Sub-Contractor Selection in Shipyard Companies Using Fuzzy-AHP Method

Shipyard industries is one of the very complex construction jobs because there is much work to be done in parallel. Activities in the shipyard industry mostly involve sub-contractors. Although many advantages are obtained, involving sub-contractors in the company also has an impact on the company’s performance. The selection of the right sub-contractor is a crucial activity and will determine the company’s performance. This research uses the Fuzzy Analytical Hierarchy Process method (Fuzzy AHP) to solve the problem of selecting sub-contractors in the Shipbuilding Company. Alternative sub-contractors were evaluated and pairwise comparisons were made between these alternatives using Fuzzy AHP with a Triangular Fuzzy Number (TFN) approach. The TFN scale can reduce the ambiguity of expert judgment on AHP. A case study was conducted on the selection of sub-contractors with the bottom cleaning and ship replating project at shipyard company in Surabaya, Indonesia. As a result, one of the sub-contractors selected as the best sub-contractor with a score of 0.167.


Introduction
Shipyard industries is one type of construction industry that has special characteristics.Activities in the Shipbuilding Industry is one of a complex construction job because there is much work to be done in parallel [1].Shipbuilding project has a time limit between order and delivery so that if it passes that time, a penalty will be imposed according to the initial contract, forcing everyone involved in the shipyard industry to work according to the target.This condition causes shipyard workers to be required to have good performance.Jobs in the shipyard industry mostly involve sub-contractors.Involving subcontractors in shipbuilding project is intended to increase efficiency in terms of both time and cost.According to Manu et al [2], although many advantages are obtained, involving sub-contractors in the company also has an impact on the company's overall performance so that the selection of the right subcontractor becomes a crucial activity and determines the company's overall performance.
Several researchers have conducted research at the contractor selection stage.Some research [3] examined the selection of contractors in textile companies using the Analytical Hyrarchy Process (AHP) method, or method in the selection of maintenance project contractors.However, the research using the AHP method has not considered the ambiguity of the expert's language [4].Morkunaite et al applied the PROMITEE method in selecting contractors for the renovation of cultural heritage buildings [5].Juan et al (2011) conducted a study in the selection of contractors who were approached by the Fuzzy QFD method.The result is that this method approach is more efficient and can solve problems faster than the PROMITEE method [6] [7].However, the method in this study is not effective when used in selection problems with complex criteria because it does not have a hierarchical settlement pattern.Rajesh (2013) tried to develop the integration of QFD with AHP to solve problems with more complex criteria in supplier selection [8].However, the criteria used are still general in nature, namely quality, cost , and delivery.
Based on several previous studies, this study uses the Fuzzy AHP method to solve the problem of selecting sub-contractors in the Shipyard Company.Fuzzy approach is used to reduce the ambiguity of expert language.This study considers seven criteria that are expected to represent the needs of shipyard companies.

Methodology
The weight of each criterion is calculated by pairwise comparisons between criteria.Fuzzification is done by changing the AHP scale into a Triangular Fuzzy Number (TFN).The geometric mean is then calculated using the Buckley method.The weight of the criteria that have been generated must be defuzzified using the Centre of Area (COA) method to normalize the fuzzy scale.The same procedure was also carried out to determine the weights of the HOWs and alternative sub-criteria.In detail the procedures carried out in this study are as follows.
1.The decision maker compares the criteria, sub-criteria, or alternatives with the Fuzzy AHP linguistic language with the TFN scale.
Calculate the fuzzy geometric mean () of each criterion, sub-criteria, or alternative using the Buckley method.The fuzzy geometric mean value can be calculated by the following equation:

Calculate the fuzzy weight ( w ~)
for each criterion, sub-criteria, or alternative with the following equation:

Because w ~
what is obtained is still a fuzzy number, it is necessary to defuzzify using the Center of Area (COA) method developed by Chou and Chang with the following equation:

, ,
IOP Publishing doi:10.1088/1755-1315/1265/1/0120073 4.The weight M is already a non-fuzzy number, but it still has to be normalized so as to produce the final weight using the following equation:

Results and Discussion
The Fuzzy AHP method was applied in the selection of sub-contractors at shipyard company in Surabaya, Indonesia on the bottom cleaning and ship replating project.Based on interviews with experts at two popular shipyard company in Surabaya, Indonesia, there are seven criteria considered in the selection of shipyard sub-contractors, including; organizational administration (C1), quality (C2), equipment (C3), performance (C4), finance (C5), timeliness (C6), and Occupational Health and Safety (C7).

Determination of AHP Fuzzy Membership Function
The AHP fuzzy membership function was created as the basis for expert judgment in pairwise comparisons between criteria.Pairwise comparisons are based on five basic linguistic terms including "equally important", "moderately more important", "more important", "very important", and "most important".Each membership function (fuzzy number scale) is defined by three symmetrical Triangular Fuzzy Number (TFN) parameters [9], the lower limit (l), the middle limit (m), and the upper limit (u) at intervals according to the definition.The use of linguistic variables is intended to examine the linguistic priorities given by the evaluator.Below are Table 1 and Figure 2 which show the fuzzy membership functions for the criteria in the selection of sub-contractors.

Pairwise Comparison Between Criteria
Pairwise comparisons were made by interviewing experts (head of the procurement division of PT PAL Indonesia).Each criterion is compared with each other with a predefined linguistic scale.Table 2 shows the results of a pairwise comparison of the seven sub-contractor selection criteria.

Fuzzy Geometric Average Calculation
After performing pairwise comparisons between criteria, the next step is to determine the geometric mean of the fuzzy numbers that have been obtained.For example, the geometric mean values for the Organizational Administration criteria are as follows: = [(0,24;0,31;0,63)] In the same way, the fuzzy geometric mean for each criterion can be seen in Table 3 below:

Fuzzy Weight Calculation
After the fuzzy geometric mean is obtained, the next step is to determine the fuzzy weight.For example, the weights for the organizational administration criteria ( w ~) are as follows: Based on the above calculation, it can be seen that the weights for organizational administrative criteria ( w ~) are 0.01 for the lower limit (l), 0.03 for the middle limit (m), and 0.09 for the upper limit (u).In the same way the weights for each criterion are shown in Table 4 below: Based on these calculations, the non-fuzzy value of administrative criteria (M1) is 0.05.This value must be normalized as the final weight of the organizational administration criteria with equation 4 as follows.

Conclusion
The selection of sub-contractors in a shipyard company is one of the most important activities because it can determine the company's performance.Selection of the best sub-contractor is a complex issue because there is a "trade off" of many criteria.The fuzzy approach to AHP can reduce language ambiguity on the AHP linguistic scale.In this study, seven alternative sub-contractors were considered based on seven criteria and 24 sub-criteria.Based on the research process that has been carried out, it produces a-selected alternative as the best sub-contractor.The selected sub-contractor was chosen because it has a higher score than other alternative sub-contractors, especially on criteria that have a high level of importance such as quality (C2) and timeliness (C6).Further research can integrate the Fuzzy AHP method with the selection of criteria to produce criteria that are more representative of the company's needs.Further research can also develop a fuzzy AHP consistency testing model.

Table 1 .
Fuzzy Membership Function

Table 2 .
Pairwise Comparison Matrix Between Criteria

Table 5 .
Final Weights for Criteria

Table 7 .
Final Weight of Each Alternative Sub-Contractor