A generalized global optimization formulation of the pooling problem with processing facilities and composite quality constraints

We present a generalized formulation of the pooling problem. Our formulation is different from the standard formulations in explicitly modeling component flows. Modeling the physical components directly, allows easy inclusion of processing facilities that may alter the flow composition. It also allows adding composite quality constraints that cannot be added directly as quality parameters as they do not blend linearly. We provide new test instances motivated by natural gas transport problems at the Norwegian Continental Shelf and give computational results. We show examples of nonlinear composite constraints on quality attributes and give computational results on the effect of adding such constraints to the new set of test instances. The increased flexibility of our formulation comes at the cost of less tight constraints and a performance penalty on existing test cases in literature. The advantage is that it can solve the more general test cases described above. We use GAMS implementations of the various formulations and solve the problems with BARON. We compare the performance of our bilinear formulation in BARON with discretizations solved as a Mixed Integer Linear Program using CPLEX. The discretized versions do not generally perform as well as the continuous model; however, they have better worst-case behavior on the new test cases.