Redo the instance in Exercise 10.7 with the discount factor β = 1. Determine all optimal…

Redo the instance in Exercise 10.7 with the discount factor β = 1. Determine all optimal policies. Give an explanation for the results obtained and compare the results with the results obtained in Exercise 10.7. Exercise 7: Consider the framework of Section 10.2. There are 3 jobs, all having a discrete uniform distribution. The processing … Continue reading "Redo the instance in Exercise 10.7 with the discount factor β = 1. Determine all optimal…"

Consider Example 10.3.5 with the linear deterioration function a(t) = 1 + t. Instead of the two…

Consider Example 10.3.5 with the linear deterioration function a(t) = 1 + t. Instead of the two jobs with exponentially distributed processing times, consider two jobs with geometrically distributed processing times with parameters q1 and q2. Compute the expected makespan under the two sequences. Example 10.3.5: Consider two jobs with exponential processing times. The rates … Continue reading "Consider Example 10.3.5 with the linear deterioration function a(t) = 1 + t. Instead of the two…"

Consider the model in Theorem 10.1.1 with breakdowns. The up-times are exponentially distributed…

Consider the model in Theorem 10.1.1 with breakdowns. The up-times are exponentially distributed with rate ν and the down-times are i.i.d. (arbitrarily distributed) with mean 1/µ. Show that the expected time job j spends on the machine is equal to where E(Xj ) is the expected processing time of job j. Give an explanation why … Continue reading "Consider the model in Theorem 10.1.1 with breakdowns. The up-times are exponentially distributed…"

Consider the same model as in Exercise 10.11 but assume now that the processing time of job j is…

Consider the same model as in Exercise 10.11 but assume now that the processing time of job j is exponentially distributed with rate λj . Assume that the repair time is exponentially distributed with rate µ. (a) Show that the number of times the machine breaks down during the processing of job j is geometrically … Continue reading "Consider the same model as in Exercise 10.11 but assume now that the processing time of job j is…"