Data-Driven Robust Resource Allocation with Monotonic Cost Functions

Ye Chen (), Nikola Marković (), Ilya O. Ryzhov () and Paul Schonfeld ()
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Ye Chen: Statistical Sciences and Operations Research, Virginia Commonwealth University, Richmond, Virginia 23284
Nikola Marković: Civil and Environmental Engineering, University of Utah, Salt Lake City, Utah 84112
Ilya O. Ryzhov: Robert H. Smith School of Business, University of Maryland, College Park, Maryland 20742; Institute for Systems Research, University of Maryland, College Park, Maryland 20742
Paul Schonfeld: Civil and Environmental Engineering, University of Maryland, College Park, Maryland 20742

Operations Research, 2022, vol. 70, issue 1, 73-94

Abstract: We consider two-stage planning problems (arising, e.g., in city logistics) in which a resource is first divided among a set of independent regions and then costs are incurred based on the allocation to each region. Costs are assumed to be decreasing in the quantity of the resource, but their precise values are unknown, for example, if they represent difficult expected values. We develop a new data-driven uncertainty model for monotonic cost functions, which can be used in conjunction with robust optimization to obtain tractable allocation decisions that significantly improve worst-case performance outcomes. Our model uses a novel uncertainty set construction that rigorously handles monotonic structure based on a statistical goodness-of-fit test with respect to a given sample of data. The practical value of this approach is demonstrated in three realistic case studies.

Keywords: Transportation; robust optimization; monotonic functions; resource allocation; city logistics (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:inm:oropre:v:70:y:2022:i:1:p:73-94

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