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We consider a bilevel continuous knapsack problem where the leader contr...
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On the Complexity of Robust Bilevel Optimization With Uncertain Follower's Objective
We investigate the complexity of bilevel combinatorial optimization with...
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Recoverable Robust Representatives Selection Problems with Discrete Budgeted Uncertainty
Recoverable robust optimization is a multistage approach, where it is p...
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Robust unrelated parallel machine scheduling problem with interval release dates
This paper presents a profound analysis of the robust job scheduling pro...
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Robust recoverable 01 optimization problems under polyhedral uncertainty
This paper deals with a robust recoverable approach to 01 programming p...
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Capital flow constrained lot sizing problem with loss of goodwill and loan
We introduce capital flow constraints, loss of good will and loan to the...
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Algorithms for robust production scheduling with energy consumption limits
In this work, we consider a scheduling problem faced by production compa...
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Robust production planning with budgeted cumulative demand uncertainty
This paper deals with a problem of production planning, which is a version of the capacitated singleitem lot sizing problem with backordering under demand uncertainty, modeled by uncertain cumulative demands. The wellknown interval budgeted uncertainty representation is assumed. Two of its variants are considered. The first one is the discrete budgeted uncertainty, in which at most a specified number of cumulative demands can deviate from their nominal values at the same time.The second variant is the continuous budgeted uncertainty, in which the sum of the deviations of cumulative demands from their nominal values, at the same time, is at most a bound on the total deviation provided. For both cases, in order to choose a production plan that hedges against the cumulative demand uncertainty, the robust minmax criterion is used. Polynomial algorithms for evaluating the impact of uncertainty in the demand on a given production plan in terms of its cost, called the adversarial problem, and for finding robust production plans under the discrete budgeted uncertainty are constructed. Hence, in this case, the problems under consideration are not much computationally harder than their deterministic counterparts. For the continuous budgeted uncertainty, it is shown that the adversarial problem and the problem of computing a robust production plan along with its worstcase cost are NPhard. In the case, when uncertainty intervals are nonoverlapping, they can be solved in pseudopolynomial time and admit fully polynomial timeapproximation schemes. In the general case, a decomposition algorithm for finding a robust plan is proposed.
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