Consider the model in Exercise 10.11. Assume that the jobs are subject to precedence constraints…

Consider the model in Exercise 10.11. Assume that the jobs are subject to precedence constraints that take the formof chains. Show that Algorithm 3.1.4 minimizes the total expected weighted completion time. Exercise 11: 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 … Continue reading "Consider the model in Exercise 10.11. Assume that the jobs are subject to precedence constraints…"

Consider the stochastic counterpart of with the processing time of job j arbitrarily distributed…

Consider the stochastic counterpart of with the processing time of job j arbitrarily distributed according to Fj . All jobs have a common random due date that is exponentially distributed with rate r. Show that this problemis equivalent to the stochastic counterpart of the problem (that is, a problem without a due date but with … Continue reading "Consider the stochastic counterpart of with the processing time of job j arbitrarily distributed…"

Consider the two processing time distributions of the jobs in Example 10.3.6. Assume the…

Consider the two processing time distributions of the jobs in Example 10.3.6. Assume the deterioration function a(t) = 1 for 0 ≤ t ≤ 1 and a(t) = t for t ≥ 1 (i.e., the deterioration function is increasing convex). Show that SEPT minimizes the makespan. Example 10.3.6: Consider two jobs with discrete processing time … Continue reading "Consider the two processing time distributions of the jobs in Example 10.3.6. Assume the…"

Consider the following discrete time stochastic counterpart of the deterministic mode The n jobs…

Consider the following discrete time stochastic counterpart of the deterministic mode The n jobs have a common random due date D. When a job is completed before the due date, a discounted reward is obtained. When the due date occurs before its completion, no reward is obtained and it does not pay to continue processing … Continue reading "Consider the following discrete time stochastic counterpart of the deterministic mode The n jobs…"