3. In a job shop opernation, four jobe msy be performed on any of four machinos.
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3. In a job shop opernation, four jobe msy be performed on any of four machinos. The bours required for each job on each machine is given in the following tables Machine A 12 16 11 16 B 23 15 12 13 C 18 17 21 17 D 13 14 16 15 The supervisor would like to assign jobs so that total time is minimized a) Develop a network representation of this problem. b) Formulate a linear programming model for this problem. (Write the complete model for the problem. Make sure to give clear definitions of your decision variables). c) Solve the problem by using Excel Solver (Hand-in the value and formulas printouts for the problem).Explanation / Answer
A simple linear programming model can be formulated and the optimal solution can be obtained. As the precedence is not required for any job as the job can be done on a machine at any time or order, thus the only requirement is that it gets finished on all the machines in the minimum possible time. The number of variables can be assigned as 16 for the machines as x1,x2,x3,x4,y1,y2,y3,y4....w4 describing the schedule of the job on a machine. Thus x1 can take values from 1,2,3,4 depending on which job is assigned as the first job on machine-x and similarly for other machines.
The aim is to minimize the total time of all the machines(including the idle time-very important )gets minimized.
The algorithm will work as:-
a)Find the minimum time a job takes on a machine, assign the job to that machine. Delete the raw and the column corresponding to that job and machine. Repeat the process, until all assigned. calculate the total time(with idle time).
b) Repeat the whole process, again canceling the cells on the matrix where the job has been completed by the machine.
c)Repeat until every job is operated on every machine.
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