Summary: The pooling problem, an optimization challenge of maximizing profit subject product availability, storage capacity, demand, and product specification constraints, has applications to petroleum refining, wastewater treatment, supply-chain operations, and communications. This review illustrates the long-standing symbiosis between the industrial challenge of optimally combining feed stocks into products and the mathematical field of global optimization.
We present five sub-classes of pooling problems: standard pooling, generalized pooling, extended pooling, nonlinear blending, and crude oil operations as representative industrial challenges. We also discuss solution techniques: successive linear programming, the global optimization algorithm GOP and other Lagrangian-based approches, the reformulation-linearization technique (RLT), and piecewise-affine underestimation in the context of the pooling problem.