Multi-criteria comparison of stacking layouts using EFAHP

۴.  Multi-criteria comparison of stacking layouts using EFAHP

1.1. Extent Fuzzy AHP

The Analytical Hierarchy Process (AHP) has been widely used to solve multiple attribute decision making problems. However, due to the existence of vagueness and uncertainty in judgments, a crisp, pair-wise comparison with a conventional AHP may be unable to accurately capture the decision-makers' ideas (Ayag, 2005). Therefore, fuzzy logic is introduced into the pair-wise comparison to deal with the deficiency in the traditional AHP, referred to as FAHP.

By the help of FAHP, the vagueness of the data involved in the decision of selecting the most efficient alternative is efficiently taken in account. It is easier to understand and it can effectively handle both qualitative and quantitative data in the multi-attribute decision making problems (kahraman et al, 2004). Chang (1996) introduced Extent Fuzzy AHP (EFAHP) a new approach for handling fuzzy AHP, with the use of triangular fuzzy numbers for pair-wise comparison scale of fuzzy AHP, and the use of the extent analysis method for the synthetic extent values of the pair-wise comparisons.

Recent overviews that include the application of EFAHP and other FAHP methods on different test cases are illustrated in Table 1.

Researcher/Year	Method	Test Case
Parkash (2003)	AHP and Extent Fuzzy AHP	land suitability analysis
Kahraman et al. (2004)	Extent Fuzzy AHP	comparing catering firms in Turkey
Tang & Beynon (2005)	Extent Fuzzy AHP	development of a capital investment
Bozbura et al (2007)	Extent Fuzzy AHP	improve the quality of prioritization of  Human Capital
Naghadehi et al (2009)	Extent Fuzzy AHP	selecting the optimum mining method
Celik et al (2009)	Extent Fuzzy AHP	analysis of shipping registry selection

Table 1: Recent overviews of EFAHP application

In this study the TFNs will be used to identify the preferences of one criterion over another and then through the extent analysis method, the synthetic extent value of the pair-wise comparison will be calculated. In other steps the weight vectors will be decided and normalized and the normalized weight vectors will be determined. Based on the different weights of criteria and attributes, the final priority of the two alternatives (vertical and horizontal layout type) will be obtained in which the first priority will be associated to the highest weight obtained.

4.3Multi-attribute comparison of two stacking layouts

There are many different qualitative and quantitative factors deal with selection of a definite stacking lay out for container terminals. Quantitative aspects can be usually analyzed by Computer simulation models. Computer simulation used in this article analyzed total idle and operation time concerning the utilization, idle time and operation time of QCs, RTGs and trucks. In order to find other effective factors for evaluating two different stacking layouts different Anzali port managers were interviewed.

Finally for the multi criteria analysis in this study, the selection of the most operative stacking layout is identified and will be based on the following important criteria:

Time: Time of different equipment operations is considered as a vital main criterion. The sub-attributes are determined as ''total operation time'' and ''total idle time'' which are obtained from simulation model.

Each layout type causes different operation and idle time for QCs, RTGs and trucks. Idle time affects capital costs of equipment while operation time has direct effects on operation costs.

Operational area: The Operational area sub-attributes are defined in terms of ''export/import simplicity'' and ''outbreak stacking area''.

Stacking layout type certainly affects the simplicity of export/import function. Layout paths type's, vertical or horizontal container stacking position and etc. may simplify or intensify export/import function. Layout type also has direct effects on the smooth movement of RTGs and trucks.

Management: ''Safety'' and ''Human resource'' are assigned as management sub-attributes.

Figure 6 illustrates the decision hierarchical structure for this study which is defined in four levels. It shows two alternatives and three main attributes and their corresponding sub-attributes. The study will analyse and determine the weights of each attribute and their corresponding sub-attributes with respect to each alternative to obtain the best stacking layout.

Table 3: Summary of priority weights (Time)

Sub-attributes of Time
	Idle Time	Operational Time	Alternative priority weight
Weight	1	0
Alternative
Layout A	0.684	0.5	0.684
Layout B	0.316	0.5	0.316

Table 4: Summary of priority weights (Operational Area)

Sub-attributes of Operational Area
	Outbreak Stacking area	Export/Import Simplicity	Alternative priority weight
Weight	0.5	0.5
Alternative
Layout A	0.684	0.5	0.5920
Layout B	0.316	0.5	0.4080

Table 5: Summary of priority weights (Management)

Sub-attributes of Management
	Human Resource	Safety	Alternative priority weight
Weight	0.316	0.684
Alternative
Layout A	0.5	0.684	0.6259
Layout B	0.5	0.316	0.3741

The summary of alternatives' priority weights is shown in table 6.

Table 6: Summary of priority weights (goal)

Main-attributes of the Goal
	Time	Operational area	Management	Alternative priority weight
Weight	0.5	0.25	0.25
Alternative
Layout A	0.684	0.5920	0.6259	0.6465
Layout B	0.316	0.4080	0.3741	0.3535

Figure 7 represents the final ranking and selection of the two alternatives.

The EFAHP analysis in this study has shown that layout A has obtained the higher priority with a ratio of 65% while Layout B has gained a priority ratio of 35%.