Question

Consider two jobs, Job 1 and Job 2, to be processed on a single machine. It takes 7 days to process job 1, whereas the processing time of job 2 is 4 days. If the production is switched from ob 1 to job 2, then the set-up takes 2 days. On the other hand, if the production is switched from ob 2 to job 1, the set-up time reduces to 1 day. The processing of the jobs cannot start before the beginning of Day 3 and both jobs are due at the beginning of Day 20. Let x1 and x2 be two integer variables representing the start date in days for job 1 and job2 4- Two jobs will not be processed concurrently: If job 1 precedes job 2, then the start date of job 2 must be greater than or equal to start date of ob 1 plus the processing of job 1 and the set-up time If job 2 precedes job 1, then the start date of job 1 must be greater than or equal to start date of job 2 plus the processing of job 2 and the set-up time Use indicator variable(s) representing the order of processing and mathematically formulate the constraint(s) that are verbally written above using indicator variable(s) and big M(s). Calculate the minimum value of M that would work. (Hint: What are the ranges for x1 and x2?)

Answer 1

Answer:

• No job uses more than one machine simultaneously .
• No machine processes more than one job simultaneously.
• Only 3 hours will be needed to complete the jobs.

Explanation:

However, Job 2 can be completed at time 3 which is late by 1 hour.

Suppose that the processing times are exponentially distributed.

Let

• The processing rate of job j on machine 1
• The processing rate of job j on machine 2

Expected make span is minimized by processing the jobs in the descending (high to low) order of processing

Make span is the completion time of the last job processed. Although make span is defined as a completion time of a job, it actually measures how long the production facility should remain open.