  Designing and analyzing algorithms with provable performance guarantees
enables efficient optimization problem solving in different application
domains, e.g.\ communication networks, transportation, economics, and
manufacturing. Despite the significant contributions of approximation
algorithms in engineering, only limited and isolated works contribute from this
perspective in process systems engineering. The current paper discusses three
representative, NP-hard problems in process systems engineering: (i) pooling,
(ii) process scheduling, and (iii) heat exchanger network synthesis. We survey
relevant results and raise major open questions. Further, we present
approximation algorithms applications which are relevant to process systems
engineering: (i) better mathematical modeling, (ii) problem classification,
(iii) designing solution methods, and (iv) dealing with uncertainty. This paper
aims to motivate further research at the intersection of approximation
algorithms and process systems engineering.
