A network flow modeling approach is proposed to minimize the operational cost of a pipeline system for the distribution of multiple refined products from a refinery to a set of depots. The demand for each product at each depot is known, along with specified time widows within which the deliveries must be effected. In addition to this, the order of arrival of the products at each depot is specified in advance. The modeling approach is based on a multi commodity network flow formulation that allows the representation of a time framework, along with dynamic aspects of the system including conservation of product flow at intermediate points, travel time of products from the refinery to their destinations, and distance traveled by the products. Additional constraints are formulated for the representation of product deliveries according to a specified order and within time windows. The network representation for a small instance of the problem, its corresponding mathematical formulation and a network illustration of its optimal solution are provided. Insights into the solution methodology for larger scenarios will be presented.
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