Browsing by Subject "Assignment problems"

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Open Access
Inequity averse optimization in operational research
(Elsevier, 2015) Karsu, Ö.; Morton, A.
There are many applications across a broad range of business problem domains in which equity is a concern and many well-known operational research (OR) problems such as knapsack, scheduling or assignment problems have been considered from an equity perspective. This shows that equity is both a technically interesting concept and a substantial practical concern. In this paper we review the operational research literature on inequity averse optimization. We focus on the cases where there is a tradeoff between efficiency and equity. We discuss two equity related concerns, namely equitability and balance. Equitability concerns are distinguished from balance concerns depending on whether an underlying anonymity assumption holds. From a modeling point of view, we classify three main approaches to handle equitability concerns: the first approach is based on a Rawlsian principle. The second approach uses an explicit inequality index in the mathematical model. The third approach uses equitable aggregation functions that can represent the DM's preferences, which take into account both efficiency and equity concerns. We also discuss the two main approaches to handle balance: the first approach is based on imbalance indicators, which measure deviation from a reference balanced solution. The second approach is based on scaling the distributions such that balance concerns turn into equitability concerns in the resulting distributions and then one of the approaches to handle equitability concerns can be applied. We briefly describe these approaches and provide a discussion of their advantages and disadvantages. We discuss future research directions focussing on decision support and robustness.
Open Access
Ordinal covering using block designs
(IEEE, 2010) Atmaca, Abdullah; Oruc, A.Y.
A frequently encountered problem in peer review systems is to facilitate pairwise comparisons of a given set of documents by as few experts as possible. In [7], it was shown that, if each expert is assigned to review k documents then ⌈n(n-1)/k(k-1)⌉ experts are necessary and ⌈n(2n-k)/k 2⌉ experts are sufficient to cover all n(n-1)/2 pairs of n documents. In this paper, we show that, if √n ≤ k ≤ n/2 then the upper bound can be improved using a new assignnment method based on a particular family of balanced incomplete block designs. Specifically, the new method uses ⌈n(n+k)/k2⌉ experts where n/k is a prime power, n divides k2, and √n ≤ k ≤ n/2. When k = √n , this new method uses the minimum number of experts possible and for all other values of k, where √n < k ≤ n/2, the new upper bound is tighter than the general upper bound given in [7]. ©2010 IEEE.
Open Access
Ordinal evaluation and assignment problems
(IEEE, 2010) Atmaca, Abdullah; Oruç, A. Yavuz
In many assignment problems, a set of documents such as research proposals, promotion dossiers, resumes of job applicants is assigned to a set of experts for ordinal evaluation, ranking, and classification. A desirable condition for such assignments is that every pair of documents is compared and ordered by one or more experts. This condition was modeled as an optimization problem and the number of pairs of documents was maximized for a given incidence relation between a set of documents and a set of experts using a set covering integer programming method in the literature[5]. In this paper, we use a combinatorial approach to derive lower bounds on the number of experts needed to compare all pairs of documents and describe assignments that asymptotically match these bounds. These results are not only theoretically interesting but also have practical implications in obtaining optimal assignments without using complex optimization techniques. ©2010 IEEE.