Competitive Facility Location And Its Design Problems

The problem of facility location is a common problem in daily life.Its core content is how to determine the location of one or more new facilities in the existing city pattern,facilities,market domain and demand,and it can also be understood as the location selection of a hub city in the region.The contents of the facilities are very wide,not only the equipment and equipment that people understand daily,but also the public service facilities,warehousing and commercial facilities,hospitals,schools and other service facilities,and may include abstract facilities such as bus lines,and even the new cities themselves.The advantages and disadvantages of facilities location will affect their service capacity,production efficiency and residents' life;the advantages and disadvantages of stores and warehouses will directly affect their profits;therefore,the role and significance of the facility location theory can't be ignored.The purpose of this paper was to study the location and its design of competitive facilities considering competitors' reactions.That was,how to locate a new facility and determine the quality of service in the case of competitors who already had similar facilities that have similar goods in the market? Before solving this problem,we first assumed that the market share of each facility depends on its distance from its customers and its quality,and it was described as a Huff probability model.In order to maximize the profits of new facilities,we putted forward a method considering the two stages of competition reaction,namely quality decision phase and location decision stage.In the quality decision-making stage,we would take the competition decision-making process between facilities,simulate it as a game,and solve the quality decision-making process through its Nash equilibrium.The solution of the quality decision process could be expressed as a function of the location of the new facility.In the case of only one facility in the market,the function was obtained by an analytic solution of a set of equations;or in the case that there were not only one(many)facilities on the market,it was obtained by polynomial approximation.During the position decision stage,we used the interval algorithm based on global optimization to determine the optimal location of the new facility.Then,we used randomly generated numerical experiments to verify the effectiveness of the method.The calculation results showed that this method can give each test case the location and quality of the new facilities and the quality of all other facilities,and find an approximate optimal solution.At the same time,the calculation time of the method was reasonable.Then,this paper used Visual Studio.Net 2010 as the development platform,uses C# language and ArcGIS Engine 10.1 component library,and combines Matlab software programming to develop a competitive facility location system.It also introduced the competitive facility location system from three aspects,including demand analysis,system design and system implementation.Finally,the competitive facility location system developed in this paper was applied to a specific case: location problem of a new shopping mall in Putuo District,Shanghai.