Pooling problems under perfect and imperfect competition

Abstract

We investigate pooling problems in which multiple players vie with one another to maximize individual profit in a non-cooperative competitive market. This competitive setting is interesting and worthy of study because the majority of prevailing process systems engineering models largely overlook the noncooperative strategies that exist in real-world markets. In this work, each player controls a processing network involving intermediate tanks (or pools) where raw materials are blended together before being further combined into final products. Each player then solves a pure or mixed-integer bilinear optimization problem whose profit is influenced by other players. We present several bilevel formulations and numerical results of a novel decomposition algorithm. We demonstrate that our provably optimal decomposition algorithm can handle some of the largest bilevel optimization problems with nonconvex lower-level problems ever considered in the literature.