The hierarchical hub location problem is encountered three-level network that is applied in production-distribution system, education system, emergency medical services, telecommunication network, etc. This paper addresses the hierarchical hub covering problem with single assignment accounting for mandatory dispersion of central hubs restriction as a special case. This formulation with incorpor...

In this paper, we present a new formulation of one-stop capacitated hub-and-spoke model as a natural extension of the uncapacitated one-stop model. The model involves arc capacity constraints as well as hub capacity constraints, which enables us to incorporate some practical factors into the model. We also present a branch-and-bound based exact solution method with Lagrangian relaxation boundin...

In this paper we consider a capacitated single allocation p-hub median problem (CSApHMP) which is to determine the location of p hubs, the allocation of non-hub nodes to hubs in the logistics network. This problem is formulated as an integer programming model with the objective of minimizing the sum of total transportation cost and fixed cost of the selected p hubs. Since the CSApHMP is NP-hard...

In this paper we consider a capacitated single allocation p-hub median problem with multiple capacity levels (CSApHMPMC) in which the decisions are to determine the location of p hubs and their capacity levels, the single allocation of non-hub nodes to hubs in the logistics network. This problem is formulated as an integer programming model with the objective of minimizing the sum of total tran...

In this paper we study the capacitated vertex cover problem, a generalization of the well-known vertex cover problem. Given a graph G = (V ,E) with weights on the vertices, the goal is to cover all the edges by picking a cover of minimum weight from the vertices. When we pick a copy of a vertex, we pay the weight of the vertex and cover up to a pre-specified number of edges incident on this ver...

In this study a hierarchical hub location problem with two layers is considered. The first layer includes small hubs and the second one includes a star-shaped network central hub. The considered case is a cargo delivery network where there is hierarchy between hubs. All the hubs and links are capacitated and there are three kinds of commodities for each of which there is a special kind of vehic...

This paper deals with a capacitated hub location problem arising in the design of telecommunications networks. The problem is different from the classical hub location problem in two ways: the cost of using an edge is not linear but stepwise and the capacity of a hub restricts the amount of traffic transiting through the hub rather than the incoming traffic. In this paper both an exact and a he...

In this paper, we present a novel multi-objective mathematical model for capacitated single allocation hub location problem. There are the vehicle capacity constraint and capacity restrictions amount of the incoming flow to the hub while the balancing requirements of incoming quantities of flow to the each hub is considered. Moreover, there is a set of available capacities for each potential hu...

In the Metric Capacitated Covering (MCC) problem, given a set of balls \({\mathcal {B}}\) in metric space P with d and capacity parameter U, goal is to find minimum sized subset \({{\mathcal {B}}}'\subseteq {\mathcal an assignment points {B}}'\) such that each point assigned ball contains it at most U points. MCC achieves \(O(\log |P|)\)-approximation using greedy algorithm. On other hand, hard...