Two-player simultaneous location game: Preferential rights and overbidding

Competitive location problems can be characterized by the fact that the decisions made by others will affect our own payoffs. In this paper, we address a discrete competitive location game in which two decision-makers have to decide simultaneously where to locate their services without knowing the decisions of one another. This problem arises in a franchising environment in which the decision-makers are the franchisees and the franchiser defines the potential sites for locating services and the rules of the game. At most one service can be located at each site, and one of the franchisees has preferential rights over the other. This means that if both franchisees are interested in opening the service in the same site, only the one that has preferential rights will open it. We consider that both franchisees have budget constraints, but the franchisee without preferential rights is allowed to show interest in more sites than the ones she can afford. We are interested in studying the influence of the existence of preferential rights and overbidding on the outcomes for both franchisees and franchiser. A model is presented and an algorithmic approach is developed for the calculation of Nash equilibria. Several computational experiments are defined and their results are analysed, showing that preferential rights give its holder a relative advantage over the other competitor. The possibility of overbidding seems to be advantageous for the franchiser, as well as the inclusion of some level of asymmetry between the two decision-makers.     

Single facility location on a network under mill and delivered pricing

^** E-mail: pelegrin{at}um.es Firms normally use either a mill price or a delivered pricepolicy, depending on market conditions (type of good, transportationway, customers location, costs, etc). In this paper, the problemof selecting the best location for an entering firm in competitionwith some pre-existing firms, under each price policy, is studiedon a network for the first time. With mill pricing, an equilibriumin price rarely exists and it is assumed that all competingfirms set a common mill price for all customers. With deliveredpricing, there exists a Nash equilibrium in price and it isassumed that the equilibrium price in each area is offered tothe customers in that area. In both cases, we consider thatcustomers buy from the cheapest facility and the same rulesare used for tie breaking in the lowest cost. While the profitmaximization problem for the entering firm always has optimalsolutions under mill pricing, this problem might not have anoptimal solution under delivered pricing. We show some discretizationresults and give procedures to find the full set of optimal,or -optimal, solutions to the problem under the two price policies.A comparison of results with the two price policies is givenby using an illustrative example.     

空间集聚、区位选择与江苏省外商直接投资:空间计量实证研究

定量概述江苏省外商直接投资发展历程,根据外商直接投资区位选择的区位成本、国际贸易、产业组织和邓宁折衷理论,从成本、经济、集聚、制度等方面,运用1999-2010年FDI数据,对江苏FDI区位选择影响因素进行空间计量实证分析,研究结果表明:1)江苏FDI发展差异总体趋势是绝对差异在逐年扩大,相对差异呈缓慢下降;2)江苏FDI空间趋于非均衡分布,"核心-外围"空间格局有所改变;3)集聚程度、经济发展水平、工业化水平、基础设施、劳动成本是江苏FDI区位选择的决定性影响因素;4)外资产出率、城市化水平、人力资本、对外开放度等负相关影响因素在江苏FDI区位选择中的重要程度显著性下降.江苏应根据后金融危机时代全球FDI新的发展趋势和特征,积极承接国际产业转移,全面参与全球产业分工,加快引导外商投资重点投向现代农业、现代服务业、新兴产业、高新技术产业等领域,优化外资投资方式、投资结构和地区分布.     

一种基于GIS的选址问题及算法

本文考虑了选址区域内存在地理阻断情况下的一种基于GIS的选址问题.对单配送中心选址模型,以GIS返回的任意两点间的最短可行路径的长度作为修正距离函数,分析了目标函数在凸形选址区域上非凸非连续的性质.进一步,采用给出了一种近似搜索算法并通过一个实例计算与重心法进行了比较.     

需求势能理论的配送中心选址方法的研究

物流配送中心选址的合理性直接影响着物流分销网络规划和优化.提出了针对物流网点选址的需求势能理论,并提出了一种基于需求势能的分销物流系统中配送中心的选址实现方法.最后通过实例证明,该方法简便快捷,结果正确合理,为解决此类配送中心选址问题提供了科学的指导依据.     

带惩罚的动态设施选址问题的近似算法

本文研究带惩罚的动态设施选址问题,在该问题中假设不同时段内设施的开放费用、用户的需求及连接费用可以不相同,而且允许用户的需求不被满足,但是要有惩罚.对此问题我们给出了第-个近似比为1.8526的原始对偶(组合)算法.     

混凝土搅拌站的选址问题研究

混凝土搅拌站的选址,在施工中占有十分重要的地位.针对混凝土需求随时间不规则变化的情况以及混凝土有效期短等特点,提出了混凝土需求不规则变化的选址模型.该模型把选址与各个时间段的资源配置结合起来确定混凝土搅拌站的位置,在保证需求最大限度得到满足的同时,使选址能够兼顾到尽可能多的需求点,最大化搅拌站的利润.应用该模型和算法成功地解决了一个实际问题,算例验证了模型和算法的有效性.     

Competitive facility location on decentralized supply chains

This paper addresses a novel competitive facility location problem about a firm that intends to enter an existing decentralized supply chain comprised of three tiers of players with competition: manufacturers, retailers and consumers. It first proposes a variational inequality for the supply chain network equilibrium model with production capacity constraints, and then employs the logarithmic-quadratic proximal prediction–correction method as a solution algorithm. Based on this model, this paper develops a generic mathematical program with equilibrium constraints for the competitive facility location problem, which can simultaneously determine facility locations of the entering firm and the production levels of these facilities so as to optimize an objective. Subsequently, a hybrid genetic algorithm that incorporates with the logarithmic-quadratic proximal prediction–correction method is developed for solving the proposed mathematical program with an equilibrium constraint. Finally, this paper carries out some numerical examples to evaluate proposed models and solution algorithms.     

US Coast Guard air station location with respect to distress calls: A spatial statistics and optimization based methodology

We study the problem of suitably locating US Coast Guard air stations to respond to emergency distress calls. Our goal is to identify robust locations in the presence of uncertainty in distress call locations. Our analysis differs from the literature primarily in the way we model this uncertainty. In our optimization and simulation based methodology, we develop a statistical model and demonstrate our procedure using a real data set of distress calls. In addition to guiding strategic decisions of placement of various stations, our methodology is also able to provide guidance on how the resources should be allocated across stations.     

Efficient computation of 2-medians in a tree network with positive/negative weights

We consider a variant of the classical two median facility location problem on a tree in which vertices are allowed to have positive or negative weights. This problem was proposed by Burkard et al. in 2000 (R.E. Burkard, E. Çela, H. Dollani, 2-medians in trees with pos/neg-weights, Discrete Appl. Math. 105 (2000) 51-71). who looked at two objectives, finding the total minimum weighted distance (MWD) and the total weighted minimum distance (WMD). Their approach finds an optimal solution in O(n²) time and O(n³) time, respectively, with better performance for special trees such as paths and stars. We propose here an O(nlogn) algorithm for the MWD problem on trees of arbitrary shape. We also briefly discuss the WMD case and argue that it can be solved in time. However, a systematic exposition of the later case cannot be contained in this paper.