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...

The problem of covering a compact canonical polygonal region, called target region, with a finite family of rectangles is considered. Tools for mathematical modeling of the problem are provided. Especially, a function, called Γ-function, is introduced which indicates whether the rectangles with respect to their configuration form a cover of the target region or not. The construction of the Γ-fu...

We consider the capacitated domination problem, which models a service-requirement assigning scenario and which is also a generalization of the dominating set problem. In this problem, we are given a graph with three parameters defined on the vertex set, which are cost, capacity, and demand. The objective of this problem is to compute a demand assignment of least cost, such that the demand of e...

In this paper, a stochastic programming approach is applied to the airline network revenue management problem. The airline network with the arc capacitated single hub location problem based on complete–star p-hub network is considered. We try to maximize the profit of the transportation company by choosing the best hub locations and network topology, applying revenue management techniques to al...

Hub location problems are strategic network planning problems. They formalise the challenge of mutually exchanging shipments between a large set of depots. The aim is to choose a set of hubs (out of a given set of possible hubs) and connect every depot to a hub so that the total transport costs for exchanging shipments between the depots are minimised. In classical hub location problems, the un...

Through observations from real life hub networks, we introduce the multimodal hub location and hub network design problem. We approach the hub location problem from a network design perspective. In hub network design problem, we jointly consider transportation costs and travel times, which are studied separately in most hub location problems presented in the literature. We allow different trans...

One main group of a transportation network is a discrete hub covering problem that seeks to minimize the total transportation cost. This paper presents a multi-product and multi-mode hub covering model, in which the transportation time depends on travelling mode between each pair of hubs. Indeed, the nature of products is considered different and hub capacity constraint is also applied. Due to ...

A hub set in a graph G is a set U ⊆ V (G) such that any two vertices outside U are connected by a path whose internal vertices lie in U . We prove that h(G) ≤ hc(G) ≤ γc(G) ≤ h(G) + 1, where h(G), hc(G), and γc(G), respectively, are the minimum sizes of a hub set in G, a hub set inducing a connected subgraph, and a connected dominating set. Furthermore, all graphs with γc(G) > hc(G) ≥ 4 are obt...

We o er a formulation that locates hubs on a network in a competitive environment; that is, customer capture is sought, which happens whenever the location of a new hub results in a reduction of the current cost (time, distance) needed by the tra c that goes from the speci ed origin to the speci ed destination. The formulation presented here reduces the number of variables and constraints as co...