In this paper we describe a problem that we de ne as the Budget-Constrained Minimum Cost Flow (BCMCF) problem. The BCMCF problem is a natural extension of the well-known Minimum Cost Flow (MCF) [2] problem, with a xed cost related to the use of arcs and a budget constraint. Network ow problems often become hard when extra constraints are added. Ahuja and Orlin [1] discuss the constrained maximu...

Algebraic connectivity, the second eigenvalue of the Laplacian matrix, is a measure of node and link connectivity on networks. When studying interconnected networks it is useful to consider a multiplex model, where the component networks operate together with interlayer links among them. In order to have a well-connected multilayer structure, it is necessary to optimally design these interlayer...

This paper proposes an optimization algorithm, the dimension-down iterative algorithm (DDIA), for solving a mixed transportation network design problem (MNDP), which is generally expressed as a mathematical programming with equilibrium constraint (MPEC). The upper level of the MNDP aims to optimize the network performance via both the expansion of the existing links and the addition of new cand...

We present in this paper a new model for robust combinatorial optimization with cost uncertainty that generalizes the classical budgeted uncertainty set. We suppose here that the budget of uncertainty is given by a function of the problem variables, yielding an uncertainty multifunction. The new model is less conservative than the classical model and approximates better Valueat-Risk objective f...

Facility location-network design (FLND) problem, which determines the location of facilities and also communication links between the demand and facility nodes, is arisen from the combination of the facility location and network design problems. This paper deals with fuzzy capacitated facility location-network design model which aims to select the facilities and candidate links in a way that yi...

The design of truthful auctions that approximate the optimal expected revenue is a central problem in algorithmic mechanism design. 30 years after Myerson’s characterization of Bayesian optimal auctions in single-parameter domains [9], characterizing but also providing efficient mechanisms for multi-parameter domains still remains a very important unsolved problem. Our work improves upon recent...

The purpose of this article is to introduce mathematical models for two budget problems. The first problem, which deals to the construction of a particular budget, is solved based on an algorithm for the maximum flow problem in bipartite network. The method constructs an efficient budget by repeating a maximum flow computation. The second problem is the budget exercise and studies how the budge...

We study a type of reverse (procurement) auction problems in the presence of budget constraints. The general algorithmic problem is to purchase a set of resources, which come at a cost, so as not to exceed a given budget and at the same time maximize a given valuation function. This framework captures the budgeted version of several well known optimization problems, and when the resources are o...