Assortment optimization refers to the problem of designing a slate of products to offer potential customers, such as stocking the shelves in a convenience store. The price of each product is fixed in advance, and a probabilistic choice function describes which product a customer will choose from any given subset. We introduce the combinatorial assortment problem, where each customer may select ...

In the last decade many important applications of eigenvalues and eigenvectors of graphs in combinatorial optimization were discovered. The number and importance of these results is so fascinating that it makes sense to present this survey. ∗This article appeared in Combinatorial and Graph-Theoretical Problems in Linear Algebra, R. A. Brualdi, S. Friedland, V. Klee, Eds., IMA Volumes in Mathema...

In this paper, a combinatorial reverse auction mechanism is proposed for selecting the most efficient service-providers for resolving sustained power interruptions in multiple regions of an electric power distribution company’s responsibility area. Through this mechanism, supplying the required service in each region is assigned to only one potential service-provider considering two criteria in...

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In this paper we propose a new method to solve biobjective combinatorial optimization problems of the max-ordering type. The method is based on the two-phases method and ranking algorithms to eÆciently construct K best solutions for the underlying (single objective) combinatorial problem. We show that the method overcomes some of the diÆculties of procedures proposed earlier. We illustrate this...

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In this paper, we present a self-organized computing approach to solving hard combinatorial optimization problems, e.g., the traveling salesman problem (TSP). First of all, we provide an analytical characterization of such an approach, by means of formulating combinatorial optimization problems into autonomous multi-entity systems and thereafter examining the microscopic characteristics of opti...