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The following describes the flow time as a function of batch size for a single station with parallel process batching:

• k = batch Size
• t₀ = time to process a single part (90)
• c_e² = squared co-efficient of variation (scv) for batch (1.0)
• r_a = arrival rate for parts (0.05)
• c_a² = scv of batch arrival (1.0)

Then the time to form the batch is given by:

The time to process the batch is as: t_a = t₀

The arrival rate for the batches is : r_b = r_a/k

The utilization is obtained as (batch arrival rate * time for batch) = r_bt_a = (r_a/k) t₀

Note that for stability we require that the utilization be less than 1 (can not have more than 100% utilization). This gives us

(r_a/k) t₀ 1 = k r_a t_a = 4.5 for our example. This implies that we need the minimum batch size to be at least 5 for the system to be stable.

We can now apply Kingman's equation to compute the flow time for batches at the station as:

Hence, the total flow time at the station is the flow time of batches plus the time to form the batch,  FT = FT_b + WT.  The previous plot shows FT as a function of batch size k.

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