We study an uncapacitated facility location model where customers are served byfacilities of level one, then each level one facility that is opened must be assigned toan opened facility of level two. We identify a polynomially solvable case, and study somevalid inequalities and facets of the associated polytope.

In this article we study the realistic network topology of Synchronous Digital Hierarchy(SDH) networks. We describe how providers fulfill customer connectivity requirements. Weshow that SDH Network design reduces to the Non-Disjoint m-Ring-Star Problem (NDRSP). Wefirst show that there is no two-index integer formulation for this problem. We thenpresent a natural 3-index formulation for the NDRSP together with some classes of validinequalities that are used as cutting planes in a Branch-and-Cut approach. We propose apolyhedral study of a polytope associated with this formulation. Finally, we present ourBranch-and-Cut algorithm and give some experimental results on both random and realinstances.

A Content Distribution Network (CDN) can be defined as an overlay system that replicatescopies of contents at multiple points of a network, close to the final users, with theobjective of improving data access. CDN technology is widely used for the distribution oflarge-sized contents, like in video streaming. In this paper we address the problem offinding the best server for each customer request in CDNs, in order to minimize theoverall cost. We consider the problem as a transportation problem and a distributedalgorithm is proposed to solve it. The algorithm is composed of two independent phases: adistributed heuristic finds an initial solution that may be later improved by adistributed transportation simplex algorithm. It is compared with the sequential versionof the transportation simplex and with an auction-based distributed algorithm.Computational experiments carried out on a set of instances adapted from the literaturerevealed that our distributed approach has a performance similar or better to itssequential counterpart, in spite of not requiring global information about the contentsrequests. Moreover, the results also showed that the new method outperforms thebased-auction distributed algorithm.

The problem of finding structures with minimum stabbing number has received considerableattention from researchers. Particularly, [10]study the minimum stabbing number of perfect matchings (mspm), spanning trees(msst) and triangulations (mstr) associated to set of points in theplane. The complexity of the mstr remains open whilst the other two are known tobe 𝓝𝓟-hard. This paper presents integer programming(ip) formulations for these three problems, that allowed us to solve them tooptimality through ip branch-and-bound (b&b) or branch-and-cut(b&c) algorithms. Moreover, these models are the basis for the developmentof Lagrangian heuristics. Computational tests were conducted with instances taken from theliterature where the performance of the Lagrangian heuristics were compared with that ofthe exact b&b and b&c algorithms. The results reveal that theLagrangian heuristics yield solutions with minute, and often null, duality gaps forinstances with several hundreds of points in small computation times. To our knowledge,this is the first computational study ever reported in which these three stabbing problemsare considered and where provably optimal solutions are given.

In this paper we consider the problem of scheduling, on a two-machine flowshop, a set ofunit-time operations subject to time delays with respect to the makespan. This problem isknown to be \hbox{${\cal NP}$}𝒩𝒫-hard in the strong sense. We propose an algorithm basedon a branch and bound enumeration scheme. This algorithm includes the implementation ofnew lower and upper bound procedures, and dominance rules. A computer simulation tomeasure the performance of the algorithm is provided for a wide range of testproblems.

In this study, we consider a scheduling environment with m(m ≥ 1) parallel machines.The set of jobs to schedule is divided into K disjoint subsets. Each subset of jobs isassociated with one agent. The K agents compete to perform their jobs on commonresources. The objective is to find a schedule that minimizes a global objective functionf 0, while maintaining the regularobjective function of each agent, f k, at a level nogreater than a fixed value, εk (fk ∈ {fkmax, ∑fk}, k = 0, ..., K). This problem is a multi-agent schedulingproblem with a global objective function. In this study, we consider the casewith preemption and the case without preemption. If preemption is allowed, we propose apolynomial time algorithm based on a network flow approach for the unrelated parallelmachine case. If preemption is not allowed, we propose some general complexity results anddevelop dynamic programming algorithms.