DEA Window Analysis for Measuring Port Performances Efficiency of Four Islands Countries Located in West Indian Ocean Countries

DEA window analysis has been a great tool used in improving the economic impacts of ports through its efficiency analysis. This has been employed to ports found in West Africa, Europe, Asia ports; nonetheless, this has not been applied to Indian Ocean Island ports. The purpose of this paper is to investigate the port efficiencies of four island port countries found in the West Indian Ocean (port Reunion, the port of Colombo, Port Louis and the port of Toamasina). DEA window analysis is used to determine port efficiency and to observe the possibility of changes in port efficiency over time. Despite the measures were put in place to improve the efficiency of the port, corruption, unskilled labour and others are some inefficiencies that hinder the performance of the port. Implications and future research directions are also included in this study.


Background
The Indian Ocean is fast becoming the new centre of economic gravity, as it ties together the economic fortunes of emerging Asia, the US, and Europe. Maritime rivalries in the Indian Ocean are an early indicator of the return of great-power economics of the country that profits this great opportunity. The place of the In-While the island of Madagascar is also on the edge of the Indian Ocean, it is surrounded by 5,000 km of coast, the southeast coast of Africa. It is estimated that most of its international trade (+90%) is made via the port of Toamasina and also via the main regional and worldwide shipping routes. Moreover, Sri Lanka, whose geographical positioning is very strategic, is located at the southern tip of the only continental mass extending to the Indian Ocean between Arab and Malay peninsulas. Their strategic position naturally gives Sri Lanka an additional competitive advantage to develop as an Asian maritime centre. The development of the port of Colombo as the central port hub of the region in the 19th and 20th centuries was also greatly facilitated by this competitive advantage of strategic positioning.

Research Objectives
Maritime transport is a global economy that accounts for 90% of the total volume of world trade. The Merchant Navy plays an essential role in the realization of commercial transactions between the different continents of the world, whether it is raw materials, food products or manufactured goods.
Maritime transport is one of the cheapest means of transport, all types, both in terms of cost of materials and capacity. It has many features that do not require continuous modifications, except at the beginning and end for the port's roads and docks.
Due to the importance of Shipping and its additional benefits, it is considered to be the backbone of the country's economy and the basis for sustainable development. Thus, without the different means of transport, in particular, maritime transport, investment opportunities and business conditions will be negatively affected by some other countries.
This paper, therefore, aims to examine the performance efficiency of following strategic seaports in West of the Indian Ocean, the port of Reunion, the port of Colombo, the Port Louis Port and the port of Toamasina. These islands in the west of the Indian Ocean are strategic in the sense that they are counted among the key to transport maritime in the Indian Ocean, added to the fact that they compete for the same markets. So after the examination of the performance effi-American Journal of Industrial and Business Management ciency for those four Island port, we need to answer this following key question: 1) Which Port is the most efficient among them four?
2) What is the main reason for inefficiency of the other port?
3) What are the solutions we should suggest about those inefficiency problems?
The remainder of this study is organized in the following way. Section 1 presents the introduction, the research question and the theoretical research basis on the topic of ports performance efficiency and DEA. Section 2 introduces the methodology adopted; then Section 3 presents the data source and discusses the empirical results of the four studied strategic island ports in the west of the Indian Ocean. The paper concludes the study in Section 4.

Literature Review
The term "performance" is generally understood as an industrial word to assess the success of an organization in achieving a certain level of its strategic objectives [1]. Logistic performance can be defined as the degree of achievement of a company's objectives [2]. Port performance criteria are often decisive for the competitiveness of ports, or factors influencing the competitiveness of ports [3].
Regularly measuring port productivity is crucial to finding opportunities for development and optimization [4]. According to [5] [6], their studies revealed that many ports were investing billions of dollars in port infrastructure to improve their existing facilities in order to cope with an increase in the volume of trade followed by an increase in the size of service needs. It also mentions that many ports need to enlarge their ports to meet the demand of companies and that it is challenging to develop a balance between economic, environmental and social problems to ensure growth lasting. The essence of the essential developing ports is considered to be the primary objective of all countries for which they must provide many benefits [7].
Maritime transport and the port industry now appear as indispensable vectors of development in a globalized economy, ports have played an essential economic role in the import and export processes to countries, in particular, heavy goods transport. Thus, all countries attach importance to seaports because they are the main gateway to income.
Several studies have recommended using DEA models to assess the performance and efficiency of the sector. Where to find [8], is analyzed one unit at a time. A unit is considered to work to determine the weight of their inputs and outputs. The same thing should be done for all the other units, determining the weights according to the particular optics of each. Then, if the unit is efficient, you will get the maximum rate when evaluating several other units. Some units may be considered adequate only by their criteria; others, or even have the freedom to choose weights for their inputs and outputs, can be efficient. In terms of productivity [9], study the importance of operational efficiency for hotel profitability, considered a significant target for investors, using Data Envelopment Analysis (DEA) and the return on assets. Efficiency and for the ROA, is in the big hotels. Highly indebted hotels have average efficiency but lower profitability than less-indebted hotels. Also, some studies have shown that the model (DEA) can be used to evaluate the services sector of public and private hospitals [10].
In this paper, the emphasis was placed on the feasibility of using the DEA model by evaluating four major ports belonging to four Indian Ocean island countries and then giving a clear view of the importance of developing inefficient ports, while [11] used DEA models to measure the efficiency of African ports. In addition to [12], evaluate ports by verifying whether or not they respond to requests. In contrast to the port performance indicators developed by UNCTAD [13], the advantage of DEA is that multiple inputs and outputs can be added to the model, and so it can provide an overall assessment of port performance [14]. There is no consensus in the selection of input and output variables [15].

DEA Analysis
The DEA is a non-parametric method of measuring the effectiveness of a decision-making unit (DMU), such as a company or a public sector Agency [16], in- where: h k is relative efficiency of k-th DMU, y rj is amount of output r produced by DMU j, x ij is amount of input i used by DMU j, n is the number of DMUs, m is the number of inputs, s is the number of outputs, u r is the weight given to output r and u i is the weight given to input i.
The first model (I) is solved n times to evaluate the relative efficiency of each DMU. Mathematically, the nonnegative constraints (3) and (4) are not sufficient for the fractional (2) to have a positive value.
For this reason, it is assumed that all the weights for inputs and outputs O. Dewarlo attribute a nonzero value.
Since the efficiency of the k-th DMU is maximized by resolving the expressions (1), (2), (3) and (4), it is evident that h k will take values from 0 to 1. If the value of h k equals 1, the k-th DMU will be effective compared to the other DMU; otherwise, the value of h k indicates the inefficiency of the k-th DMU. The inefficiency of some DMU can be treated as "less effective DMU" If the value of h k is close to 1.
This problem is defined as the fractional linear programming model (I), known as "CCR ratio model", which can be reduced, using transformations, to the linear programming model (II). The DEA model (II) is formulated in the following form: where: h k -relative efficiency of k-th DMU; n-number of DMUs that should be compared; m-number of input values; s-number of output values; μ r -weight of the output value r; v i -weight of the input value i. If the value of h k in the objective function is 1, the k-th DMU is relatively efficient. However, if it is less than 1, the efficiency of DMU k is relatively low, and the value of h k represents the percentage of each DMU decrease its inputs.
DMU k can only be considered completely efficient if the values of other DMUs do not provide evidence that one of them is an input or output without affecting other inputs or outputs. Looking at expressions (5), (6), (7), (8) and (9)

Variable Specification and Data
The paper analyzes the efficiency of four ports for four Indian Ocean island countries: the port of Reunion, the port of Sri Lanka, the port of Mauritius and the port of Madagascar, as we have shown in Table 1.
The assessment of port efficiency using DEA begins with the appropriate choice of input and output variables. The total Quay length, the terminal area in Ha, the total numbers of cranes are chosen as input variables, while the total port cargo throughput per year is the output variable [19]. One DMU corresponds to one port.
In the process of evaluating the efficiency of the port, one of the most important inputs is the quay length. Yen-Chun Jim Wu and Mark Goh [20] suggest that quay length is crucial to the efficiency of Chinese ports. In general, quay length differs from port to port on inland waterways. River ports are smaller than seaports, and the quay length corresponds to the size of the ships that operate on the river. Since the shipping company main aim is to reduce the sum of the ships turnaround time, the optimum assignment of arrived ships to ports quay length becomes important strategy, while ports, competing for the clients (shipping companies) increase their efficiency.
The terminal area is dedicated to ending operations of receiving, storing, storing, retrieving, picking orders, packing and shipping. The field of support activities, such as the Office, is not included. Also, covered storages and open storages are included, while racks, hazardous materials and the free port area, for example, are not included. The total area determines the amount of cargo that could be transferred and stored in the port area in case of direct non-boarding or transfer of cargo outside the port area on rail/road vehicles.
The number of cranes directly influences the increase in port capacity and is therefore included in the input variables. More cranes bring greater efficiency and flexibility, allowing the port to work with more vessels simultaneously. Because port facilities are very costly, it is desirable to optimize their performance, to make better management decisions. In particular, heuristics for port operations and functional and process modelling are used to program crane loading/unloading operations to minimize the maximum time required to servicing a given set of vessels [21]. As a result, the total time that ships spend in the port is lower; the terminals are more available to other ships and the service offered to port customers improves.
The port throughput can measure the total amount of cargo that is transferred to the operational coastal zone during the year in total tons of cargo. Table 2 lists the characteristics of the variables used to estimate the relative competitiveness of the selected port. Table 3 lists the statistics used in the Excel DEA solver, including maximum, minimum, average, and standard deviation.

Efficiency Analysis of Each Port
Efficiency analysis of the proposed ports is performed using DEA window analy-     We can see that Port Louis has the highest flow, and there is not so much variation; it was almost stable for all the years under study. The port of Toamasina as we have seen have so much variation in the total cargo throughput during this 11 year time study period. The Colombo Port and the port Reunion have almost the same variation, and they have an excellent performance because their total cargo throughput continues to increase during this time period of 2008-2018.
In order to monitor changes in port efficiency during the selected period or and they include the terminal area, total quay length, the total number of cranes.
A single output variable, total cargo throughput, is also selected. We had chosen window six from the DEA solver result for this study, so we have a six windows table for the first six successive years. The length of the window is defined as six.
Six rows per port represent six Windows. Each port is represented as a different DMU for each year. Based on the results of the model, the first of the rank was Port Louis, in terms of total quay length, the smallest one comparing to the other three ports, even though they made the extension from 2017, it remains the smallest, but they have a high throughput, which led to the conclusion that Port Louis is the most efficient port of this study with an average efficiency score of 94%.
Port Reunion and Port of Toamasina are almost similar just 3% difference of efficiency average, as we have seen in Figure 3, even though the Reunion is an   Island with the small territory of land they are more efficient compared to Madagascar, even Madagascar is a big island with a large territory. There is some extension for Port of Toamasina, the project has already started since 2015, and it will be done for 2023, the government has already started the plan and the investment for the construction. In the project, the Terminal area will be increased, the Total quay length also and the number of cranes, so maybe the total cargo throughput will increase also. Moreover, maybe the Port of Toamasina will be more efficient compared to neighbour island port in the Indian Ocean.
As we have seen, Colombo Port has low percentages of 75% efficiency average score. It is the last position of rank among the four ports. Colombo port has the most extensive surfaces in term of the terminal area, and total quay Length compares to the other three ports, but the throughput of the port is low, it can be concluded that it is the most inefficient one in Six windows of the four ports in this study.
However, if we classify these four ports according to the throughputs, in Figure 1, we see that the Port Louis is still in the first position, in the second position is the port of Toamasina, in the third position in the port of Colombo and the port of Reunion obtained the last position. Thus, we can conclude that Port Louis is the most efficient of these four ports in this study. Thus, we can learn that the high total amount of Throughputs of a port does not necessarily mean that this port is more efficient.
Those following reasons cause most sources of inefficiency, first the lack of employees trained for work in the port because almost the people who work in the port has not been learned specialization for the maritime field that is one of the problems which made the port not efficient. Second, the high level of corruption in the port, this problem affects almost those port belongs to underdeveloped countries, it is a big problem because we can find it in every sector in the port and it creates a disorder for the management in the port, and it causes the inefficiency of the port. Third, the lack of modern information and communica- is a huge lack of information, that is one of the big inefficiency reasons because the risk of mistake is high and the information is not updated on time like the case of the port of Toamasina (Madagascar). Then, the high ports cost also is one of the reasons which make the port inefficient, because high port cost but low services quality, it makes the shipping company not interested in coming to those ports. Moreover, also the container port congestion creates a huge problem because it makes the transhipment slower and creates a delay time for the travel time of the vessel was passing by this port. Another reason that created the inefficiency of a port for underdeveloped countries west of the Indian Ocean is the high risk of political instability as the case of Madagascar in 2009, the whole system in the port was changed and create so much disorder and even the transport the company was going to leave the countries because their investments are not safe. Add to this the lack of maritime authority and the low connection of the ports to the hinterland. All these reasons make the port of the island in the west Indian Ocean inefficient.
The results obtained have valuable implications for port authorities and the government for each of the island countries in this study. Improving the efficiency of ports should be the primary objective of port authorities. It will help increase the port's performance and become the most efficient port in the western Indian Ocean. Most of the solutions to these inefficiency problems depend on the local government, and in particular the port authorities of these island countries. The government should put in place a serious investigation into the management of port authorities, which should hire the right people in the right place. Therefore, serious measures should be taken to reduce the corruption within the port, and political authorities should work harder and faster to make safe a peace life in these beautiful islands. The islands located in the Western In-

Conclusion
This study was conducted to estimate the efficiency of four ports belonging to propriately to a given output in Table 3. However, the average efficiency in all ports is less than 100%. This means that all ports have more inefficiencies (port of Toamsina, port Colombo) or less (Port Louis, port reunion). There are two primary sources of inefficiencies. Firstly, it is suggesting for low-efficiency ports to attract more customers from the shipping company, to show them the advantages of the port compared to nearby ports, or to increase the amount of cargo that can be transferred by optimizing the effectiveness of the working system.
Secondly, ports should lease their equipment to other companies in order to level the output (throughput) obtained with the use of inputs (total terminal area, total quay length and number of cranes). For all ports, it is essential to look at the strategic plan to improve port operations, better use of port capabilities and research tools to improve the service of these ports. Progress is being made in measuring the efficiency of ports in relation to port production activities. The lack of data availability affects the number of research analysis for the ports, as well as the number of inputs and outputs, and may obscure the real reasons for port efficiency. Thus, the research carried out here could be the beginning of a more sophisticated analysis of the port belonging to some islands of the Western Indian Ocean.

Conflicts of Interest
The author declares no conflicts of interest regarding the publication of this paper.