Two New Location Covering Problems: The Partial P-Center Problem and the Partial Set Covering Problem

Two new covering problems are introduced. The partial covering P-center problem minimizes a coverage distance in such a way that a given fraction of the population is covered. The partial set covering problem seeks the minimum number of facilities needed to cover an exogenously specified fraction of the population within a given coverage distance. The problems are formulated as integer linear programming problems. Bisection search algorithms are outlined for the two problems. The search algorithm repeatedly solves a Lagrangian relaxation of the maximal covering problem. Computational results for the Lagrangian relaxation of the maximal covering problem and for the bisection search algorithms are presented on problems with up to 150 nodes.     

Two New Location Covering Problems: The Partial P-Center Problem and the Partial Set Covering Problem

Two new covering problems are introduced. The partial covering P-center problem minimizes a coverage distance in such a way that a given fraction of the population is covered. The partial set covering problem seeks the minimum number of facilities needed to cover an exogenously specified fraction of the population within a given coverage distance. The problems are formulated as integer linear programming problems. Bisection search algorithms are outlined for the two problems. The search algorithm repeatedly solves a Lagrangian relaxation of the maximal covering problem. Computational results for the Lagrangian relaxation of the maximal covering problem and for the bisection search algorithms are presented on problems with up to 150 nodes.     

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.     

Analysis of Errors Due to Demand Data Aggregation in the Set Covering and Maximal Covering Location Problems

In this paper, we extend the concepts of demand data aggregation error to location problems involving coverage. These errors, which arise from losses in locational information, may lead to suboptimal location patterns. They are potentially more significant in covering problems than in p-median problems because the distance metric is binary in covering problems. We examine the Hillsman and Rhoda (1978) Source A, B, and C errors, identify their coverage counterparts, and relate them to the cost and optimality errors that may result. Three rules are then presented which, when applied during data aggregation, will reduce these errors. The third rule will, in fact, eliminate all loss of locational information, but may also limit the amount of aggregation possible. Results of computational tests on a large-scale problem are presented to demonstrate the performance of rule 3.     

论中亚的民族主义问题

本民族主义在中亚各国的表现进行了综合分析,特别对各国主体民族意识方面的表现进行了阐述。作认为,尽管中亚国家的民族自我中心主义对提升主体民族的凝聚力有帮助作用,然而却导致了非主体民族与主体民族的矛盾,甚至产生了危害国家安全的异己力量。中亚国家的民族主义思潮严重影响到中亚地区的社会稳定,对我国西北边疆地区的社会稳定也带来消极的影响。中亚国家已经认识到民族主义的危害,并采取了相应的对策,抵制民族主义的泛滥,携手共同打击民族分裂主义势力、宗教极端主义势力和国际恐怖主义势力等三股恶势力。     

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.     

Multiple Facilities Location in the Plane Using the Gravity Model

Two problems are considered in this article. Both problems seek the location of p facilities. The first problem is the p median where the total distance traveled by customers is minimized. The second problem focuses on equalizing demand across facilities by minimizing the variance of total demand attracted to each facility. These models are unique in that the gravity rule is used for the allocation of demand among facilities rather than assuming that each customer selects the closest facility. In addition, we also consider a multiobjective approach, which combines the two objectives. We propose heuristic solution procedures for the problem in the plane. Extensive computational results are presented.     

Applications of the Location Set-covering Problem

The location set-covering problem is extended to apply to three new situations. (1) The demands are assumed to occur continuously alone arcs of a network. (2) A mobile unit departs from one of the locations to be chosen and picks up the demand, providing service at a still more distant point. (3) New demands and sites occur over time.     

The Maximal Covering Problem with Some Negative Weights

This article presents the maximal covering problem on a network when some of the weights can be negative. Integer programming formulations are proposed and tested with ILOG CPLEX. Heuristic algorithms, an ascent algorithm, and simulated annealing are proposed and tested. The simulated annealing approach provides the best results for a data set comprising 40 problems.     

The Optimal Nodal Location of Public Facilities With Price-Sensitive Demand

The purpose of this paper is to present some models for the location of public facilities in nodal networks that explicitly maximize social welfare by accounting for price-elastic demand functions. The models presented here are general; yet they are mathematically equivalent to the plant location problem and are therefore amenable to solution procedures developed for the plant location problem. The models presented here distinguish between two institutional environments that reflect the degree of power of the consumer to choose which facility to patronize. If consumers can be assigned arbitrarily to facilities and can be denied service, then the environment is one of public fiat. If consumers must be served at the facility of their choice, then a “serve-allcomers” environment exists. Separate models for each environment are specified, and the relationship between optimal assignments and pricing policies is developed.     

A Covering Tour Model for Planning Mobile Health Care Facilities in SuhumDistrict, Ghama

The provision of adequate primary health care in developing countries is often troublesome. The problem is to provide a sufficient number of facilities to be geographically accessible, yet few enough to be properly stocked and staffed. In many less developed countries accessibility problems are exacerbated by extensive rainy seasons in which travel is only possible on paved roads. Using the covering tour model we investigate the use of mobile facilities to resolve this dilemma in Suhum District, Ghana. The model minimizes a mobile facility's travel while serving all population centers within range of a feasible stop. Computational results show that in the rainy season the model cannot provide full coverage; over six percent of the population is beyond a covering distance of eight kilometers. In the dry season, 99 percent of the population can be served by a tour at a covering distance of seven kilometers.Beyond a distance of four kilometers, the dry season problem becomes a trade-off between the distance traveled by healthcare patrons and mobile facilities. These results illustrate the importance of flexibility of mobile systems: if accessibility cannot be provided in all seasons it may still be provided at favorable times of the year.     

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.     

唐代平卢军南下后的种族与文化问题

平卢军是一支胡化程度相当深的队伍,安史之乱爆发后,在忠于朝廷的势力中又分化为“胡化汉人军事集团”和“营州高句丽武人集团”两大派别。在两大派别陆续南下的过程中,他们都把胡族文化的影响输入到了中原地区,并使一部分地区(淮西)出现了比较严重的胡化倾向。军队或地域的胡化现象是淮西和淄青两镇得以长期割据、对抗中央的重要基础之一。由于各自不同的社会情势,淮西的胡化现象有逐渐加深、趋于河朔化的趋势;而淄青地区的平卢军人则胡化程度逐渐减轻,并最终被完全汉化。淮西和淄青两地不同的胡化趋势不仅深刻地影响了中唐时期的局势,甚至还影响到了晚唐时期的政局。     

左南城故址小议

民和回族土族自治县满坪镇东一里许的集场村有座城隍庙,又名瑞昙寺,依台地而建,气势雄伟。据传,此地为西晋左南县县衙所在地,隍庙古建筑曾毁于清同治年间。隍庙东侧的一处地方现在仍叫做“衙门前”。     

竝方国族氏考

本文运用殷周甲骨卜辞与殷周金文方国族氏徽文字互证的方法,对殷周时期的“竝”方国进行了综合研究,考证出“竝”方国的地望在今河南固始附近。