Browsing by Subject "Assignment"

Now showing 1 - 3 of 3

Open Access
On envy-free perfect matching
(Elsevier, 2019) Arbib, C.; Karaşan, Oya Ekin; Pınar, Mustafa
Consider a situation in which individuals –the buyers –have different valuations for the products of a given set. An envy-free assignment of product items to buyers requires that the items obtained by every buyer be purchased at a price not larger than his/her valuation, and each buyer’s welfare (difference between product value and price) be the largest possible. Under this condition, the problem of finding prices maximizing the seller’s revenue is known to be APX -hard even for unit-demand bidders (with several other inapproximability results for different variants), that is, when each buyer wishes to buy at most one item. Here, we focus on Envy-free Complete Allocation, the special case where a fixed number of copies of each product is available, each of the n buyers must get exactly one product item, and all the products must be sold. This case is known to be solvable in O(n4) time. We revisit a series of results on this problem and, answering a question found in Leonard (1983), show how to solve it in O(n3) time by connections to perfect matchings and shortest paths.
Open Access
Self-consistent computation of electronic and optical properties of a single exciton in a spherical quantum dot via matrix diagonalization method
(American Institute of Physics, 2009-08-21) Sahin, M.; Nizamoglu, S.; Kavruk, A. E.; Demir, Hilmi Volkan
In this study, we develop and demonstrate an efficient self-consistent calculation schema that computes the electronic structure and optical properties of a single exciton in a spherical quantum dot (QD) with an interacting pair of electron and hole wave functions. To observe modifications on bands, wave functions, and energies due to the attractive Coulomb potential, the full numeric matrix diagonalization technique is employed to determine sublevel energy eigenvalues and their wave functions in effective mass approximation. This treatment allows to observe that the conduction and valance band edges bend, that the electron and hole wave functions strongly localize in the QD, and that the excitonic energy level exhibits redshift. In our approach for the Coulomb term between electron and hole, the Poisson-Schrodinger equations are solved self-consistently in the Hartree approximation. Subsequently, exciton binding energies and associated optical properties are computed. The results are presented as a function of QD radii and photon energies. We conclude that all of these numerical results are in agreement with the experimental studies.
Open Access
Shortest-route formulation of mixed-model assembly line balancing problem
(Elsevier, 1999) Erel, E.; Gokcen, H.
A shortest-route formulation of the mixed-model assembly line balancing problem is presented. Common tasks across models are assumed to exist and these tasks are performed in the same stations. The formulation is based on an algorithm which solves the single-model version of the problem. The mixed-model system is transformed into a single-model system with a combined precedence diagram. The model is capable of considering any constraint that can be expressed as a function of task assignments.