Parallel Asset Replacement Problem under Economies of Scale with Multiple Challengers

Abstract

The parallel replacement problem under economies of scale (PRES) determines minimum cost replacement schedules for each individual asset in a group of assets that operate in parallel. A fixed cost is incurred in any period in which an asset is purchased. These fixed costs induce economies of scale, making replacement schedules for these assets economically interdependent. We prove that PRES is NP-hard and present integer programming formulations for four variants of the problem in which multiple asset types, or challengers, are available for replacement (MPRES). We then derive valid inequalities for PRES and MPRES, which are similar in structure to flow cover inequalities developed in the context of fixed charge network problems. Experiments illustrate that the inequalities are effective in improving the integrality gap of MPRES instances.

Additional information

Notes on contributors

İ. Esra Büyüktahtakın

İ. Esra Büyüktahtakın is Assistant Professor in the Department of Industrial and Manufacturing Engineering at Wichita State University. She has been the President of the Institute For Operations Research and Management Science (INFORMS) Junior Faculty Interest Group (JFIG) since 2014. From 2009 to 2011, Dr. Büyüktahtakın worked as Visiting Assistant Professor in the Department of Systems and Industrial Engineering at the University of Arizona. She completed her Ph.D. in Industrial and Systems Engineering at the University of Florida in 2009, and holds M.S. degrees from Lehigh University (2007) and Bilkent University (2005). Her areas of expertise include optimization, in particular mixed-integer programming and dynamic programming, with applications in invasive species control, sustainable biofuel production and logistics, supply chain management, production planning, and asset management. Dr. Büyüktahtakın has more than seventeen publications and conference proceedings many of which are resulted from collaborations across other disciplines including Ecology, Environmental Sustainability, Agricultural and Resource Economics, and Computer Science. Her awards include the NSF EPSCoR First Award in 2012, the Strategic Engineering Research Fellowship (SERF) by the College of Engineering of WSU in 2012, and the best paper award at the International Conference on Agriculture, Environment and Biological Sciences in 2014.

J. Cole Smith

J. Cole Smith is a professor of Industrial and Systems Engineering (ISE) at the University of Florida. His research has been supported by the NSF, DARPA, AFOSR, and the ONR, and he has spent one summer as a distinguished visiting professor with the Department of Defense. His research regards mathematical optimization models and algorithms, especially those arising in combinatorial optimization. Dr. Smith has collaborated with colleagues across many different disciplines, including Mathematics, Ecology, Psychology, Computer Science, and Biomedical Engineering. His awards include the Young Investigator Award from the ONR, the Hamid K. Elden Outstanding Young Industrial Engineer in Education award, the Operations Research Division Teaching Award, and the best paper award from IIE Transactions in 2007.

Joseph C. Hartman

Joseph C. Hartman, Ph.D., P.E., serves as Dean of Engineering at the University of Massachusetts Lowell.  A graduate of the University of Illinois at Urbana-Champaign and Georgia Tech, he previously served on the faculty at the University of Florida and Lehigh University.  His interests are in economic decision analysis and applied operations research.  His work has been recognized with four Eugene L. Grant awards, the Wellington Award, and IIE Fellow. He is author of the textbook Engineering Economy and the Decision-Making Process, and was the previous Editor for The Engineering Economist.

Shangyuan Luo

Shangyuan Luo, Ph.D., is a VP at UBS AG, Stamford, Connecticut. He has advanced degrees in Industrial and Systems Engineering from Lehigh University and Financial Engineering from Columbia University.