Optimal Location of Administrative Center: A Case Study of Province No. 1, Nepal

In developing nations, administrative facilities do not centers the majority of residing population because of poor geographical accessibility. Selection of optimal administrative center in such locations is a tedious task as the decision is contingent upon various factors. While making such decisions, major focus should be on accessibility of residing people. Thus, this study examines the role of two major factors, population distribution and transportation network distribution, in the selection of administrative centers of any location considering the case study of Province no. 1, Nepal. Keywords— Administrative center, Location, Developing countries, Gravity model.

and public, is restricted by the structure of the designed transportation network and will be genuine only if it serves the people in a right way. Even when facilities are located in an optimum location, residing population will not get adequate services if the networks are not designed appropriately. Therefore, to obtain the solution for above mentioned problem, it is requisite to scrutinize models where transportation networks are designed considering both present and future location of facility. In this study, transportation network configuration and new administrativ e center are to be optimally designed at the same time so as to allow the residents to access the facilities and thus cater their needs. As per a 17 January 2018 cabinet meeting held in Nepal, the city of Biratnagar has been declared the interim administrative center of Province No. 1. However, the decision is made without any proper investigation of the factors. After Kathmandu, Biratnagar is the second most densely populated city. However, it does not necessarily mean that accessibility is not complicated for all th e population of Province no. 1 as transportation network distribution has not been taken into account for making this arbitrary choice. It has always been difficult to plan for the public facilities and location in the most efficient way as many factors are involved. According to the 2011 census, there are around 4.5 million people residing in the 14 districts of Province no. 1. The selection of public facility location should be favourable for the whole population. Everyone has the right to use public services and facility provided by the government in the most convenient way. If a certain portion of population is only considered while determining Public Facility Location, it might create conflict among other people. Therefore, there should be equalization of public service facility to prevent such negative aspects. The study takes place comparing the accessibility among the 19 cities where 14 of them are district headquarters and 5 of them are commercial centers. The required data that are

II. REVIEW OF LITERATURE
Several studies have been done to fix the factors that make the location most appropriate for public facilities. Many problems are to be encountered while selecting the optimal Public Facility Location and various researches have been done to understand these problems. In the developing nations like Nepal, local political leader or government officer makes the choice of public facility location due to which it is less likely for the selected location to be optimum (Rahman and Smith, 2000). Thus, the choice shall be done by eligible person along with proper research. Studies have shown that the use of mathematical model for locational analysis has been very effective to choose the most optimal location (Rahman and Smith, 2000). For any public facilities, the choice of the location will have to satisfy two major purposes : to be close as far as possible to the demand of the population (so that the transportation cost will be low) and to keep the cost of constructing the facility to a minimum extent (which can be done by decreasing the number of facilities and by settling on a lowcost location) (Leonardi, 1981). There are mainly two problems that arises with the two aims mentioned above: problem of allocation concerned with the aim of minimi zin g transport cost and the problem of facility location concerned with the aim of selecting low-cost location (Leonardi, 1981). While picking out the administrative center, the major focus should be on minimizing the allocation-problem that is, lessening transportation costs. Aggregate approach, useful to handle allocation-problem when the list of users is so huge that it is not possible to keep data of every user and to get preference orders is despairing, gives rise to gravityinteraction models (Leonardi, 1981). Gravity models were developed empirically at the beginning however, many theoretical justifications have been proposed for them, which have made it an important topic of consideration for theoretical economists and geographers, mathematicians, and statisticians, besides regional scientists (Leonardi, 1981). Gravity model can consider both factors (road network and demographic), so helps to measure the relative distance clearly and not only the absolute distance while determinin g administrative center (Haynes and Fotheringham, 1984).
Before fixing administrative center for a province, areas that are eligible to become administrative center are to be investigated in a proper manner. Mostly, these areas to be researched are city centers and sub-centers. Several studies have been done in order to know the most efficient center in an area. Many research works have been carried out to explain theoretically, the most appropriate center using finite source of data since the 1950s but it has been few years that number of approaches have been introduced to define the city centers using variety of data sources . The group of four people have done a research work on identifying city centers using human travel flows generated from location-based social networking data using different methods (Sun et al., 2016). The city centers are the crucial part of any cities and Socioeconomic activities are concentrated in these centers (Anas, Arnott and Small, 1998). Since, most of the activities are clustered in these part of the city, they being administrative center, is the most sensible thing. It is obvious that the administrative center will have abundant number of public facilities however, it does not necessarily mean that all of the public facilities are to be established at administrative center only. The place where the decision is made to locate the public facilities will have its land value increased as the demand will be higher (Fujita, 1986). Therefore, the choice may create conflict among people as everyone will want to have their land value increased. Proper research should be done before fixing the public facilit y location as people at different locality may have different demand. The public facilities should be constructed evenly on different sectors according to the demand of the people and only then it will help to minimize the negative aspects such as imbalance between rich and poor people, huge inconsistency between urban and rural areas and so on (Fei, Wei and Ming, 2013).

III. METHODOLOGY
The study starts with the problem formulation with respect to the relevant literatures followed by collection of data.

A. DATA COLLECTION AND EXTRACTION
This study is undertaken considering Province no. 1 of Nepal as the study location. All the district headquarters and some vital commercial centers within the province have been considered as nodes. The network and node distribution with the study area is shown in Figure 1. Two categories of data viz. demographic and road network data were needed for the study. These data were collected from the secondary sources. The demographic data for each district within the study zone was collected from national population census data 2011 and is presented in Table 2.

B. MODEL FRAMEWORK
The study location consists of a number of nodes connected by a transportation (road) network. Considering the entire nodes, distance matrix can be formed in the transportation network. Commonly, shortest path algorithms such as Dijkstra (Gallo and Pallottino, 1986) can be used to calculate distance between any two destinations in the network. Moreover, a short path matrix of the network can be found utilizing Floyd-Warshall algorithm (Floyd, 1962) which gives the shortest distance to other destinations. The shortest path matrix of the network is presented in Table 3.

Case I: Considering Road Networks Only
First, only the road networks within the study zone was analysed. For each node, the sum of distance to all the nodes considered was calculated using equation [1]. The problem can be formulated as the minimization of Interaction (Di) of the set of nodes i. Min Di = ∑dij [1] Where, dij is the distance between the considered i th node and j other nodes. One node with least Di can be considered as the efficien t administrative center location based on transportation network only. Here, Node N10 (Itahari) has least Di, thus N10 (Itahari) is the administrative center if only the road networks are considered.

Case II: Considering Population and Road Networks
Demographic data consideration has been done to analyse the effect of population and population distribution in the determination of most appropriate administrative center. This consideration helps in identifying the location that will be nearer to higher proportion of the population. It is assumed that the total population of the district is concentrated on the district headquarter and they have to travel from the same. In the case, where there are commercial centers, the total population of the district is divided into district headquarter and commercial centers in an equal ratio. Demographic and geographic centers should be combined in order to take the study into shape. The gravity model has been used to incorporate the demographic and geographic centers here. The fusion between these two centers for any location helps to obtain the appropriate administrative center considering residing population and road networks.

Gravity Model
Newton's gravitational law is used to calculate the relationship between the objects. This newton law has been modified to predict the movement of people and informatio n between the cities by the social scientists which is termed as gravity model. The effect of road network and demographic condition for the selection of appropriate administrativ e center can be modelled using gravity model. For each city, let the population be represented by P, and the distance between cities be represented by d. Each pair of cities is designated by the subscripts i and j. Interaction between any pair of cities is specified as Tij. To generalize, this interaction can be expressed as a ratio of the multiplied populations over the distance between any pair of cities, Tij=PiPj/dij [2] The above equation [2] is a basic equation of gravity model which requires certain modifications depending upon different cases. The distance element dij of the basic equation is multiplied by an exponent β. To derive the correct exponent(β) for gravity model formulation many literatures have stimulated by physical science interpretations, including the Newtonian analogy where the square of distance, dij 2 , is the appropriate power (Haynes and Fotheringham, 1984). So, the equation can be written as: Tij=PiPj/dij 2 [3] This equation [3] has been used to integrate the network analysis and demographic analysis in this study to obtain the interaction of each nodes considering demographic and geographic center. In this case, the problem is formulated as the maximizat io n of Interaction (Ii) of each nodes from the set of nodes is as shown in equation [4].
Max Ii = ∑Tij [4] International  One node with maximu m Ii can be considered the most efficient administrative center location based on population and transportation networks of the study area. Here, Node N8 (Biratchowk) has maximu m Ii, thus N8 (Biratchowk) is the efficient administrative center when both the factors are considered (demographic and road network).

IV. RESULTS AND DISCUSS IONS
Planners often mislead in locating public facility centers in developing countries. This study explores how the administrative center location becomes inefficient when considering transportation network only. Two different results are obtained when only transportation network is taken into account and when both transportation network and population distributions within the study zone are considered, which justifies the inefficiency. The case study of Province No. 1, Nepal shows that Biratchowk is the most efficient administrative center of the study area considering both residing population and existing road networks distribution. If the network distribution is only considered in the study, the location of administrative center comes out to be Itahari. This may mislead in solving the problem of locating administrative center. Hence, while considering these type of problems the effects of both demographic and geographic distribution should be taken into consideration.