One-to-many pipeline types

Most of the literature on pipeline transportation considers customer demands for the products at the depots to be served at the end of the planning horizon. An exception is proposed in Cafaro and Cerda (2008) where customer demands at the depots are associated with due-dates such that backorder costs are incorporated in the objective function. Moreover, the work proposes a rolling horizon model for updating and re-scheduling previously determined schedules according to updated demand characteristics. 

In contrast, in Rejowski and Pinto (2008) the speed of pumping is a decision variable which leads to a non-linear term in the objective function since both pump rate and batch length have to be determined. Furthermore, this work is noteworthy as it explicitly accounts for the inventory holding costs, but at the expense of another non-linear term in the objective function. Note that the time-continuous formulation requires that both the period s length and the tank level in a period are decision variables. The product of these terms determines the holding costs. Cafaro and Cerda (2004, 2008) approximate the holding costs by averaging the stock levels at the depots. 

Despite the complexity of the scheduling decisions, aU proposed models can be solved with standard solvers in a reasonable amount of time. This is because only small problem instances are solved w.r.t. the number of products to be scheduled and the number of 

To tackle more realistic planning problems of real-world pipeline systems, models for multi-source pipeline systems have been developed recently. This extension of one-to-many systems considerably increases complexity. Hence, first approaches provide a heuris-tical decomposition that decomposes a problem into three blocks  

Allocation decision determine which locations are potential candidates for injecting and receiving batches. 

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