Question: A workstation has two different machines for performing two distinct processing tasks. The workstation has one operator that performs all work done in the workstation on all jobs. That is, the operator stays with a job and moves it from machine to machine to accomplish the necessary processing. Jobs arrive to the workstation at a mean rate λ (exponentially distributed inter-arrival times). Each job is first processed by the operator on Machine 1 which takes an exponentially distributed length of time with mean rate μ. Then the job and operator go to Machine 2 for further processing. The processing time on the second machine is also exponentially distributed but with a mean rate γ. The operator works on one job at a time and completes it before starting on a new job. The company limits the jobs in this workstation to 3.
(a) Define an appropriate state space representation for this model.
(b) Using your state space, develop a state diagram to model this situation.
(c) Write the utilization equation for machine one, using the state probabilities.
(d) Write the operator utilization equation, using the state probabilities.
(e) Write the workstation work-in-process equation, using the state probabilities.
(f) Write the throughput equation, using the state probabilities.