Conditions under which adjustability lowers the cost of a robust linear program

Ali Haddad-Sisakht and Sarah M. Ryan ()
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Ali Haddad-Sisakht: Iowa State University
Sarah M. Ryan: Iowa State University

Annals of Operations Research, 2018, vol. 269, issue 1, No 11, 185-204

Abstract: Abstract The adjustable robust counterpart (ARC) of an uncertain linear program extends the robust counterpart (RC) by allowing some decision variables to adjust to the realizations of some uncertain parameters. The ARC may produce a less conservative and costly solution than the RC does but cases are known in which it does not. While the literature documents some examples of cost savings provided by adjustability (particularly affine adjustability), it is not straightforward to determine in advance whether they will materialize. The affine adjustable robust counterpart, while having a tractable structure, still may be much larger than the original problem. We establish conditions under which affine adjustability may lower the optimal cost with a numerical condition that can be checked in small representative instances. As demonstrated in applications, the conditions provide insights into constraint relationships that allow adjustability to have its intended effect.

Keywords: Robust counterpart; Adjustable robust counterpart; Affinely adjustable robust counterpart; Box uncertainty sets (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10479-018-2954-4

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