Allocating nodes to hubs for minimizing the hubs processing resources: A case study

This paper addresses the problem of allocating the terminal nodes to the hub nodes in a telecommunication network. Since the flow processing induces some undesirable delay, the objective is to minimize the total flow processed by the hubs. This study focuses on a real life network of the tunisian operator Tunisie Telecom whose operations managers are concerned by the quality of service. We provide three compact formulations that give optimal solutions for networks of large size. In particular, the last two are obtained by applying the Reformulation-Linearization Technique to a nonlinear formulation of the problem. The latter formulation derived within this approach is the most computationally effective, as pointed out by the computational experiments conducted on the real life network of Tunisie Telecom with 110 nodes and 5 hubs. Finally, we discuss and compare between the single allocation and double allocation configurations

Some Fixed Point Results on Rectangular Metric-Like Spaces Endowed with a Graph

The objective of this paper is to establish the existence and uniqueness of fixed points on rectangular metric-like spaces endowed with a graph. We introduce the notion of some generalized G-contractions principle. The usefulness of the considered metric space in real work is highlighted. The obtained results generalize some notes in the literature. Some examples are presented to support the main results

Optimum multi-period, multi-plant, and multi-supplier production planning for multi-grade petrochemicals

A multi-period production and inventory control problem for a multi-grade, multi-supplier petrochemical product is formulated and optimally solved. Raw materials are available from several suppliers, and several plants (chemical reactors) are used for making the petrochemical product. Several grades of the petrochemical product can be produced by changing the conditions inside each reactor. During transition from one grade to another, a certain amount is produced of off-spec material. The quantity of off-spec production is sequence dependent, i.e. it depends on the two grades that the transition takes place between. The problem is formulated and solved by means of a graphical network model as well as a mixed-integer programming (MIP) model. The MIP model determines, for each time period, the sequence and quantities of different grades produced in each plant, the amounts of raw materials purchased from each supplier, and the inventory levels of each grade. The objective is to maximize the total profit, which is equal to the sale revenue of all regular grades and off-spec materials, minus the raw material costs and inventory holding costs

Enhanced compact models for the connected subgraph problem and for the shortest path problem in digraphs with negative cycles

We investigate the minimum-weight connected subgraph problem. The importance of this problem stems from the fact that it constitutes the backbone of many network design problems having applications in several areas including telecommunication, energy, and distribution planning. We show that this problem is NP-hard, and we propose a new polynomial-size nonlinear mixed-integer programming model. We apply the Reformulation-Linearization Technique (RLT) to linearize the proposed model while keeping a polynomial number of variables and constraints. Furthermore, we show how similar modelling techniques enable an enhanced polynomial size formulation to be derived for the shortest elementary path. This latter problem is known to be intractable and has many applications (in particular, within the context of column generation). We report the results of extensive computational experiments on graphs with up to 1000 nodes. These results attest to the efficacy of the proposed compact formulations. In particular, we show that the proposed formulations consistently outperform compact formulations from the literature. 2013 Elsevier Ltd.Scopu

Suitable Mass Density Function for an Artificial Satellite to Prevent Chaotic Motion after Collision with Space Debris

Artificial satellites are widely used in different areas such as communication, position systems, and agriculture. The number of satellites orbiting Earth is becoming huge, and many are set to be launched soon. This huge number of satellites in addition to space debris are sources of concern. Indeed, some incidents have occurred either between satellites or because of space debris. These incidents are a threat for the hit satellite and can be a source of irreversible damages. A hit satellite may diverge to a chaotic motion with all the entailed consequences. The inertia moment of a satellite is a main factor to determine if the hit satellite is heading toward a chaotic motion or not. The inertia moment is determined over the mass density function. In this paper, a circularly orbiting artificial satellite was modeled as a thin rotating rod. The objective was to determine a suitable mass density function for this satellite allowing the prevention as much as possible of the chaotic motion after being hit. This unknown density mass function satisfies a system of equations reflecting some physical constraints. Conventional procedures are not applicable to solve this system of equations. The presented resolution method is based on several mathematical transformations, allowing converting this system into a highly nonlinear one with several unknowns. Several mathematical techniques were applied, and an analytical solution was obtained. Finally, from the mechanical engineering point of view, the obtained mass density function corresponds to a Functionally Graded Material (FGM)

Enhanced compact models for the connected subgraph problem and for the shortest path problem in digraphs with negative cycles

We investigate the minimum-weight connected subgraph problem. The importance of this problem stems from the fact that it constitutes the backbone of many network design problems having applications in several areas including telecommunication, energy, and distribution planning. We show that this problem is NP-hard, and we propose a new polynomial-size nonlinear mixed-integer programming model. We apply the Reformulation-Linearization Technique (RLT) to linearize the proposed model while keeping a polynomial number of variables and constraints. Furthermore, we show how similar modelling techniques enable an enhanced polynomial size formulation to be derived for the shortest elementary path. This latter problem is known to be intractable and has many applications (in particular, within the context of column generation). We report the results of extensive computational experiments on graphs with up to 1000 nodes. These results attest to the efficacy of the proposed compact formulations. In particular, we show that the proposed formulations consistently outperform compact formulations from the literature. 2013 Elsevier Ltd.Scopu

AN EXACT ALGORITHM MINIMIZING THE MAKESPAN FOR THE TWO-MACHINE FLOWSHOP SCHEDULING UNDER RELEASE DATES AND BLOCKING CONSTRAINTS

This paper describes the problem of two-machine permutation flowshop scheduling with release dates where blocking constraint is authorized. The objective is the minimization of the makespan. This problem is proved as an NP-hard problem. Four lower bounds were developed in this paper to test experimental results with different classes. An optimal solution is also proposed based on the mathematical formulation and solved using the Cplex program.

An optimization-based heuristic for the machine reassignment problem

We address the machine reassignment problem proposed in the context of the ROADEF/EURO challenge 2012 in partnership with Google. The problem consists in reassigning a set of processes to a set of multiple-resource machines so as to minimize a weighted function of the machines load, the resources balance, and the costs of moving processes while satisfying numerous constraints. We propose an optimization-based heuristic that requires decomposing the problem into a sequence of small-sized instances that are iteratively solved using a general MIP solver. To speed-up the solution process several algorithmic expedients are embedded. Extensive computational experiments provide evidence that the proposed approach exhibits a very good performance.Scopu

Synchronous Routing for Personal Rapid Transit Pods

Personal rapid transit (PRT) is a public and automated transport system in which a fleet of small driverless vehicles operate in order to transport passengers between a set of stations through a network of guided ways. Each customer is carried from one station to another directly with no stop in intermediate stations. This mode of transport can result in a high level of unused capacity due to the empty moves of the vehicles. In this paper, we model the problem of minimizing the energy consumed by the PRT system while assuming predeterministic list of orders; then we solve it using some constructive heuristics. Experiments are run on 1320 randomly generated test problems with various sizes. Our algorithms are shown to give good results over large trip instances