Minimally nonideal matrices are a key to understanding when the set covering problem can be solved using linear programming. The complete classification of minimally nonideal matrices is an open problem. One of the most important results on these matrices comes from a theorem of Lehman, which gives a property of the core of a minimally nonideal matrix. Cornuéjols and Novick gave a conjecture on...

Given a set S of n points in the plane, the disjoint two-rectangle covering problem is to find a pair of disjoint rectangles such that their union contains S and the area of the larger rectangle is minimized. In this paper we consider two variants of this optimization problem: (1) the rectangles are free to rotate but must remain parallel to each other, and (2) one rectangle is axis-parallel bu...

We consider important generalizations of a wide class of traditional deterministic inventory and facility location models that we call inventory/facility location models with market selection. Instead of the traditional setting, we are given a set of markets, each specified by a sequence of demands and associated with a revenue. Decisions are made in two stages. We first make a decision of what...

K e y w o r d s S e t c o v e r i n g problems, Fuzzy sets, Fuzzy set-covering problem, Algebraic sum operator. 1. I N T R O D U C T I O N A classical set-covering problem considers the subsets I = {1, 2 , . . . , m} and J = {1, 2 , . . . , n} of integers. A collection p of subset Pj of I is a cover of I, if the union of the members of go is I, i.e., let Pj C I, go = {Pj : j C J0}, J0 C J, go i...

The Travelling Salesmen Problem (TSP) is one of the most important and famous combinational optimization problems that aim to find the shortest tour. In this problem, the salesman starts to move from an arbitrary place called depot and after visiting all nodes, finally comes back to depot. Solving this problem seems hard because program statement is simple and leads this problem belonging to NP...

We show that if f : M →M is a pseudo-Anosov homeomorphism on an orientable surface with oriented unstable manifolds and a quadratic expanding factor, then there is a hyperbolic toral automorphism on T2 and a map h : M → T2 such that h is a semi-conjugacy and (M, h) is a branched covering space of T2. We also give another characterization of pseudo-Anosov homeomorphisms with quadratic expansion ...

Abstract This paper studies a generalization of the shortest path tour problem with time windows ( GSPTPTW ). The aim is to find single-origin single-destination path, which has pass through an ordered sequence not necessarily disjoint node-subsets. Each node window for each node-subset it belongs. We investigate theoretical properties and propose dynamic programming approach solve it. Numerica...

The problem of maximal hub covering as a challenging problem in operation research. Transportation programming seeks to find an optimal location of a set of hubs to reach maximum flow in a network. Since the main structure's parameters of the problem such as origin-destination flows, costs and travel time, change periodically in the real world applications, new issues arise in handling it. In t...

In the Euclidean traveling salesman and buyers problem (TSBP), we are given a set of convex regions in d-dimensional space, and we wish to nd a minimum-cost tour that visits all the regions. The cost of a tour depends on the length of the tour itself and on the distance that buyers within each region need to travel to meet the salesman. We show that constantfactor approximations to the TSBP and...