Computing and minimizing the relative regret in combinatorial optimization with interval data

Authors:
Igor Averbakh
Affiliations:
Division of Management, University of Toronto at Scarborough, 1265 Military Trail, Scarborough, Ont., Canada M1C 1A4
Venue:
Discrete Optimization
Year:
2005

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Abstract

We consider combinatorial optimization problems with uncertain parameters of the objective function, where for each uncertain parameter an interval estimate is known. It is required to find a solution that minimizes the worst-case relative regret. For minmax relative regret versions of some subset-type problems, where feasible solutions are subsets of a finite ground set and the objective function represents the total weight of elements of a feasible solution, and for the minmax relative regret version of the problem of scheduling n jobs on a single machine to minimize the total completion time, we present a number of structural, algorithmic, and complexity results. Many of the results are based on generalizing and extending ideas and approaches from absolute regret minimization to the relative regret case.