Developing and Applying a Disaggregated Retail Location Model with Extended Retail Demand Estimations

The spatial interaction model (SIM) is an important tool for retail location analysis and store revenue estimation, particularly within the grocery sector. However, there are few examples of SIM development within the literature that capture the complexities of consumer behavior or discuss model developments and extensions necessary to produce models which can predict store revenues to a high degree of accuracy. This article reports a new disaggregated model with more sophisticated demand terms which reflect different types of retail consumer (by income or social class), with different shopping behaviors in terms of brand choice. We also incorporate seasonal fluctuations in demand driven by tourism, a major source of non‐residential demand, allowing us to calibrate revenue predictions against seasonal sales fluctuations experienced at individual stores. We demonstrate that such disaggregated models need empirical data for calibration purposes, without which model extensions are likely to remain theoretical only. Using data provided by a major grocery retailer, we demonstrate that statistically, spatially, and in terms of revenue estimation, models can be shown to produce extremely good forecasts and predictions concerning store patronage and store revenues, including much more realistic behavior regarding store selection. We also show that it is possible to add a tourist demand layer, which can make considerable forecasting improvements relative to models built only with residential demand.     

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.     

Accounting for Temporal Demand Variations in Retail Location Models

This article develops and calibrates a spatial interaction model (SIM) incorporating additional temporal characteristics of consumer demand for the U.K. grocery market. SIMs have been routinely used by the retail sector for location modeling and revenue prediction and have a good record of success, especially in the supermarket/hypermarket sector. However, greater planning controls and a more competitive trading environment in recent years has forced retailers to look to new markets. This has meant a greater focus on the convenience market which creates new challenges for retail location models. In this article, we present a custom built SIM for the grocery market in West Yorkshire incorporating trading and consumer data provided by a major U.K. retailer. We show that this model works well for supermarkets and hypermarkets but poorly for convenience stores. We then build a series of new demand layers taking into account the spatial distributions of demand at the time of day that consumers are likely to use grocery stores. These new demand layers include workplace populations, university student populations and secondary school children. When these demand layers are added to the models, we see a very promising increase in the accuracy of the revenue forecasts.     

Extensions to the Hub Location Problem: Formulations and Numerical Examples

Although a tremendous amount of analytical research is being conducted on the hub location problem, few models exist that extend the number of characteristics found in actual hub-and-spoke networks. Four extensions are presented in this paper: (1) a capacitated network model; (2) a minimum threshold model; (3) a model that endogenously determines the number of open hubs for the network; and (4) a model that incorporates a flow-dependent cost function for the spokes as well as the interhub links. Both the capacitated and the minimum threshold models drop the assumption of a completely interconnected network commonly found in hub location models. Numerical results show that total network costs are often minimized by closing a few interhub links. The third extension is the first known hub location model to determine the optimal number of hubs based on the needs of the network. In this model, the number of open hubs depends on the distribution of flows in the network and how cost effectively the flows can be moved across the network. Previous models that endogenously determined the number of open hubs utilized a fixed cost for establishing each hub in order to limit the number of hubs in the network. The final extension recognizes the potential of all links to amalgamate flows and includes a separate flow-dependent cost function for the spokes in addition to the one for the interhub links. Numerical results are shown for all four models.     

The Probabilistic Minisum Flow Interception Problem: Minimizing the Expected Travel Distance until Intercept under Probabilistic Interception

We develop a variant of the flow interception problem (FIP) in which it is more desirable for travelers to be intercepted as early as possible in their trips. In addition, we consider flows being intercepted probabilistically instead of the deterministic view of coverage assumed in the FIP literature. We call the proposed model the probabilistic minisum FIP (PMFIP); it involves minimizing the sum of the expected distance that each flow travels until intercepted at a facility among placed facilities. This extension allows us to evaluate the effect of facility location under any given value of the interception probability and to apply the model to a variety of situations. We apply the proposed model to an example network by assuming a hypothetical situation in which people gather at a stadium from various nodes on the network, and receive some goods or services on the way to the stadium. We analyze optimal solutions obtained by varying the number of facilities and interception probability. It is shown that the expected travel distance until intercept is greatly reduced by means of a few optimally located facilities under a moderate interception probability.     

我国旅游资源、区位和入境旅游收入的空间错位分析

旅游资源和区位是影响区域入境旅游发展的两大基本要素。本文以我国大陆31个省区为区域研究单元,借用重力模型和二维组合矩阵方法,分析了旅游资源、区位和入境旅游收入三者之间的空间错位现象。结果发现：（1）区位指数和入境旅游收入指数重心偏向我国东部地区,旅游资源丰度指数重心偏向中西部地区;（2）资源与收入、区位与收入、资源与区位三组二维组合关系均存在明显的空间错位,可以将这种二维组合关系划分为五种类型来描述各省区的旅游发展现状。     

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.     

The Expected Maximum Distance Objective in Facility Location

Abstract In this paper we introduce a new objective function for the minimax location problem. Every demand point generates demand for service with a given probability (during a given period of time) and the objective is to minimize the expected maximum distance. The planar problem is proven to be convex and thus standard solution techniques such as using the Solver in Excel can be applied for its solution. Properties for the problem on the network are proven and an efficient algorithm proposed for its solution.     

A Decision-Making and Search Model For Intraurban Migration

Most of the research on the intraurban migration attempting to develop models of the mobility process has presented intuitively appealing statements about the residential decision process, but stopped short of a formal development of these concepts. If it is to be possible to predict the mobility pattern within the city, both the search and selection process must be more clearly specified. In this paper, a preliminary theoretical model containing decision rules similar to those found in optimal search models is developed. The model explicitly incorporates the spatial and temporal aspects of residential choice and has the potential to predict the probability that a prospective migrant will search for a new residence in a given area of the city, the time when the search process will come to a conclusion and, by implication, the expected location of the new residence. The preliminary results from the model suggest a major elaboration of the spatial and temporal aspects of residential choice under conditions of uncertainty in terms of a set of empirically measurable determinants, relating to a household's preferences, beliefs, and degree of risk aversion.     

Designing Reliable Center Systems: A Vector Assignment Center Location Problem

The p‐center problem is one of the most important models in location theory. Its objective is to place a fixed number of facilities so that the maximum service distance for all customers is as small as possible. This article develops a reliable p‐center problem that can account for system vulnerability and facility failure. A basic assumption is that located centers can fail with a given probability and a customer will fall back to the closest nonfailing center for service. The proposed model seeks to minimize the expected value of the maximum service distance for a service system. In addition, the proposed model is general and can be used to solve other fault‐tolerant center location problems such as the (p, q)‐center problem using appropriate assignment vectors. I present an integer programming formulation of the model and computational experiments, and then conclude with a summary of findings and point out possible future work.     

SPATIAL EQUILIBRIUM WITH FOOTLOOSE FIRMS*

ABSTRACT. We determine the location equilibria in a duopoly model under a novel solution concept. Typically, spatial equilibrium is described as either a simultaneous price and location game, or else as a two-stage location-then-price game. We introduce a new alternative, a two-stage price-then-location game. It is well known that no (pure strategy) equilibrium usually exists under the two standard solution concepts when products are homogeneous. We show this is also true for the new concept. We then provide numerical results for a specific functional form (the logit model) which introduces product heterogeneity into the standard framework, restoring equilibrium when the degree of substitutability between products is not too small.     

COMPENSATION FOR COMMUTES IN THE LAND AND LABOR MARKETS: SOME EVIDENCE FROM THE TOKYO METROPOLITAN AREA*

ABSTRACT. Recent research suggests that in nonmonocentric cities compensation for commutes takes the form of both lower housing prices and higher wages. This paper develops a random utility model that predicts the probability of an actor choosing to commute between each residence and job in a metropolitan area conditional on the observed location of housing units and job sites. The model allows commuting time, origin-specific amenities, land prices, destination-specific amenities and wages to influence actors' choices. We estimate the model using maximum likelihood and generalized least squares techniques and data on commuting between each of 38 origin and 15 destination jurisdictions in the Tokyo metropolitan area. The empirical results show that, all else equal, a one percent increase in commuting time reduces the probability that a route (origin-destination combination) will be chosen by almost five percent. Origin-specific amenities are not completely capitalized into land prices and destination-specific amenities are not completely capitalized into wages. Desirable residential amenities include school quality and a low ratio of day to night population. Desirable workplace amenities include a large share of white collar jobs and a high density of employment.     

A Micro-Econometric Store Choice Model Incorporating Multi- and Omni-Channel Shopping: The Case of Furniture Retailing in Germany

Online retailing and multi-/omni-channel shopping are gaining in importance. However, there is a significant lack of research focused on incorporating online shopping into models of spatial shopping behavior. The present study aims (1) to construct a store choice model which includes both physical and online stores as well as the opportunity for omni-channel shopping, and (2) to identify the main drivers of spatial shopping behavior given the availability of both channels. Based on a representative survey, this study employs a revealed-preference approach toward store choice and expenditures in furniture retailing. The statistical analysis is performed using a hurdle model approach, with the expenditures of individual consumers at (online or physical) furniture stores serving as the dependent variable. Results show that channel choice (online vs. offline) is mainly influenced by psychographic characteristics, place of residence, and age of the consumers. Store choice and expenditures are primarily explained by store features such as assortment size, omni-channel integration, and accessibility. This study demonstrates that e-shopping can be integrated into a store choice model and that both the modeling approach and the subsequent findings are of significance for retail companies and spatial planning.     

A SPATIAL COMPETITION APPROACH TO CENTRAL PLACE THEORY: SOME BASIC PRINCIPLES*

ABSTRACT. This paper investigates the potential offered by the model of spatial competition for the study of central place theory. We consider n firms selling m substitutable or complementary goods to a continuum of consumers evenly distributed along a linear segment. Consumers have the same income and the same utility function which is quadratic in the goods supplied by the firms and linear in the numeraire. The main results are as follows. (1) In any location equilibrium in which all goods are consumed everywhere, each good supplied by a single firm is sold at the market center. In Christaller's terminology, this means that when the exhaustive principle holds in equilibrium, highest-order goods are made available at the center. (2) When all goods (excluding the numéraire) are complements to each other and each good is sold by a single firm, there always exists an equilibrium in which all the firms locate coincidentally. (3) If the stores selling a given good are under the control of a single owner then, in any equilibrium for which the exhaustive principle holds, the stores are located in a way such that the total transport cost (borne by consumers) is minimized.     

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.     

A Network Approach to Commuting

In this paper we present a model for commuting in a network of towns. A basic assumption is that all individuals have a given residential location and that every node in the network has a fixed number of jobs. We then propose a general model for the commuting of labor between the nodes in the network.     

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.     

明清时期山西的城市洪灾及其防治

明清时期山西的城市洪灾普遍而严重,曾遭受洪水冲击的城市达到62座。地方社会的防治措施大致可以归纳为“拦”、“疏”、“蓄”三类。具体而言,“拦”,即在城郊修筑拦洪堤堰以障水,这是明清山西城市防洪的主要措施,其中某些城市堤堰的筑造技术值得关注;“疏”,即通过开凿水口、疏浚城壕及新凿河渠等手段,使洪水远离城区;“蓄”,就是在城内利用既有低洼之地或新凿陂池,以蓄积雨洪。以上举措并未能彻底改变山西城市洪灾普遍且严重的状况,探究起来,城市的地理坐落、生态环境破坏导致的水土流失、城市建成区的扩展等,是不容忽视的三大诱发因素。     

基于经济学基础的酒店收益管理研究

收益管理是近年来在服务行业应用广泛的一种新型管理模式,收益管理给国外许多酒店带来明显的效益增长,因而成为酒店经营研究中被学者持续关注的热点问题。在我国酒店业,收益管理还是一个较新的概念,收益管理研究的发展尚处于起步阶段,酒店企业全面应用收益管理的实践甚少,本文将结合国内外收益管理的研究现状,分析收益管理的经济学基础,为我国酒店业实施收益管理提供一种新思路和借鉴。     

Use of the Mathematical Method in the Solution of a Location Problem

Cost minimization criteria are applied to a study of the optimal location of plants for the manufacture of service-industry machines, including street-cleaning equipment, laundry, and dry-cleaning machines. Future national and regional demand for such machines is estimated. The matrix technique is used to identify the economic region for which the aggregate cost of production and transportation of service-industry machines would be minimized. That region is found to be the Volga-Vyatka region, where the estimated cost of producing 315 million rubles worth of service-industry machines is put at 19.5 million rubles. The author does not necessarily exclude the location of manufacturing plants in other regions, if the purpose is to provide employment, as in areas of depleted mineral deposits of the Urals and the Donets Basin or in the agricultural districts of the Southwest and Central Asia.