Browsing by Subject "Knapsack problems"
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Item Open Access Finding robustly fair solutions in resource allocation(Bilkent University, 2022-07) Elver, İzzet EgemenIn this study, we consider resource allocation problems where the decisions affect multiple beneficiaries and the decision maker aims to ensure that the effect is distributed to the beneficiaries in an equitable manner. We specifically consider stochastic environments where there is uncertainty in the system and propose a robust programming approach that aims at maximizing system efficiency (measured by the total expected benefit) while guaranteeing an equitable benefit allocation even under the worst scenario. Acknowledging the fact that the robust solution may lead to high efficiency loss and may be over-conservative, we adopt a parametric approach that allows controlling the level of conservatism and present the decision maker alternative solutions that reveal the trade-off between the total expected benefit and the degree of conservatism when incorporating fairness. We obtain tractable formulations, leveraging the results we provide on the properties of highly unfair allocations. We demonstrate the usability of our approach on project selection and shelter allocation applications.Item Open Access On the optimality of the greedy solutions of the general knapsack problems(Taylor & Francis, 1992) Vizvári, BelaIn this paper we submit a unified discussion of some closely related results which were achieved independently in number theory and integer programming, and we partially generalize them. In the unified discussion we treat together two problems where the greedy method has different characters, in the first one it is an internal-point algorithm, in the second one it is an outer-point method. We call a knapsack problem “pleasant” if the greedy solution is optimal for every right-hand side. A sufficient and two finite necessary and sufficient conditions for the pleasantness of a problem are discussed. The sufficient condition can be checked very easily. The paper is finished with an error analysis of some nonpleasant problems. AMS 1980 Subject Classification: Primary: 90C 10.Item Open Access A stability concept for zero-one knapsack problems and approximation algorithms(Taylor & Francis, 1995) Oğuz, O.; Magazine, M. J.The concept of reducing the feasible range of decision variables or fixing the value of the variables is extended for the knapsack problem to include sets of variables. The ease of fixing these variables is measured by a stability index. The potential use of the concept is discussed in the context of approximation algorithms. Generalization to general zero-one problems is also considered.