A polyhedral study of nonconvex piecewise linear optimization

Ph.D.Committee Chair: George L. Nemhause

Nonconvex, lower semicontinuous piecewise linear optimization. Discrete Optimization

Abstract A branch-and-cut algorithm for solving linear problems with continuous separable piecewise linear cost functions was developed in 2005 by Keha et. al. This algorithm is based on valid inequalities for an SOS2 based formulation of the problem. In this paper we study the extension of the algorithm to the case where the cost function is only lower semicontinuous. We extend the SOS2 based formulation to the lower semicontinuous case and show how the inequalities introduced by Keha et. al. can also be used for this new formulation. We also introduce a simple generalization of one of the inequalities introduced by Keha et. al. Furthermore, we study the discontinuities caused by fixed charge jumps and introduce two new valid inequalities by extending classical results for fixed charge linear problems. Finally, we report computational results showing how the addition of the developed inequalities can significantly improve the performance of CPLEX when solving these kinds of problems

MINIMIZING MAKESPAN WITH MULTIPLE ORDERS PER JOB IN A TWO MACHINE FLOWSHOP WITH ITEM PROCESSING

Abstract: New semiconductor wafer fabrication facilities use Front Opening Unified Pods (FOUPs) as a common unit of wafer transfer. Since the number of pods is limited due to high costs, and the increase in wafer size to 300-mm reduces the number of wafers required for a customer order, combining multiple orders into a single job is a necessity for efficient production. We investigate the multiple orders per job scheduling problem in the context of a 2-machine flowshop. A lower bound for the makespan performance measure is provided. An optimization model is presented that addresses both job formation and job sequencing

The diagnostic value of FNDC5/Irisin in renal Cell Cancer

ABSTRACT Purposes: The aim of this study was to determine the diagnostic significance of fibronectin type III domain containing protein 5 (FNDC5)/Irisin levels in the sera of patients with renal cell cancer. Materials and Methods: In the study, 48 individuals were evaluated. The patient group included 23 subjects diagnosed with renal tumor, and the control group of 25 healthy individuals. Patients diagnosed with renal tumor received surgical treatment consisting of radical or partial nephrectomy. Blood specimens were collected and serum FNDC5/Irisin and carcinoembryonic antigen (CEA) levels were determined using enzyme-linked immunosorbent assay (ELISA). Results: FNDC5/irisin and CEA levels in renal cancer patients were significantly higher compared with the control group (p=0.0001, p=0.009, respectively). Also, FNDC5 levels was more sensitive and specific than CEA levels. The best cut-off points for FNDC5/irisin were >105pg/mL and CEA were >2.67ng/mL for renal cancer. Conclusions: FNDC5/Irisin may be used as a diagnostic biomarker for renal cancer