Decomposition methods for large-scale network expansion problems

Network expansion problems are a special class of multi-period network design problems in which arcs can be opened gradually in different time periods but can never be closed. Motivated by practical applications, we focus on cases where demand between origin-destination pairs expands over a discrete time horizon. Arc opening decisions are taken in every period, and once an arc is opened it can be used throughout the remaining horizon to route several commodities. Our model captures a key timing trade-off: the earlier an arc is opened, the more periods it can be used for, but its fixed cost is higher, since it accounts not only for construction but also for maintenance over the remaining horizon. An overview of practical applications indicates that this trade-off is relevant in various settings. For the capacitated variant, we develop an arc-based Lagrange relaxation, combined with local improvement heuristics. For uncapacitated problems, we develop four Benders decompositi

Satellite Network, Design, Optimization, and Management

We introduce several network design and planning problems that arise in the context of commercial satellite networks. At the heart of most of these problems we deal with a traffic routing problem over an extended planning horizon. In satellite networks route changes are associated with significant monetary penalties that are usually in the form of discounts (up to 40%) offered by the satellite provider to the customer that is affected. The notion of these rerouting penalties requires the network planners to consider management problems over multiple time periods and introduces novel challenges that have not been considered previously in the literature. Specifically, we introduce a multiperiod traffic routing problem and a multiperiod network design problem that incorporate rerouting penalties. For both of these problems we present novel path-based reformulations and develop branch-and-price-and-cut approaches to solve them. The pricing problems in both cases present new challenges and we develop special purpose approaches that can deal with them. We also show how these results can be extended to deal with traffic routing and network design decisions in other settings with much more general rerouting penalties. Our computational work demonstrates the benefits of using the branch-and-price-and-cut procedure developed that can deal with the multiperiod nature of the problem as opposed to straightforward, myopic period-by-period optimization approaches. In order to deal with cases in which future demand is not known with certainty we present the stochastic version of the multiperiod traffic routing problem and formulate it as a stochastic multistage recourse problem with integer variables at all stages. We demonstrate how an appropriate path-based reformulation and an associated branch-and-price-and-cut approach can solve this problem and other more general multistage stochastic integer multicommodity flow problems. Finally, we motivate the notion of reload costs that refer to variable (i.e., per unit of flow) costs for the usage of pairs of edges, as opposed to single edges. We highlight the practical and theoretical significance of these cost structures and present two extended graphs that allow us to easily capture these costs and generate strong formulations

Models for planning the evolution of local telecommunication networks

Includes bibliographical references.Research initiated through a grant from GTE Laboratories, Inc. Supported in part by an AT&T research award. Supported in part by the Systems Theory and Operations Research Program of the National Science Foundation. ECS-8316224 Supported in part by ONR. N0000-14-86-0689A. Balakrishnan ... [et al.]

Models for planning the evolution of local telecommunication networks

Includes bibliographical references.Research initiated through a grant from GTE Laboratories, Inc. Supported in part by an AT&T research award. Supported in part by the Systems Theory and Operations Research Program of the National Science Foundation. ECS-8316224 Supported in part by ONR. N0000-14-86-0689A. Balakrishnan ... [et al.]

On the Value of Multistage Risk-Averse Stochastic Facility Location With or Without Prioritization

We consider a multiperiod stochastic capacitated facility location problem under uncertain demand and budget in each period. Using a scenario tree representation of the uncertainties, we formulate a multistage stochastic integer program to dynamically locate facilities in each period and compare it with a two-stage approach that determines the facility locations up front. In the multistage model, in each stage, a decision maker optimizes facility locations and recourse flows from open facilities to demand sites, to minimize certain risk measures of the cost associated with current facility location and shipment decisions. When the budget is also uncertain, a popular modeling framework is to prioritize the candidate sites. In the two-stage model, the priority list is decided in advance and fixed through all periods, while in the multistage model, the priority list can change adaptively. In each period, the decision maker follows the priority list to open facilities according to the realized budget, and optimizes recourse flows given the realized demand. Using expected conditional risk measures (ECRMs), we derive tight lower bounds for the gaps between the optimal objective values of risk-averse multistage models and their two-stage counterparts in both settings with and without prioritization. Moreover, we propose two approximation algorithms to efficiently solve risk-averse two-stage and multistage models without prioritization, which are asymptotically optimal under an expanding market assumption. We also design a set of super-valid inequalities for risk-averse two-stage and multistage stochastic programs with prioritization to reduce the computational time. We conduct numerical studies using both randomly generated and real-world instances with diverse sizes, to demonstrate the tightness of the analytical bounds and efficacy of the approximation algorithms and prioritization cuts

Optimisation of connections to a fibre network

Stronger competition together with the development of new technologies have forced the Telecom Service Providers (TSP's) in the Netherlands to look for sophisticated optimisation methods to reduce the costs of their communication services especially for new areas such as the application of fibre technology.Fibre is being considered as the transmission medium of the future because fibre deadens the signals much less than the traditional media such as copper and coax, a lot of data can be transmitted at the same time and there are only a few failures. Another advantage is that fibre cables are thin and light so that they can be put into the ground rather easily.This article describes optimisation models with the objective to minimise the costs of constructing and managing a fibre network.The optimisation models have been developed to support decisions about the design and use of a fibre network and are based on the practical situation at Enertel being one of the new TSP’s. For Enertel a national backbone was already realised. The main problem to be solved concerned the optimisation of the access to the fibre network.

Modeling Industrial Lot Sizing Problems: A Review

In this paper we give an overview of recent developments in the field of modeling single-level dynamic lot sizing problems. The focus of this paper is on the modeling various industrial extensions and not on the solution approaches. The timeliness of such a review stems from the growing industry need to solve more realistic and comprehensive production planning problems. First, several different basic lot sizing problems are defined. Many extensions of these problems have been proposed and the research basically expands in two opposite directions. The first line of research focuses on modeling the operational aspects in more detail. The discussion is organized around five aspects: the set ups, the characteristics of the production process, the inventory, demand side and rolling horizon. The second direction is towards more tactical and strategic models in which the lot sizing problem is a core substructure, such as integrated production-distribution planning or supplier selection. Recent advances in both directions are discussed. Finally, we give some concluding remarks and point out interesting areas for future research

Integrated production-distribution systems : Trends and perspectives

During the last two decades, integrated production-distribution problems have attracted a great deal of attention in the operations research literature. Within a short period, a large number of papers have been published and the field has expanded dramatically. The purpose of this paper is to provide a comprehensive review of the existing literature by classifying the existing models into several different categories based on multiple characteristics. The paper also discusses some trends and list promising avenues for future research

The Incremental Cooperative Design of Preventive Healthcare Networks

This document is the Accepted Manuscript version of the following article: Soheil Davari, 'The incremental cooperative design of preventive healthcare networks', Annals of Operations Research, first published online 27 June 2017. Under embargo. Embargo end date: 27 June 2018. The final publication is available at Springer via http://dx.doi.org/10.1007/s10479-017-2569-1.In the Preventive Healthcare Network Design Problem (PHNDP), one seeks to locate facilities in a way that the uptake of services is maximised given certain constraints such as congestion considerations. We introduce the incremental and cooperative version of the problem, IC-PHNDP for short, in which facilities are added incrementally to the network (one at a time), contributing to the service levels. We first develop a general non-linear model of this problem and then present a method to make it linear. As the problem is of a combinatorial nature, an efficient Variable Neighbourhood Search (VNS) algorithm is proposed to solve it. In order to gain insight into the problem, the computational studies were performed with randomly generated instances of different settings. Results clearly show that VNS performs well in solving IC-PHNDP with errors not more than 1.54%.Peer reviewe

Robust optimization criteria: state-of-the-art and new issues

Uncertain parameters appear in many optimization problems raised by real-world applications. To handle such problems, several approaches to model uncertainty are available, such as stochastic programming and robust optimization. This study is focused on robust optimization, in particular, the criteria to select and determine a robust solution. We provide an overview on robust optimization criteria and introduce two new classifications criteria for measuring the robustness of both scenarios and solutions. They can be used independently or coupled with classical robust optimization criteria and could work as a complementary tool for intensification in local searches