This is under Operations Management or Operations Research of Industrial Enginee

Question

This is under Operations Management or Operations Research of Industrial Engineering. Topic is called Queueing Theory. Manufacturing Systems Modeling and Analysis Second Edition. Please do process.

41. Consider a processing time, T, with measured parameters ET-6 and C2 [T] = 2, that has four iid. sub-tasks, T for i = 1, 2, 3, 4. (a) Determine E[T] and C2 [T] for the sub-tasks (b) Assume that the variability of each sub-task can be reduced (identically) so that [T] 2, Determine the squared coefficient of variation of the total processing time and the percentage improvement over the "old" processing time variability.

Explanation / Answer

Answer ,

E[T] = E[T1] +E[T2] +E[T3] + E[T4]

V[T] = V[T1] +V[T2] +V[T3] + V[T4]

C2[T] = V[T]

            ----------

            E[T]2

Since the four subtasks are independent and identically distributed random variables, the above equations become,

E[T] = 4 * E[T1]

V[T] = 4 *V[T1]

Hence, the individual processing time variables are:-

E[Ti] = E[T] / 4

Now, V[T] = C2[T] * E[T]2

C2[Ti] = V[Ti]

            ----------

            E[Ti]2

Answer, E[Ti] = 1.5, V[Ti] = 9 and C2[Ti] = 8

Part B

Let the new C2[Ti] = 2.

The we know that ,

C2[Ti] = V[Ti] / E[Ti] 2 = ( V[T] / 4 ) / (E[T] 2/4 2 )= 4 C2[T],

Previous, C2[T] = 2 .

Previous, C2[T] = 2 .

This reduction in processing time variability would reduce the associated workstation cycle time in the queue. The processing time variability is reduced by 4 times or ¼ th of its previous value which is a 400 % improvement.

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