Browsing by Subject "Knapsack Problem"

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Open Access
Balance in resource allocation problems: a changing reference approach
(2018-05) Erkan, Hale
Fairness has become one of the primary concerns in resource allocation problems, especially in settings which are associated with public welfare. Using a pure e ciency maximizing approach may not be applicable while distributing resources among entities, hence we propose a novel structure for integrating balance into the allocation process. In the proposed approach, balance is de ned and measured as the deviation from a reference distribution determined by the decision maker. We acknowledge that 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 (bene t). We illustrate our approach using a project portfolio selection problem. We formulate a mixed integer mathematical programming model for the problem with maximizing e ciency and minimizing imbalance objectives. The bi-objective model is initially solved with the epsilon constraint method. However for larger problem instances this approach fails to nd solutions within reasonable time limits. Hence we implement metaheuristic algorithms and report on their performance. As an alternative solution method, an interactive algorithm is presented and used to nd the most preferred solution of the decision maker. The proposed resource allocation model provides important insights to decision makers regarding the tradeo between e ciency and fairness, and provides a useful tool to incorporate speci c balance concerns into the problem.
Open Access
Two approaches for fair resource allocation
(2018-05) Yavuz, Mirel
Fairness has become one of the primary concerns in several Operational Research (OR) problems, especially in resource allocation problems. It is crucial to ensure a fair distribution of the resources across the entities so that the proposed solutions will be both applicable and acceptable. In many real-life systems, the most e cient solution will not be the most fair solution, which creates a trade-o between e ciency and fairness. We propose two approaches in order to help the decision makers (DM) to nd an e cient solution which take fairness of the distribution of resources into account. First approach we propose is optimizing a speci c subset of the set of Schur-concave functions, namely ordered weighted averaging (OWA) functions, which are able to re ect both e ciency and fairness concerns. We do not assume that the weights of the DM to be used in OWA functions are readily available. We explore a wide range of weight vectors and report results for these di erent choices of weights. We illustrate the approach using a workload allocation problem and a knapsack problem and visualize the trade-o between fairness and e ciency. In some applications, the DM may provide a reference point such that the aim would be nding an e cient solution which is more preferable than this reference in terms of fairness. For such cases we propose a second approach that maximizes e ciency while controlling fairness concerns via a constraint. Similar to the rst approach, fairness concerns are re ected using OWA function forms. However, the resulting formulation yields to non-linearity. Thus, a hybrid interactive algorithm is presented that tackles this nonlinearity using an enumerative approach. The algorithm nds an e cient solution which OWA dominates the reference point by interacting with the DM. The algorithm is tested on knapsack problems and shows successful performance.