Browsing by Subject "Knapsack problem"

Now showing 1 - 5 of 5

Open Access
Balance in resource allocation problems: a changing reference approach
(Springer, 2020) Karsu, Özlem; Erkan, Hale
Fairness is one of the primary concerns in resource allocation problems, especially in settings which are associated with public welfare. Using a total benefit-maximizing approach may not be applicable while distributing resources among entities, and hence we propose a novel structure for integrating balance into the allocation process. In the proposed approach, imbalance is defined and measured as the deviation from a reference distribution determined by the decision-maker. What is considered balanced by the decision-maker might change with respect to the level of total output distributed. To provide an allocation policy that is in line with this changing structure of balance, we allow the decision-maker to change her reference distribution depending on the total amount of output (benefit). We illustrate our approach using a project portfolio selection problem. We formulate mixed integer mathematical programming models for the problem with maximizing total benefit and minimizing imbalance objectives. The bi-objective models are solved with both the epsilon-constraint method and an interactive algorithm.
Open Access
Data dependent worst case bound improving techniques in zero-one programming
(Elsevier BV, 1991) Oğuz, Osman
A simple perturbation of data is suggested for use in conjunction with approximation algorithms for the purpose of improving the available bounds (upper and lower), and the worst case bounds. The technique does not require the approximation algorithm (heuristic) to provide a worst case bound to be applicable.
Open Access
Ensuring multidimensional equality in public service
(Elsevier Ltd, 2021-10-23) Akoluk, Damla; Karsu, Özlem
Service planning problems typically involve decisions that lead to the distribution of multiple benefits to multiple users, and hence include equality and efficiency concerns in a multidimensional way. We develop two mathematical modeling-based approaches that incorporate these concerns in such problems. The first formulation aggregates the multidimensional efficiency and equality (equitability) concerns in a biobjective model. The second formulation defines an objective function for each benefit, which maximizes the total social welfare obtained from that specific benefit distribution; this results in an n-objective model, where n is the number of benefits. We illustrate and compare these approaches on an example public service provision problem.
Open Access
Ensuring multidimensional fairness in public service
(2020-12) Akoluk, Damla
In this study, we focus on service planning problems, in which decisions lead to distributions of multiple benefits to multiple users, hence involve fairness and efficiency concerns in a multidimensional way. We develop two mathematical modeling-based approaches that incorporate these concerns in such problems. The first formulation aggregates the multidimensional efficiency concerns and multidimensional fairness concerns in a bi-objective model. The second formulation defines an objective function for each benefit, which maximizes the total social welfare obtained from that specific benefit distribution, hence results in an nobjective model, where n is the number of benefits. We illustrate and compare these approaches on an example public service provision problem.
Open Access
In Press, Corrected Proof: Ensuring multidimensional equality in public service
(Elsevier, 2021-10-23) Akoluk, Damla; Karsu, Özlem
Service planning problems typically involve decisions that lead to the distribution of multiple benefits to multiple users, and hence include equality and efficiency concerns in a multidimensional way. We develop two mathematical modeling-based approaches that incorporate these concerns in such problems. The first formulation aggregates the multidimensional efficiency and equality (equitability) concerns in a biobjective model. The second formulation defines an objective function for each benefit, which maximizes the total social welfare obtained from that specific benefit distribution; this results in an n-objective model, where n is the number of benefits. We illustrate and compare these approaches on an example public service provision problem.