ADVANCES FOR THE POOLING PROBLEM: MODELING, GLOBAL OPTIMIZATION, AND COMPUTATIONAL STUDIES

Abstract

The pooling problem, an optimization challenge of maximizing proflt subject prod- uct availability, storage capacity, demand, and product speciflcation constraints, has applica- tions to petroleum reflning, wastewater treatment, supply-chain operations, and communica- tions. This review illustrates the long-standing symbiosis between the industrial challenge of optimally combining feed stocks into products and the mathematical fleld of global optimization. We present flve 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 algo- rithm GOP and other Lagrangian-based approches, the reformulation-linearization technique (RLT), and piecewise-a-ne underestimation in the context of the pooling problem.