)

[Izzati Moy]

Hello, I'm new at Aimms and I'm having a problem in solving the identical parallel machine. Anyone can help me in how to enter data in processing time? 

Develop the minimum makespan , assuming 2 processors are to be used in parallel.

Tasks	1	2	3
Processing Times	8	7	5

The coding that I have done.  

 

Model Main_Makespan {

    Parameter MaxTasks {

        Text: "Number of elements in the set Tasks";

        Range: integer;

    }

    Set Tasks {

        Text: "Set of all Tasks";

        Index: i;

        Definition: ElementRange(1,MaxTasks, prefix: "Task-");

    }

    Parameter MaxProcessors {

        Text: "Number of elements in the set Processors";

        Range: integer;

    }

    Set Processors {

        Text: "Set of all processors";

        Index: j;

        Definition: ElementRange(1,MaxProcessors, prefix: "M-");

    }

    Parameter ProcessingTime {

        IndexDomain: j;

        Text: "Time required to process task i on processor j";

    }

    Variable X {

        IndexDomain: (i,j);

        Range: binary;

    }

    Variable Makespan {

        Text: "Total time to process all tasks on all processors";

        Range: free;

        Definition: sum(j,ProcessingTime(j));

    }

    Constraint Constraint1 {

        IndexDomain: j;

        Definition: sum(i,X(i,j)*ProcessingTime(j)) <= Makespan;

    }

    Constraint Constraint2 {

        IndexDomain: i;

        Definition: sum(j,X(i,j)) = 1;

    }

    Constraint Constraint3 {

        Definition: Makespan >= 0;

    }

    MathematicalProgram MinimizeMakespan {

        Objective: Makespan;

        Direction: minimize;

        Constraints: AllConstraints;

        Variables: AllVariables;

        Type: Automatic;

    }

    Procedure MainInitialization {

        Body: {

            MaxTasks := 3;

            MaxProcessors := 2;

        }

    }

    Procedure MainExecution {

        Body: {

            solve MinimizeMakespan;

            if (MinimizeMakespan.ProgramStatus<> 'Optimal')

            then empty X(i,j), Makespan;

            endif;

        }

    }

    Procedure MainTermination {

        Body: {

            return DataManagementExit();

        }

    }

}

[Marcel Hunting]

Hi,

Your table indicates that the processing times depend on the Tasks (and not the Processors). Therefore the ProcessingTime should have index domain 'i', the index of the set Tasks. The data can then be assigned using for example

ProcessingTime := data { Task-1 : 8,  Task-2 : 7, Task-3 : 5 } ;

Best regards,

Marcel Hunting

AIMMS Optimization Specialist

[Izzati Moy]

Thanks for your help but I don't understand "ProcessingTime should have index domain 'i', the index of the set Tasks", and what should I coding this formula Makespan= completion of ProcessingTime (maximum), 

sum(j,ProcessingTime(j)); Is it wrong?

On 8 March 2016 at 22:10, Marcel Hunting <Marcel....@aimms.com> wrote:

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Hi,

Your table indicates that the processing times depend on the Tasks (and not the Processors). Therefore the ProcessingTime should have index domain 'i', the index of the set Tasks. The data can then be assigned using for example

ProcessingTime := data { Task-1 : 8,  Task-2 : 7, Task-3 : 5 } ;

Best regards,

Marcel Hunting

AIMMS Optimization Specialist

On Monday, March 7, 2016 at 7:33:22 PM UTC+1, Izzati Moy wrote:

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