Nine Jobs need to be completed within eight weeks.The number of weeks required t

Question

Nine Jobs need to be completed within eight weeks.The number of weeks required to complete each job is given in the file( See picture attached). For exmaple, job 2 requires three weeks. Each job requires 40 hours of labor per week. Each week, 160 hours of regular time labor are available. Up to 40 hours of overtime labor can be purchased each week at a cost of $10 per hour. Additional overtime house cost 20 per hour.

A: Determine how o minimize the over time cost incurred in completing the jobs within eight weeks.

B: The same file( See picture attached) also lists the due date for each job For exmaple, job 2 should be completed within 6 weeks. A penalty of 500 is incurred for each day a job is late. Determine how to minimize the sum of overtime.

I need Algebraic model and Formulas for excel

Explanation / Answer

After Calculation of the OT It is clear that if we need to compleate the 9 jobs in 8 weeks we have to take labor on over time i.e Only 0.89 weeks are avaliable for each job that means as 160 reguls hours of labor are avaliable for each week it mean we have 1280 hours to comleate the job.

as time required to comleate the jobs is given and it come as 32 weeks it means 1280 hours needed to compleate the jobs as per regular 40 hrs standard for a week.

aviliable time =1280 Hrs

Needed Time= 1280 Hours

Calculation for OT

There is no option to reduce the OT as we dont have the spare time not even mentions extra time which we can use for the jobs

As we use the proper OT for the labour the jobs will be compleated with in the specified time and no panelty will be charged.

Job   week 1 4 2 3 3 5 4 4 5 4 6 2 7 3 8 2 9 5 32 Total week given Total Jobs Week for each job Hrs for each job 8 9 0.89 35.56 Job   Week due date Week /job less time Hrs/Job Total OT required OT At    10 $ OT At 20 $ Ot cost for 10 $ Ot cost for 20 $ 1 4 7 0.89 3.11 35.56 124.44 40 84.44 400 1688.89 2 3 6 0.89 2.11 35.56 84.44 40 44.44 400 888.89 3 5 5 0.89 4.11 35.56 164.44 40 124.44 400 2488.89 4 4 4 0.89 3.11 35.56 124.44 40 84.44 400 1688.89 5 4 5 0.89 3.11 35.56 124.44 40 84.44 400 1688.89 6 2 4 0.89 1.11 35.56 44.44 40 4.44 400 88.89 7 3 4 0.89 2.11 35.56 84.44 40 44.44 400 888.89 8 2 4 0.89 1.11 35.56 44.44 40 4.44 400 88.89 9 5 5 0.89 4.11 35.56 164.44 40 124.44 400 2488.89 Total 32 8 24.00 320.00 960.00 360.00 600.00 3600 12000

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