Hub location under competition

Ankara : The Department of Industrial Engineering and the Graduate School of Engineering and Science of Bilkent University, 2013.Thesis (Master's) -- Bilkent University, 2013.Includes bibliographical references leaves 64-69.Hubs are consolidation and dissemination points in many-to-many flow networks. The hub location problem is to locate hubs among available nodes and allocate non-hub nodes to these hubs. The mainstream hub location studies focus on optimal decisions of one decision-maker with respect to some objective(s) even though the markets that benefit hubbing are oligopolies. Therefore, in this thesis, we propose a competitive hub location problem where the market is assumed to be a duopoly. Two decision-makers (or firms) sequentially decide the locations of their hubs and then customers choose the firm according to provided service levels. Each decision-maker aims to maximize his/her market share. Having investigated the existing studies in the field of economy, retail location and operation research, we propose two problems for the leader (former decision-maker) and follower (latter decision-maker): (r|Xp) hub-medianoid and (r|p) hub-centroid problems. After defining them as combinatorial optimization problems, the problems are proved to be NP-hard. Linear programming models are presented for these problems as well as exact solution algorithms for the (r|p) hub-centroid problem that outperform the linear model in terms of memory requirement and CPU time. The performance of models and algorithms are tested by the computational analysis conducted on two well-known data sets from the hub location literature.Mahmutoğulları, Ali İrfanM.S

Hub location under competition

Hubs are consolidation and dissemination points in many-to-many flow networks. Hub location problem is to locate hubs among available nodes and allocate non-hub nodes to these hubs. The mainstream hub location studies focus on optimal decisions of one decision-maker with respect to some objective(s) even though the markets that benefit hubbing are oligopolies. Therefore, in this paper, we propose a competitive hub location problem where the market is assumed to be a duopoly. Two decision-makers (or firms) sequentially decide locations of their hubs and then customers choose one firm with respect to provided service levels. Each decision-maker aims to maximize his/her own market share. We propose two problems for the leader (former decision-maker) and follower (latter decision-maker): (r|Xp)hub-medianoid and (r|p)hub-centroid problems, respectively. Both problems are proven to be NP-complete. Linear programming models are presented for these problems as well as exact solution algorithms for the (r|p)hub-centroid problem. The performance of models and algorithms are tested by computational analysis conducted on CAB and TR data sets. © 2015 Elsevier B.V. and Association of European Operational Research Societies (EURO) within the International Federation of Operational Research Societies (IFORS). All rights reserved

The Hub Location and Pricing Problem

This paper introduces the joint problem of locating hubs on a network and determining transportation prices between the hubs. Two levels of decision makers are present in the problem acting non-cooperatively: hub transportation provider and customers. The objective of the hub transportation provider is to locate hubs and to set the prices (per unit of commodity) of crossing the hub arcs maximizing its prot, whereas the customers aim is to send their commodities, in the cheapest way, having the possibility of using the hub arcs at the price set by the hub transportation provider or using the existing network at a predefinedtariff. The problem is modeled as a nonlinear bilevel programming formulation, which is in turn linearized, and strengthened through variable reductions as well as valid inequalities. The case in which the price of each hub arc is determined by applying a common discount factor to the predefined tariff in the existing network is also studied. Computational results of mixed integer programming models and a metaheuristic on instances adapted from the literature are presented

Trade-offs between the stepwise cost function and its linear approximation for the modular hub location problem

There exist situations where the transportation cost is better estimated as a function of the number of vehicles required for transporting a load, rather than a linear function of the load. This provides a stepwise cost function, which defines the so-called Modular Hub Location Problem (MHLP, or HLP with modular capacities) that has received increasing attention in the last decade. In this paper, we consider formulations to be solved by exact methods. We show that by choosing a specific generalized linear cost function with slope and intercept depending on problem data, one minimizes the measurement deviation between the two cost functions and obtains solutions close to those found with the stepwise cost function, while avoiding the higher computational complexity of the latter. As a side contribution, we look at the savings induced by using direct shipments in a hub and spoke network, given the better ability of a stepwise cost function to incorporate direct transportation. Numerical experiments are conducted over benchmark HLP instances of the OR-library

The distributed p-median problem in computer networks

Many distributed services in computer networks rely on a set of active facilities that are selected among a potentially large number of candidates. The active facilities then contribute and cooperate to deliver a specific service to the users of the distributed system. In this scenario graph partitioning or clustering is often adopted to determine the most efficient locations of the facilities. The identification of the optimal set of facility locations is known as the p-median problem in networks, is NP-hard and is typically solved by using heuristic methods. The goal is to select p locations among all candidate network nodes such that some cost function is minimised. A typical example of such a function is the overall communication cost to deliver the service to the users of the distributed system. Locating facilities in near-optimal locations has been extensively studied for different application domains. Most of these studies have investigated sequential algorithms and centralised approaches. However, centralised approaches are practically infeasible in large-scale and dynamic networks, where the problem is inherently distributed or because of the large communication overhead and memory requirements for gathering complete information about the network topology and the users. In this work distributed approaches to the p-median problem are investigated. Two solutions are proposed for addressing the facility locations problem in a fully distributed environment. Two different iterative heuristic approaches are applied to gradually improve a random initial solution and to converge to a final solution with a local minimum of the overall cost. While the first approach adopts a fine granularity by identifying a single change to improve the solution at each iteration, the second approach applies changes to every component of the solution at each iteration. An experimental comparative analysis based on simulations has shown that the approach with a finer granularity is able to deliver a better optimisation of the overall cost with longer convergence time. Both approaches have excellent scalability and provide an effective tool to optimise the facility locations from within the network. No prior knowledge of the system is required, no data needs to be gathered in a centralised server and the same process is used to identify and to deploy the facility locations solution in the network since the process is fully decentralised

Planning and Scheduling Optimization

Although planning and scheduling optimization have been explored in the literature for many years now, it still remains a hot topic in the current scientific research. The changing market trends, globalization, technical and technological progress, and sustainability considerations make it necessary to deal with new optimization challenges in modern manufacturing, engineering, and healthcare systems. This book provides an overview of the recent advances in different areas connected with operations research models and other applications of intelligent computing techniques used for planning and scheduling optimization. The wide range of theoretical and practical research findings reported in this book confirms that the planning and scheduling problem is a complex issue that is present in different industrial sectors and organizations and opens promising and dynamic perspectives of research and development

Network design under uncertainty and demand elasticity

Network design covers a large class of fundamental problems ubiquitous in the fields of transportation and communication. These problems are modelled mathematically using directed graphs and capture the trade-off between initial investment in infrastructure and operational costs. This thesis presents the use of mixed integer programming theory and algorithms to solve network design problems and their extensions. We focus on two types of network design problems, the first is a hub location problem in which the initial investments are in the form of fixed costs for installing infrastructure at nodes for them to be equipped for the transhipment of commodities. The second is a fixed-charge multicommodity network design problem in which investments are in the form of installing infrastructure on arcs so that they may be used to transport commodities. We first present an extension of the hub location problem where both demand and transportation cost uncertainty are considered. We propose mixed integer linear programming formulations and a branch-and-cut algorithm to solve robust counterparts for this problem. Comparing the proposed models' solutions to those obtained from a commensurate stochastic counterpart, we note that their performance is similar in the risk-neutral setting while solutions from the robust counterparts are significantly superior in the risk-averse setting. We next present exact algorithms based on Benders decomposition capable of solving large-scale instances of the classic uncapacitated fixed-charge multicommodity network design problem. The method combines the use of matheuristics, general mixed integer valid inequalities, and a cut-and-solve enumeration scheme. Computational experiments show the proposed approaches to be up to three orders of magnitude faster than the state-of-the-art general purpose mixed integer programming solver. Finally, we extend the classic fixed-charge multicommodity network design problem to a profit-oriented variant that accounts for demand elasticity, commodity selection, and service commitment. An arc-based and a path-based formulation are proposed. The former is a mixed integer non-convex problem solved with a general purpose global optimization solver while the latter is an integer linear formulation with exponentially many variables solved with a hybrid matheuristic. Further analysis shows the impact of considering demand elasticity to be significant in strategic network design