Abstract
Alternate optimal solutions in the mathematical programming solution of a real-world problem are rare, unless there are multiple objective functions. In a recent application of 2 mathematical programming solvers to a problem of crude oil logistics, I obtained 2 different optimal solutions. The almost optimal solutions obtained from the convex combinations of the 2 optimal solutions, are feasible as real transportation choices, if the optimal solutions cannot be implemented. It was observed that the 2 solutions led to different capacity utilization at the refineries downstream, and so do the many solution alternatives. This is useful information for the petroleum company during downtime for maintenance or capacity expansion.
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