On the Logit Approach to Competitive Facility Location

The random utility model in competitive facility location is one approach for estimating the market share captured by a retail facility in a competitive environment. However, it requires extensive computational effort for finding the optimal location for a new facility because its objective function is based on a k -dimensional integral. In this paper we show that the random utility model can be approximated by a logit model. The proportion of the buying power at a demand point that is attracted to the new facility can be approximated by a logit function of the distance to it. This approximation demonstrates that using the logit function of the distance for estimating the market share is theoretically founded in the random utility model. A simplified random utility model is defined and approximated by a logit function. An iterative Weiszfeld-type algorithm is designed to find the best location for a new facility using the logit model. Computational experiments show that the logit approximation yields a good location solution to the random utility model.     

COMPETITIVE FACILITIES: MARKET SHARE AND LOCATION WITH RANDOM UTILITY*

ABSTRACT. A new approach is proposed for calculating the expected market share. It is assumed that consumers patronize a facility according to a utility function, selecting the facility with the highest utility value. However, consumers'ratings of the utility components are stochastic by some random distribution. Therefore, the buying power of customers located at the same point is divided among several facilities. A probability that a consumer patronizes a certain facility can be calculated. Consequently, the expected market share by competing facilities can be estimated. This calculation is more than 1,000 times faster than repeating a simulation enough times to achieve a reasonable accuracy. The distance decay calculated using the new approach is approximately exponential. A procedure for finding the optimal location anywhere in the plane for a new facility that maximizes the market share is also introduced.     

MARKET CAPTURE BY TWO COMPETITORS: THE PREEMPTIVE LOCATION PROBLEM*

ABSTRACT. We consider a location and allocation game for two competitor firms, A and B, that each seek to locate p facilities in a network. A market is captured by a particular firm if that market's closest facility belongs to that firm rather than a competitor. The question is as follows: Firm A wants to locate its p facilities so that B, which enters also with p facilities after Firm A has located its facilities, will capture the minimum market value possible. That is, Firm A wishes to preempt Firm B in its bid to capture market share to the maximum extent possible. A model is presented that addresses this issue, together with solution methods and computing times.     

Surviving in a Competitive Spatial Market: The Threshold Capture Model

Many facility location decision models ignore the fact that for a facility to survive it needs a minimum demand level to cover costs. In this paper we present a decision model for a firm that wishes to enter a spatial market where there are several competitors already located. This market is such that for each outlet there is a demand threshold level that has to be achieved in order to survive. The firm wishes to know where to locate its outlets so as to maximize its market share taking into account the threshold level. It may happen that due to this new entrance, some competitors will not be able to meet the threshold and therefore will disappear. A formulation is presented together with a heuristic solution method and computational experience.     

LOCATION AND SPATIAL PRICING FOR PUBLIC FACILITIES

ABSTRACT. Past analysis of public facility location has generally assumed a single goal, such as cost minimization or welfare maximization, and exogenous spatial pricing. This paper considers optimal facility location under a variety of goals. Furthermore, the facility manager is allowed to engage in freight absorption so that the delivered price to consumers need not reflect actual transportation costs. A systematic interaction among management goals, freight absorption, and the optimal size and spacing of public facilities is found.     

LOCATION OF PUBLIC FACILITIES WITH SPILLOVER EFFECTS: VARIABLE LOCATION AND PARAMETRIC SCALE*

ABSTRACT This paper studies the location of public facilities of two neighboring local governments which consider not only the influence of the land market but also the spillover effects that each jurisdiction may have on the other. We obtain the following results: (1) in most cases, one of the cities behaves as an isolated city in choosing the facility location while the other enjoys the spillover effect as a free rider; (2) we also find that the equilibrium location in the two noncooperative city case is not socially optimal except for a special case.     

OPTIMUM LOCATION OF PUBLIC FACILITIES UNDER THE INFLUENCE OF THE LAND MARKET*

ABSTRACT. This paper discusses the problem of the optimal location of public facility(ies) in a long narrow city, especially taking into consideration the externality-internalizing effect of the land market. It shows a systematic approach to dealing with the land market mechanism in first a one-facility and then a two-facility case. The analysis assures the importance of posing the location-optimizing problem even under the influence of the land market.     

Facility Location Under Zone Pricing

Zone pricing consists in determining simultaneously several delivered prices together with the zones where these prices apply. A model and algorithm are proposed to determine optimal facility locations, prices, tariff-zones, and market areas in order to maximize the firm's profit under zone pricing. The resulting nonlinear mixed-integer program is tackled by projecting the objective function on the price space, solving repeatedly uncapacitated facility location problems for fixed values of the prices. The implicit profit function so defined is optimized by branch-and-bound. Computational results are reported.     

携程旅行网旅游“新零售”空间格局及形成机制——以上海市线下门店为例

基于携程位于上海市的线下门店及相关POI 数据，运用 GIS 空间分析和地理探测器等方法，探讨携程旅游“新零售”空间格局、区位选址及形成机制。结果表明：①携程旅游“新零售”在发展初期，其区位选址仍具有向心性，但不如传统零售业对城市中心区位需求强烈，向中心城区边缘及城市近郊区域下沉趋势明显；②呈现集聚分布特征，形成“多中心-外扩”式分布模式；③区位选址依赖于以写字楼为主的线下生活服务场景，对商务办公区的偏好超越对商业中心的偏好。交通区位、传统旅行社分布、地租水平影响次之，CBD 趋近度、商圈等级影响较小；④携程线下门店空间格局及区位特征是企业业务板块规划、地理实体空间竞争、区域产业配套水平共同作用形成的结果。     

On Covering Problems and the Central Facilities Location Problem

A number of variations of facilities location problems have appeared in the research literature in the past decade. Among these are problems involving the location of multiple new facilities in a discrete solution space, with the new facilities located relative to a set of existing facilities having known locations. In this paper a number of discrete solution space location problems are treated. Specifically, the covering problem and the central facilities location problem are shown to be related. The covering problem involves the location of the minimum number of new facilities among a finite number of sites such that all existing facilities (customers) are covered by at least one new facility. The central facilities location problem consists of the location of a given number of new facilities among a finite number of sites such that the sum of the weighted distances between existing facilities and new facilities is minimized. Computational experience in using the same heuristic solution procedure to solve both problems is provided and compared with other existing solution procedures.     

A Family of Location Models for Multiple-Type Discrete Dispersion

One of the defining objectives in location science is to maximize dispersion. Facilities can be dispersed for a wide variety of purposes, including attempts to optimize competitive market advantage, disperse negative impacts, and optimize security. With one exception, all of the extant dispersion models consider only one type of facility, and ignore problems where multiple types of facilities must be located. We provide examples where multiple-type dispersion is appropriate and based on this develop a general class of facility location problems that optimize multiple-type dispersion. This family of models expands on the previously formulated definitions of dispersion for single types of facilities, by allowing the interactions among different types of facilities to determine the extent to which they will be spatially dispersed. We provide a set of integer-linear programming formulations for the principal models of this class and suggest a methodology for intelligent constraint elimination. We also present results of solving a range of multiple-type dispersion problems optimally and demonstrate that only the smallest versions of such problems can be solved in a reasonable amount of computer time using general-purpose optimization software. We conclude that the family of multiple-type dispersion models provides a more comprehensive, flexible, and realistic framework for locating facilities where weighted distances should be maximized, when compared with the special case of locating only a single type of facility.     

Elimination of Source A and B Errors in p-Median Location Problems

The p-median problem is a powerful tool in analyzing facility location options when the goal of the location scheme is to minimize the average distance that demand must traverse to reach its nearest facility. It may be used to determine the number of facilities to site, as well as the actual facility locations. Demand data are frequently aggregated in p-median location problems to reduce the computational complexity of the problem. Demand data aggregation, however, results in the loss of locational information. This loss may lead to suboptimal facility location configurations (optimality errors) and inaccurate measures of the resulting travel distances (cost errors). Hillsman and Rhoda (1978) have identified three error components: Source A, B, and C errors, which may result from demand data aggregation. In this article, a method to measure weighted travel distances in p-median problems which eliminates Source A and B errors is proposed. Test problem results indicate that the proposed measurement scheme yields solutions with lower optimality and cost errors than does the traditional distance measurement scheme.     

Multi‐Type,Multi‐Zone Facility Location

The placement of facilities according to spatial and/or geographic requirements is a popular problem within the domain of location science. Objectives that are typically considered in this class of problems include dispersion, median, center, and covering objectives—and are generally defined in terms of distance or service‐related criteria. With few exceptions, the existing models in the literature for these problems only accommodate one type of facility. Furthermore, the literature on these problems does not allow for the possibility of multiple placement zones within which facilities may be placed. Due to the unique placement requirements of different facility types—such as suitable terrain that may be considered for placement and specific placement objectives for each facility type—it is expected that different suitable placement zones for each facility type, or groups of facility types, may differ. In this article, we introduce a novel mathematical treatment for multi‐type, multi‐zone facility location problems. We derive multi‐type, multi‐zone extensions to the classical integer‐linear programming formulations involving dispersion, centering and maximal covering. The complexity of these formulations leads us to follow a heuristic solution approach, for which a novel multi‐type, multi‐zone variation of the non‐dominated sorting genetic algorithm‐II algorithm is proposed and employed to solve practical examples of multi‐type, multi‐zone facility location problems.     

Equity and Efficiency in Public Facility Location

In designing a system of urban public service centers, planners should consider both equity and efficiency effects in selecting the size of each center and the spacing between centers. The paper establishes theoretical and operational concepts for evaluating equity and efficiency, as affected by size and spacing alternatives. No objective means exists for determining the relative importance of equity and efficiency, so the decision, ultimately, is subjective. However, theoretical, empirical and simulation evidence indicate that equity is more sensitive than efficiency to the selection of size and spacing, within a wide range of alternatives. This suggests that the equity criterion is important in the design of public service systems, and deserves more attention in the public facility location literature than it has received in the past.     

An Interactive Approach to the Central Facility Location Problem: Locating Pediatric Hospitals in Warsaw

Most of the conventional approaches to the central facility location problem neglect the interaction of analyst and decision-maker during the locational choice process. This paper presents a new interactive approach to the central facility location problem. It is assumed that the problem is formulated by an analyst as a multiobjective optimization problem. Then the decision-maker searches for a satisfactory solution working directly with the computer system. The interactive procedure was implemented on IBM-PC XT/AT as the decision support system DINAS (Dynamic Interactive Network Analysis System) which enables the solution of various multiobjective location-allocation problems. DINAS has been successfully used for solving a real-world planning problem, namely for finding locations for pediatric hospitals in the Warsaw region.     

Adaptive Cell Tower Location Using Geostatistics. 基于地统计学的适应性基站发射塔选址研究

In this article, we address the problem of allocating an additional cell tower (or a set of towers) to an existing cellular network, maximizing the call completion probability. Our approach is derived from the adaptive spatial sampling problem using kriging, capitalizing on spatial correlation between cell phone signal strength data points and accounting for terrain morphology. Cell phone demand is reflected by population counts in the form of weights. The objective function, which is the weighted call completion probability, is highly nonlinear and complex (nondifferentiable and discontinuous). Sequential and simultaneous discrete optimization techniques are presented, and heuristics such as simulated annealing and Nelder–Mead are suggested to solve our problem. The adaptive spatial sampling problem is defined and related to the additional facility location problem. The approach is illustrated using data on cell phone call completion probability in a rural region of Erie County in western New York, and accounts for terrain variation using a line‐of‐sight approach. Finally, the computational results of sequential and simultaneous approaches are compared. Our model is also applicable to other facility location problems that aim to minimize the uncertainty associated with a customer visiting a new facility that has been added to an existing set of facilities.     

The Location Invariance Theorem in Weberian Space Under Uncertainty

This paper examines the validity of the location invariance theorem in Weberian space under various types of uncertainty. The main results are: Given that the firm's location is constrained to remain at a specified distance from the output market, the optimal location is invariant to any change in product demand if and only if the production function is homothetic for a firm facing demand price uncertainty, or if the production function is homothetic and both inputs are risk-neutral for a firm facing technological uncertainty. Alternatively, given that the distance from the firm's location to the output market is a variable, location invariance occurs for a firm facing demand price uncertainty if the production function is linear homogeneous. In the presence of input price uncertainty the optimal location always varies with a change in product demand. The results can include those previously obtained for linear stochastic location models as special cases and some are new contributions to the literature.     

古城西安住宅消费市场满意度重要性与差异性分析

本文以古城西安为例,在第一手调查资料的基础上,构建了住宅市场消费满意评价模型,采用消费者指标选择累积统计的方法,构建了重要性与满意差异模型,进行了重要性与满意差异分析。研究结果显示:评价项目中,住房价格与中观小区空间因素满意评价较低;满意且重要区域主要集中于宏观区域因素;重要不满意区域,价格因素主导突出。     

Pursuing the Peripheral Path? A Path-Dependent Analysis of the Frankfurt and Munich Fairs

As a result of increasing competition and internationalization, many Western European cities have invested in exhibition facilities. Surprisingly, many new exhibition centres emerge in the urban periphery. An assessment of the 34 largest exhibition centres in Western Europe shows that only 16 are still centrally located while 18 now have a peripheral location. This is a drastic break from the traditional location of these centres in inner city cores. Behind this observation of spatial change is a complex set of dilemmas about investments in current or new locations. A fresh analytical model (based on assumptions of path dependency) is constructed and employed to analyse time and place specific determinants and opportunities. Two contrasting cases are selected in comparable German cities. Frankfurt decided to renew its facilities in the centre of the city, whereas Munich opened a relocated exhibition centre in 1998. Based on these case studies, the paper concludes that there is no autonomous force pulling exhibition centres towards the periphery, but it is rather a misfit between the central location and new physical, functional, spatial, and institutional demands that causes a facility to move.     

Theoretical and Computational Links between the p-Median,Location Set-covering,and the Maximal Covering Location Problem

It has been shown that the p-median problem, the location set-covering and the maximal covering location problems are important facility location models. This paper gives a historical perspective of the development of these models and identifies the theoretical links between them. It is shown that the maximal covering location problem can be structured and solved as a p-median problem in addition to the several approaches already developed. Computational experience for several maximal covering location problems is given.