Operations management mba engineering

Question

Compute the cycle time and flow time in minutes, and capacity in jobs per hour, for the overall process flow. (Service occurs simultaneously). Please see the flow diagram below.

Answer 1

1) normalize times

1. put every activity time in minutes per job.

2) get the flow time (a.k.a. throughput time)

1. move left → right through the process.
2. if steps are in series, add their times.
3. if a block of steps runs simultaneously/parallel for the same job, take the max of those times (because the job can’t leave until all parallel pieces finish).
4. Flow time = sum of all series blocks, using max() for any simultaneous block.

3) get station capacities

For each resource/station jjj:

1. effective processing time per job: tjt_jtj​ (minutes/job)
2. number of identical servers in parallel at that station: mjm_jmj​
3. Capacityj_jj​ = mjtj=\; \dfrac{m_j}{t_j}=tj​mj​​ jobs/min
4. convert to jobs/hour by ×60\times 60×60

If a job requires multiple simultaneous stations (e.g., two different tasks done at once), each of those stations must be available for that job. The overall capacity is constrained by the slowest (lowest capacity) among the required stations (and any other series stations).

4) overall capacity & cycle time

1. Overall capacity =min⁡(Capacityj)=\min(\text{Capacity}_j)=min(Capacityj​) across all required stations (the bottleneck).
2. Cycle time (time between completed jobs at steady state)
3. = 1Overall capacity=\; \dfrac{1}{\text{Overall capacity}}=Overall capacity1​ minutes/job.