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hw11_solns - ORIE 4580/5580 Solutions for Homework...

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ORIE 4580/5580 Solutions for Homework Assignment 11 Question 1: Using policy 1, the first machine starts at time 0 with the job that takes the longest processing time and finishes this job at max{T 1 , T 2 , T 3 }. The second machine starts at time 0 with the job that takes the second longest processing time and finishes at median{T 1 , T 2 , T 3 }. The second machine finishes first and will complete the only remaining job at median{T 1 , T 2 , T 3 } + min{T 1 , T 2 , T 3 }. Therefore, the time it takes the first policy to complete all three jobs = max{max{T 1 , T 2 , T 3 }, median{T 1 , T 2 , T 3 } + min{T 1 , T 2 , T 3 }}. Similarly, under policy 2, the first machine starts at time 0 with the job that takes the shortest processing time and finishes this job at min{T 1 , T 2 , T 3 }. The second machine starts at time 0 with the job that takes the second shortest processing time and finishes at median{T 1 , T 2 , T 3 }. The first machine finishes first and will complete the only remaining job at min{T 1 , T 2 , T 3 } + max{T 1 , T 2 , T 3 }. Therefore, the time it takes the second policy to complete all three jobs = max{median{T 1 , T 2 , T 3 }, min{T 1 , T 2 , T 3 } + max{T 1 , T 2 , T 3 }}. a) By using only 10 replications and no common random numbers, a 95% confidence interval for θ 1 - θ 2 is [-1.259,0.955]. The width of the confidence interval is 2.214 . Because 0 is included in the confidence interval, at this level of α (5%), we fail to reject the null hypothesis that the two systems have equal means. Note that you may observe different values due to randomness. A portion of the worksheet (with formulae) used to obtain these numbers is shown here (see details in the accompanying spreadsheet): A B C D E F 2 T1 T2
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