Categorization of pipeline types

Of special relevance among these types are the one-to-many and many-to-many networks as these show the most challenging planning problems. In the single product case, the main problem is to keep the flow in balance along the pipeline or pipeline segments such that inflow and outflow are equal at any time. 

A more complicated problem is met in the multi-product case where batches of products have to be routed through the pipeline (network) whereby a batch may also be split into sub-batches at pipeline forks. In the oases of multiple sources, additionally a coordinated pumping planning is required under consideration of the pumping capacity, the due dates of the batches, and the segment-wise flow balances. 

Pipelines are typically operated with a unidirectional material flow. In typical settings the associated partners along the pipeline can be categorized distinctly in (pure) 

There might be additional chemical or technical restrictions that have to be taken into account for pipeline transport planning such as the interruptibility of pipeline operation. E.g. if a product remains too long in a pipeline without movement, chemical reactions may take place which may cause corrosion or polymerization processes. This would lead to a failure and cause expensive maintenance and/or cleaning operations. However, the most obvious technical restriction is probably the pump rate of a pipeline. The pump rate measures the transport speed on a volume-per-time basis. Typically, there is an upper bound for the tolerable pressure inside a pipeline determining the maximum pump rate (say p ). The realized pump rate might be smaller and depends on the power of pumps at the pumping stations.  

A relevant restriction to be fulfilled for operating pipeUnes is the flow balance. I.e., the input flow equals the output flow implying constant physical conditions (such as pressure) for all pipeline segments. For instance, assume a serially operated multi-access pipehne where N is the set of access points consisting of destination points and M feeding locations such that = 0 and JM = N. The flow rate p is measured 

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