Two Jobs ‘M’ Machine Case

• Two axes for representing the tasks 1 and 2. These are drawn at right angles to each other. For measuring the X and Y axis, same scale is being used. The operation time on machines are arranged as per the technological order of the sequencing problem. Here Y axis depicts the operation time and sequence of task 2 while the X axis depicts the operation time and sequence of task 1.
• That common area which depicts the operating time of both these tasks 1 and 2 is shaded. Since the operation of more than one job at a time is not possible on a single machine, this shaded area portrays the unachievable region in the graph.
• Processing of both these jobs is depicted by a continued path. This consists of vertical, horizontal and a diagonal region of 45 degrees. By avoiding this shaded area, the path begins at the graph’s lower left corner and stops moving beyond its upper right corner. Since the shaded area depicts that both these jobs are operated concurrently on the same machine, the path is prohibited from touching this area.

The horizontal movement in a graph represents that job 1 is in progress while the job 2 is waiting for getting processed. A vertical movement indicates that job 2 is currently in progress while the previous job 1 is waiting to be processed. However, if this path indicates a diagonal movement, it means that both job 1 and 2 are being operated on separate machines concurrently.

• The least elapsed time for a particular job = operating time of a task + unused time of that same job.
• A practicable path minimizes the total operation time and maximizes the diagonal movement.

It’s very important that students have a better understanding of this chapter by practicing some sums on this chapter as given in examples. This will give them the required grasp on this subject.

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• Introduction learning objectives
• Duality in linear programming
• Learning objectives
• Learning objectives the transportation problems

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• Learning objectives the transportation problems
• Special case of traveling sales man problem

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