Question

An assignment problem is solved to minimize the total processing time of four jobs (1, 2, 3 and 4) on four different machines such that each job is processed exactly by one machine and each machine processes exactly one job. The minimum total processing time is found to be 500 minutes. Due to a change in design, the processing time of Job 4 on each machine has increased by 20 minutes. The revised minimum total processing time will be ________________ minutes (in integer).

Hint:

For assignment problems, the change in total processing time due to a modification can be calculated by multiplying the number of machines by the increase in time for each job.

Answer 1

Correct Answer: 520

Step 1: Understand the Original Problem

There are 4 jobs and 4 machines. Each job is processed by exactly one machine, and each machine processes exactly one job. The minimum total processing time is 500 minutes.

Step 2: Identify the Change

The processing time of Job 4 has increased by 20 minutes on every machine.

Step 3: Analyze the Effect

Job 4 must be assigned to one machine in every valid assignment. Since the processing time of Job 4 increases by 20 minutes regardless of the machine chosen, the total processing time will increase by 20 minutes.

Step 4: Revised Minimum Processing Time

Revised Minimum Time = 500 + 20 = 520 minutes

Final Answer

520 minutes