A Flexible Manufacturing System consists of 2-Automatic-Machine- Tools used for the manufacture of 7-Jobs. Both the...

 

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A Flexible Manufacturing System consists of 2-Automatic-Machine- Tools used for the manufacture of 7-Jobs. Both the machines have a tool-slot holder / pallet-holder, of a circular form as shown in the figure. There is a limitation of the total number of tools which may be fixed on the tool-slot holder. A table given below mentions the processing time of a job on a particular type of machine. There are 7- Jobs to be processed on the 2-Machines. The number of tools required for a particular job is shown in the row St, which indicates the number of tools required for each of the Jobs J1 to J7 on any of the machines. It may be noted that the tool used by a job is not common to other jobs, in other words the tool slot variable Si represents a Disjoint- Set. Calculate an optimum schedule for this machine-loading problem, given the processing times of the two machines. The Jobs are to be assigned to a particular machine such that the Makespan is minimized. Processing Times and the Tool-requirement for the Seven-Jobs J3 J7 6 9 7 3 MJ M1 M2 Si Statement of optimization: J1 2 1 2 J2 4 5 3 883 5682 J4 J5 J6 7 8 2 7 5 U₁= P₁1X11 + P21X21 ++P71X71 U₂ = P12X12 + P22X22 ++P72X72 Ti 10 10 Minimize: u; where u = ₁ + ₂ The real valued functions u₁ and u are the processing times on the Machine M1 and M2 respectively and are stated as: Here X₁; = 0,1 are the decision variables indicating the particular machine loading. Here, u stands for the machine loading in terms of the Makespan, pis and Piz indicates the processing times on machine 1&2 respectively, and X₁₁ and X₁ are the binary decision variables of loading the machine 1&2 with the part-t. It may be noted that X₁1&X₁2 are mutually exclusive, hence if machine-1 is to be loaded with the part-i the machine-2 is not to be loaded with the same part. State the Minimum value of Makespan required. A Flexible Manufacturing System consists of 2-Automatic-Machine- Tools used for the manufacture of 7-Jobs. Both the machines have a tool-slot holder / pallet-holder, of a circular form as shown in the figure. There is a limitation of the total number of tools which may be fixed on the tool-slot holder. A table given below mentions the processing time of a job on a particular type of machine. There are 7- Jobs to be processed on the 2-Machines. The number of tools required for a particular job is shown in the row St, which indicates the number of tools required for each of the Jobs J1 to J7 on any of the machines. It may be noted that the tool used by a job is not common to other jobs, in other words the tool slot variable Si represents a Disjoint- Set. Calculate an optimum schedule for this machine-loading problem, given the processing times of the two machines. The Jobs are to be assigned to a particular machine such that the Makespan is minimized. Processing Times and the Tool-requirement for the Seven-Jobs J3 J7 6 9 7 3 MJ M1 M2 Si Statement of optimization: J1 2 1 2 J2 4 5 3 883 5682 J4 J5 J6 7 8 2 7 5 U₁= P₁1X11 + P21X21 ++P71X71 U₂ = P12X12 + P22X22 ++P72X72 Ti 10 10 Minimize: u; where u = ₁ + ₂ The real valued functions u₁ and u are the processing times on the Machine M1 and M2 respectively and are stated as: Here X₁; = 0,1 are the decision variables indicating the particular machine loading. Here, u stands for the machine loading in terms of the Makespan, pis and Piz indicates the processing times on machine 1&2 respectively, and X₁₁ and X₁ are the binary decision variables of loading the machine 1&2 with the part-t. It may be noted that X₁1&X₁2 are mutually exclusive, hence if machine-1 is to be loaded with the part-i the machine-2 is not to be loaded with the same part. State the Minimum value of Makespan required.

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