Effective planning of a transportation network influences tactical and operational activities and has a great impact on business. Planning typically considers multiple aspects such as variable transportation costs, various levels of customer service offered, security of goods, and traveling time. These aspects often vary with time. Although the minimum cost flow problem is a widely seen approac...

It is shown that an acyclic multigraph with a single source and a single sink is series-parallel if and only if for arbitrary linear cost functions and arbitrary capacities the corresponding minimum cost flow problem can be solved by a greedy algorithm. Furthermore, for networks of this type with m edges and n vertices, two O(mn + m log m)-algorithms are presented. One of them is based on the g...

In this paper we broadly generalize the assignment auction algorithm to solve linear minimum cost network flow problems. We introduce a generic algorithm, which contains as special cases a number of known algorithms, including the e-relaxation method, and the auction algorithm for assignment and for transportation problems. The generic algorithm can serve as a broadly useful framework for the d...

The existing works considering the flow-based discount factor in the hub and spoke problems, assume that increasing the amount of flow passing through each edge of network continuously decreases the unit flow transportation cost. Although a higher volume of flow allows for using wider links and consequently cheaper transportation, but the unit of flow enjoys more discounts, quite like replacing...

In this paper we study two basic problems related to dynamic flows: maximum multicommodity flow and the minimum cost multicommodity flow problems. We consider these problems on dynamic networks with time-varying capacities of edges. For minimum cost multicommodity flow problem we assume that cost functions, defined on edges, are nonlinear and depending on time and flow, and the demand function ...

Abstract The robust minimum cost flow problem under consistent constraints (RobMCF $$\equiv $$ ? ) is a new extension of the (MCF) problem. In RobMCF problem, we consider demand and supply that are subject to uncertainty. For all realizations, however, require value on an arc needs be equal if it included in ...

In the construction of a communication network, the (Euclidean) length of the network is an important but not unique factor determining the cost of the network. Among many possible network models, Gilbert proposed a flow-dependent model in which flow demands are assigned between each pair of points in a given point set A, and the cost per unit length of a link in the network is a function of th...

A critical issue in the design of routing protocols for wireless sensor networks is the efficient utilization of resources such as scarce bandwidth and limited energy supply. Many routing schemes proposed in the literature try to minimize the energy consumed in routing or maximize the lifetime of the sensor network without taking into consideration limited capacity of wireless links. This can l...