Robust counterpart optimization techniques for linear optimization and mixed integer linear optimization problems are studied in this paper. Different uncertainty sets, including those studied in literature (i.e., interval set; combined interval and ellipsoidal set; combined interval and polyhedral set) and new ones (i.e., adjustable box; pure ellipsoidal; pure polyhedral; combined interval, ellipsoidal, and polyhedral set) are studied in this work and their geometric relationship is discussed. For uncertainty in the left hand side, right hand side, and objective function of the optimization problems, robust counterpart optimization formulations induced by those different uncertainty sets are derived. Numerical studies are performed to compare the solutions of the robust counterpart optimization models and applications in refinery production planning and batch process scheduling problem are presented.

Aim To identify possible novel biomarkers in gingival crevicular fluid (GCF) samples from chronic periodontitis (CP) and periodontally healthy individuals by high-throughput proteomic analysis. Materials and Methods GCF samples were collected from twelve CP and twelve periodontally healthy subjects. Samples were trypically digested, eluted using high-performance liquid chromatography, and fragmented using tandem mass spectrometry (MS/MS). MS/MS were analyzed using PILOT_PROTEIN to identify all unmodified proteins within the samples. Results Using the database derived from Homo sapiens taxonomy and all bacterial taxonomies, 432 human (120 new) and 30 bacterial proteins were identified. The human proteins, angiotensinogen, clusterin and thymidine phosphorylase were identified as biomarker candidates based on their high-scoring only in samples from periodontal health. Similarly, neutrophil defensin-1, carbonic anhydrase-1 and elongation factor-1 gamma were associated with CP. Candidate bacterial biomarkers include 33 kDa chaperonin, iron uptake protein A2 and phosphoenolpyruvate carboxylase (health-associated) and ribulose biphosphate carboxylase, a probable succinyl-CoA:3-ketoacid-coenzyme A transferase, or DNA-directed RNA polymerase subunit beta (CP-associated). Most of these human and bacterial proteins have not been previously evaluated as biomarkers of periodontal conditions and require further investigation. Conclusions The proposed methods for large-scale comprehensive proteomic analysis may lead to the identification of novel biomarkers of periodontal disease.

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Probabilistic guarantees on constraint satisfaction for robust counterpart optimization are studied in this paper. The robust counterpart optimization formulations studied are derived from box, ellipsoidal, polyhedral, “interval+ellipsoidal” and “interval+polyhedral” uncertainty sets (Li, Z., Ding, R., and Floudas, C.A., A Comparative Theoretical and Computational Study on Robust Counterpart Optimization: I. Robust Linear and Robust Mixed Integer Linear Optimization, Ind. Eng. Chem. Res, 2011, 50, 10567). For those robust counterpart optimization formulations, their corresponding probability bounds on constraint satisfaction are derived for different types of uncertainty characteristic (i.e., bounded or unbounded uncertainty, with or without detailed probability distribution information). The findings of this work extend the results in the literature and provide greater flexibility for robust optimization practitioners in choosing tighter probability bounds so as to find less conservative robust solutions. Extensive numerical studies are performed to compare the tightness of the different probability bounds and the conservatism of different robust counterpart optimization formulations. Guiding rules for the selection of robust counterpart optimization models and for the determination of the size of the uncertainty set are discussed. Applications in production planning and process scheduling problems are presented.

Enterprise-wide optimization for the petroleum refining industry involves optimization of the supply chain involving manufacturing and distribution with emphasis on integration of the different decision making levels. The key manufacturing operations include crude oil loading and unloading, mixing of crude oil, production unit operations of conversion and separation, operations of blending, and distribution of products. Other components of the petroleum supply chain network include oil explorations, crude oil procurement, and sales and distribution of products. The main issues present in the petroleum industry across various decision levels (strategic, tactical, and operational) and within oil refinery operations are discussed. This paper presents an extensive literature review of methodologies for addressing scheduling, planning, and supply chain management of oil refinery operations. An attempt is also made to identify the future challenges in efficiently solving these problems.