The topological ordering algorithm sorts nodes of a directed graph such that the order of the tail of each arc is lower than the order of its head. In this paper, we introduce the notion of covering between nodes of a directed graph. Then, we apply the topological orderingalgorithm on graphs containing the covering nodes. We show that there exists a cut set withforward arcs in these...

Abstract One of the basic assumptions in hub covering problems is considering the covering radius as an exogenous parameter which cannot be controlled by the decision maker. Practically and in many real world cases with a negligible increase in costs, to increase the covering radii, it is possible to save the costs of establishing additional hub nodes. Change in problem parameters during the pl...

abstract one of the basic assumptions in hub covering problems is considering the covering radius as an exogenous parameter which cannot be controlled by the decision maker. practically and in many real world cases with a negligible increase in costs, to increase the covering radii, it is possible to save the costs of establishing additional hub nodes. change in problem parameters during the pl...

In the Covering Salesman Problem (CSP), a distribution of nodes is provided, and the objective is to identify the shortest-length tour of a subset of all given nodes such that each node is not on the tour which is within a radius r of any node on the tour. In this paper, we define a new covering problem called the CSP with Nodes and Segments (CSPNS). The main difference between the CSP and the ...

in this paper, we develop a capacitated location-covering model considering interval values for demand and service parameters. we also consider flexibility on distance standard for covering demand nodes by the servers. we use the satisfaction degree to represent the constraint of service capacity. the proposed model belongs to the class of mixed integer programming models. our model can be redu...

In this paper, we develop a capacitated location-covering model considering interval values for demand and service parameters. We also consider flexibility on distance standard for covering demand nodes by the servers. We use the satisfaction degree to represent the constraint of service capacity. The proposed model belongs to the class of mixed integer programming models. Our model can be redu...

The present study introduced a novel hierarchical hub set covering problem with capacity constraints. This study showed the significance of fixed charge costs for locating facilities, assigning hub links and designing a productivity network. The proposed model employs mixed integer programming to locate facilities and establish links between nodes according to the travel time between an origin-...

The goals of hub location problems are finding the location of hub facilities and determining the allocation of non-hub nodes to these located hubs. In this work, we discuss the multi-modal single allocation capacitated p-hub covering problem over fully interconnected hub networks. Therefore, we provide a formulation to this end. The purpose of our model is to find the location of hubs and the ...

    Hub covering location problem, Network design,   Single machine scheduling, Genetic algorithm,   Shuffled frog leaping algorithm   Hub location problems (HLP) are synthetic optimization problems that appears in telecommunication and transportation networks where nodes send and receive commodities (i.e., data transmissions, passengers transportation, express packages, postal deliveries, etc....