Cost-of-Quality Optimization via Zero-One Polynomial Programming

Abstract

In this paper, we consider a Cost-of-Quality (CoQ) optimization problem that finds an optimal allocation of prevention and inspection resources to minimize the expected total quality costs under a prevention-appraisal-failure framework, where the quality costs in the proposed model are involved with prevention, inspection, and correction of internal and external failures. Commencing with a simple structure of the problem, we progressively increase the complexity of the problem by accommodating realistic scenarios regarding preventive, appraisal, and corrective actions. The resulting problem is formulated as a zero-one polynomial program, which can be solved either directly using a mixed-integer nonlinear programming solver such as BARON, or using a more conventional mixed-integer linear programming (MILP) solver such as CPLEX after performing an appropriate linearization step. We examine two case studies from the literature (related to a lamp manufacturing context and an order entry process) to illustrate how the proposed model can be utilized to find optimal inspection and prevention strategies, as well as to analyze sensitivity with respect to different cost parameters. We also provide a comparative numerical study of using the aforementioned solvers to optimize the respective model formulations. The results provide insights into the use of such quantitative methods for optimizing the CoQ, and indicate the efficacy of using the linearized MILP model for this purpose.

Keywords:

• Cost-of-Quality
• Zero-One Polynomial Programming
• Linearization

Additional information

Notes on contributors

Churlzu Lim

Churlzu Lim is an Associate Professor of the Systems Engineering and Engineering Management Department at the University of North Carolina at Charlotte. His research interests include cost-of-quality optimization, risk-averse stochastic programming, project funding risk management, network interdiction, and portfolio optimization. He earned his Ph.D. at Virginia Polytechnic Institute and State University with his dissertation research on nondifferentiable optimization. He received M.S. and B.S. from Korea Advanced Institute of Science and Technology. He is currently a member of IIE and INFORMS.

Hanif D. Sherali

Hanif D. Sherali is a University Distinguished Professor Emeritus in the Industrial and Systems Engineering Department at Virginia Polytechnic Institute and State University. His areas of research interest are in mathematical optimization modeling, analysis, and design of algorithms for specially structured linear, nonlinear, and continuous and discrete nonconvex programs, with applications to transportation, location, engineering and network design, production, economics, and energy systems. He has published over 331 refereed articles in various operations research journals and has (co-) authored nine books. He is a Fellow of INFORMS and IIE, and an elected member of the National Academy of Engineering.

Theodore S. Glickman

Theodore S. Glickman is a Professor of Decision Sciences in the George Washington University School of Business. He has also held academic positions at Boston University, Virginia Tech, and Johns Hopkins University. In other professional capacities, he was a management consultant at KPMG and a senior policy analyst at the U.S. Department of Transportation and Resources for the Future. His research interests include risk analysis and optimization models, with applications to transportation, the environment, and national security. He has published numerous peer-reviewed journal articles and book chapters and co-edited the book Readings in Risk. Dr. Glickman earned a Ph.D. in Operations Research at Johns Hopkins and a B.S. in Physics at Stony Brook University.