Two approaches for fair resource allocation
Author
Yavuz, Mirel
Advisor
Karsu, Özlem
Date
2018-06Publisher
Bilkent University
Language
English
Type
ThesisItem Usage Stats
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Abstract
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.
Keywords
Resource Allocation ProblemFairness
Knapsack Problem
Interactive Algorithm
Ordered Weighted Averaging