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Principle (Serial Process Batching): In a unit operation with significant setups, the capacity grows in the batch size, but at a diminishing rate. This implies that the minimum batch size required for stability may be larger than one.

Motivation

The need for serial process batching arises when there are sequence dependent setups, for example when there are multiple job types processed at a station and a time-consuming setup is required each time we change job types. For example, a painting operation where the apparatus must be cleaned when colors are changed typically uses serial process batches larger than one for the sake of efficiency.  Because larger batch sizes reduce the number of setups, and hence the capacity lost to them, larger batches increase capacity.  However, because the time it takes to form a batch increases in the batch size, larger batches also increase flow time.
 

Example

The following figure illustrates the mechanics underlying serial process batching.  Parts of type A and type B arrive independently at Station 1.  We assume that the batch sizes are fixed, so that Station 1 waits until a full batch of either A or B is available before beginning processing.  Once a batch is formed it waits in a queue of batches at Station 1.  When it reaches the head of the queue, parts are processed one at a time.  The parts are then moved downstream to Station 2, either in a batch (with move batching) or one-at-a-time (with splitting).  Notice that it is not essential to move the parts in batches, even though they are processed as such (i.e., process batching is a separate decision from move batching).  Finally, we assume that each time a batch is finished a setup is done.
 
 
 

The following figure illustrates the effect of serial process batch size on flow time. Click here for the actual parameters and the mathematical derivation of the equations. Note that the flow time blows up for batch size less than a critical value (four in this case) because below this the number of setups causes utilization to exceed 100%.  Flow time is minimized at a batch size around eight, because this batch size balances the queueing caused by high utilization with the delay induced by wait-to-batch size.  Above the optimal batch size, the flow time increases roughly linearly, because the time to form a batch increases linearly in the batch size.  Finally, the flow time is larger if process batches are moved intact from Station 1 to Station 2.  The reason is that move batching induces additional wait-for-batch time on the outbound side of Station 1.
 
 

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