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Infinite Buffer Closed Lines - Worst Case for Performance

The worst case for this line happens when all the parts, that is the maximum WIP arrives simultaneously. This is a case of extreme batching. However, one must observe, that there is no randomness involved in this case. The arrivals are deterministically lumped. As in the best case, we illustrate the operations for the case of a four-station line with parameters:

Bottleneck rate r_b= 0.5 parts/hour

Raw processing time T₀ = 8 hours

Critical WIP W₀ = 0.5 * 8 = 4 parts

Congestion co-efficient a = W₀, maximum for worst case.
 

The following figures illustrate the operation of this line for the case of WIP level = 4 (the critical WIP) and derive the relationship between cycle time, throughput and WIP.
 

Time = 0

Time = 8

Time = 16

Time = 24

Time = 32

A Cycle of Events for the Best Case with WIP = 4

 

• Green job always waits behind every other job at every station (and so spends 8 hrs at each station).
• Think of this as occuring because all moves between stations are made in bulk, where the batch size equals the total number of jobs in the system.

Performance for the Worst Case

From the above examples we observe the following relationships between flow time and throughput for the infinite buffer closed line as it varies with WIP, for the worst case.
 

Relationship between Throughput and WIP for Worst Case

 

Relationship between Flow Time and WIP for Worst Case

 

Performance Equations for Worst Case, General Relationships

From above, the worst case flow time for a given WIP level, w, is given by,
 

FTworst = w T0

and the worst case throughput for a given WIP level, w, is given by,
 

THworst= 1 / T0

 
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