Bilevel models on the competitive facility location problem

Facility location and allocation problems have been a major area of research for decades, which has led to a vast and still growing literature. Although there are many variants of these problems, there exist two common features: finding the best locations for one or more facilities and allocating demand points to these facilities. A considerable number of studies assume a monopolistic viewpoint and formulate a mathematical model to optimize an objective function of a single decision maker. In contrast, competitive facility location (CFL) problem is based on the premise that there exist competition in the market among different firms. When one of the competing firms acts as the leader and the other firm, called the follower, reacts to the decision of the leader, a sequential-entry CFL problem is obtained, which gives rise to a Stackelberg type of game between two players. A successful and widely applied framework to formulate this type of CFL problems is bilevel programming (BP). In this chapter, the literature on BP models for CFL problems is reviewed, existing works are categorized with respect to defined criteria, and information is provided for each work.WOS:000418225000002Scopus - Affiliation ID: 60105072Book Citation Index- Science - Book Citation Index- Social Sciences and HumanitiesArticle; Book ChapterOcak2017YÖK - 2016-1

City decision-making : optimization of the location and design of urban green spaces

Le besoin grandissant pour une planification urbaine plus durable et pour des interventions publiques visant à l'amélioration du bien-être collectif, ont grandement contribué à un engouement pour les espaces verts. Les parcs sont reconnus pour leur impact positif en zone urbaine dense, et nous sommes intéressés par l'application des concepts théoriques du domaine de la recherche opérationnelle pour assister les décideurs publics afin d'améliorer l'accessibilité, la distribution et la conception des parcs. Étant donné le contexte, nous sommes particulièrement motivés par le concept d'équité, et étudions le comportement des usagers des parcs à l'aide d'un modèle d'interaction spatiale, tel qu'appliqué dans les problèmes d'emplacement d'installations dans un marché compétitif. Dans cette recherche, nous présentons un modèle d'emplacement d'installations à deux étapes pouvant être adapté pour assister les décideurs publics à l'échelle de la ville. Nous étudions spécifiquement l'application aux espaces verts urbains, mais soulignons que des extensions du modèle peuvent permettre d'aborder d'autres problèmes d'emplacements d'installations sujets à des enjeux d'équité. La première étape de notre problème d'optimisation a pour but d'évaluer l'allocation la plus équitable du budget de la ville aux arrondissements, basé sur une somme du budget pondérée par des facteurs d'équité. Dans la deuxième étape du modèle, nous cherchons l'emplacement et la conception optimale des parcs, et l'objectif consiste à maximiser la probabilité totale que les individus visitent les parcs. Étant donné la non-linéarité de la fonction objective, nous appliquons une méthode de linéarisation et obtenons un modèle de programmation linéaire mixte en nombres entiers, pouvant être résolu avec des solveurs standards. Nous introduisons aussi une méthode de regroupement pour réduire la taille du problème, et ainsi trouver des solutions quasi optimales dans un délai raisonnable. Le modèle est testé à l'aide de l'étude de cas de la ville de Montréal, Canada, et nous présentons une analyse comparative des résultats afin de justifier la performance de notre modèle.The recent promotion of sustainable urban planning combined with a growing need for public interventions to improve well-being and health in dense urban areas have led to an increased collective interest for green spaces. Parks have proven a wide range of benefits in urban areas, and we are interested in the application of theoretical concepts from the field of Operations Research to assist decision-makers to improve parks' accessibility, distribution and design. Given the context of public decision-making, we are particularly concerned with the concept of fairness, and are focused on an advanced assessment of users' behavior using a spatial interaction model (SIM) as in competitive facility locations' frameworks. In this research, we present a two-stage fair facility location and design (2SFFLD) model, which serves as a template model to assist public decision-makers at the city-level for the urban green spaces (UGSs) planning. We study the application of the 2SFFLD model to UGSs, but emphasize the potential extension to other applications to location problems concerned with fairness and equity. The first-stage of the optimization problem is about the optimal budget allocation based on a total fair-weighted budget formula. The second-stage seeks the optimal location and design of parks, and the objective consists of maximizing the total expected probability of individuals visiting parks. Given the non-linearity of the objective function, we apply a ``Method-based Linearization'' and obtain a mixed-integer linear program that can be solved with standard solvers. We further introduce a clustering method to reduce the size of the problem and determine a close to optimal solution within reasonable time constraints. The model is tested using the case study of the city of Montreal, Canada, and comparative results are discussed in detail to justify the performance of the model

Combinatorial Optimization

This report summarizes the meeting on Combinatorial Optimization where new and promising developments in the field were discussed. Th

Designing Networks with Good Equilibria under Uncertainty

We consider the problem of designing network cost-sharing protocols with good equilibria under uncertainty. The underlying game is a multicast game in a rooted undirected graph with nonnegative edge costs. A set of k terminal vertices or players need to establish connectivity with the root. The social optimum is the Minimum Steiner Tree. We are interested in situations where the designer has incomplete information about the input. We propose two different models, the adversarial and the stochastic. In both models, the designer has prior knowledge of the underlying metric but the requested subset of the players is not known and is activated either in an adversarial manner (adversarial model) or is drawn from a known probability distribution (stochastic model). In the adversarial model, the designer's goal is to choose a single, universal protocol that has low Price of Anarchy (PoA) for all possible requested subsets of players. The main question we address is: to what extent can prior knowledge of the underlying metric help in the design? We first demonstrate that there exist graphs (outerplanar) where knowledge of the underlying metric can dramatically improve the performance of good network design. Then, in our main technical result, we show that there exist graph metrics, for which knowing the underlying metric does not help and any universal protocol has PoA of $\Omega(\log k)$, which is tight. We attack this problem by developing new techniques that employ powerful tools from extremal combinatorics, and more specifically Ramsey Theory in high dimensional hypercubes. Then we switch to the stochastic model, where each player is independently activated. We show that there exists a randomized ordered protocol that achieves constant PoA. By using standard derandomization techniques, we produce a deterministic ordered protocol with constant PoA.Comment: This version has additional results about stochastic inpu

An Evolutionary Model for Spatial Location of Economic Facilities

Locating an economic facility, warehouse, plant, retail store, etc., is one of the most important questions that a business company faces. In this paper we consider a normative model for a certain class of relocation processes. That is, when one location structure is gradually substituted by another one. This happens in response to external factors such as appearance of competitors or change of demand. Thus, we are facing with sequential decisions and the model and algorithm corresponding to them become endogenously dynamic. An evolutionary model for location of economic facilities is presented. Its application to an empirical case, namely changing locations of alcohol distribution stores, is briefly presented