Debmallya Chatterjee: Delphi-FAHP and Promethee: An ...
Transcript of Debmallya Chatterjee: Delphi-FAHP and Promethee: An ...
TWP: 111_1505
Delphi-FAHP and PROMETHEE:
An integrated approach in healthcare facility location selection
by
Debmallya Chatterjee Associate Professor,
T.A Pai Management Institute,
Manipal-576104, Karnataka, India.
Phone: 0820- 2701023, email: [email protected]
Working Paper No: TWP No. 111 / 2015-16 / 05
Abstract: Fuzzy AHP and PROMETHEE-GAIA are among the two most prominent MCDM
tools used by the researchers in facility location selection. However both the methods have
their weaknesses reported by the researchers. AHP suffers the problem of size and developing
consensus where PROMETHEE can be improved with the hierarchical structure of AHP. This
paper makes an attempt to embed Delphi to Fuzzy AHP and then integrate it with
PROMETHEE-GAIA to develop a robust model in healthcare facility location selection. The
purpose is to overcome the weaknesses of both the individual methods by this amalgamation.
A case of thirteen alternative locations from six different subdivisions from India is considered
to demonstrate the applicability of this integrated method.
Key words: Delphi, Fuzzy AHP, PROMETHEE, GAIA, healthcare, location selection
Debmallya Chatterjee: Delphi-FAHP and Promethee: An integrated Approach to Healthcare Facility..… TWP111_1505
1
Delphi-FAHP and PROMETHEE: An integrated approach in healthcare facility location selection
1 Introduction
Facility location selection has always been one of the major multi criteria decision making
problems that researchers talked about in last couple of decades. Because of its multicriteria
nature this decision making attracted different tools including analytical hierarchy process
(AHP) developed by Saaty (1980). A number of researchers used AHP or its fuzzy extension
in facility location selection where they provided evidence on the efficacy of this MCDM tool
(Shim, 1989; Jesuk, 2005; Cheng-Ru, 2007). Similarly the outranking method known as
Preference Ranking Organization MeTHod for Enrichment Evaluations (PROMETHEE)
developed by Brans and Vincke (1985), was also extensively used by researchers in various
field of decision making including facility location selection (Behzadian et al., 2009; Walther
et al., 2008; Frikha et al., 2011; Athawale et al., 2012).
However in spite of an extensive use, researchers identified some perennial problems with AHP
and its fuzzy extensions. First the process of generating consensus among the expert opinions
more or less relies on an aggregation method with a high chance of losing important
information (Macharis et al., 2004). In fact researchers are of the opinion that generating
consensus can improve accuracy in results and thus can be beneficial to the outcomes (Okoli
and Pawlowski, 2004, Soltani et al., 2011). Second, most of the studies demonstrate the
applicability of this MCDM tool only with a limited number of alternatives. With a set of 10
alternatives the numbers of pair wise comparisons become 45 and with 25 alternatives it
reaches 300.Third is to limit the scale to a 9 point scale which cannot cope with the fact that an
alternative can be multiple times better that the other (Macharis et al., 2004). Interestingly the
first problem can be overcome by embedding Delphi technique with AHP. The second and the
third problems can be addressed using the PROMETHEE method. In fact there can be any
number of alternatives that can be compared using this outranking method without much
difficulty and also it has no restriction on scale. However few studies also voiced for improving
PROMETHEE by embedding AHP or its fuzzy extension (FAHP). The ability of AHP to
decompose the decision problem and building hierarchy of criteria can improve the generation
of criteria weights in PROMETHEE. Studies including Giannopoulos and Founti (2010),
Venkatesan and Kumanan (2012) and also Bansal and Kumar (2013) demonstrated an efficacy
in the applications of AHP-PROMETHEE hybrid approach in different fields of study.
Debmallya Chatterjee: Delphi-FAHP and Promethee: An integrated Approach to Healthcare Facility..… TWP111_1505
2
Among all other facility location selection problems health care facility location selection using
MCDM tools got importance since last decade. Not only physical access and other criteria
affects the quality and operations of the medical services provided through the facility but also
the success or the failure of such a facility depends largely on the location selected (Paul, 1997;
Kuo et al., 1999). In last couple of decades a good number of researchers acknowledged the
need to analyze this location selection decisions in health care sector and applied different
MCDM tools to facilitate the decision making (Hanes and McKnight, 1984; Paul and Batta,
2008). A large amount of such decision making was done with the application of AHP or its
fuzzy extension (FAHP). Researchers like Wu et al (2007) used AHP to select location for the
Taiwanese hospitals in obtaining competitive advantage. Vahidnia et al (2009) used FAHP and
GIS to select location for hospitals in Tehran metropolitan area. In a similar approach Soltani
and Marandi (2011) tried to address the hospital location selection in Shiraj metropolitan area,
Iran by combining AHP and GIS.
Nevertheless the present study did not come across any prior work in health care facility
location selection where the researchers used Delphi to generate consensus among expert
opinions in an AHP or FAHP environment. The use of PROMETHEE in the domain is also not
available. Though some researchers like Bansal and Kumar (2013) used AHP-PROMETHEE
hybrid method in decision making but such a study is absent in health care facility location
selection.
The aim of this paper is to study the selection of health care facility location using an integration
of Delphi embedded FAHP and PROMETHEE approach. Six sub criteria under three main
criteria are selected from literature to evaluate the alternative locations. To clearly understand
importance and the conflicts between criteria, geometric analysis of interactive aid (GAIA) is
also used. A case of thirteen alternative locations from six different sub divisions of the district
of Burdwan, West Bengal, India is considered for illustration.
The paper is organized as follows: Detailed overview of the techniques such as FAHP, Delphi,
PROMETHEE-GAIA with their applicability are given in section 2. In section 3 the
methodology of the research is presented. Section 4 demonstrates the application of the
integrated approach of Delphi-FAHP and PROMETHEE in health facility location selection in
India. Section 5 analyses the results and finally conclusion, limitation and suggestions for
future studies are given in section 6.
Debmallya Chatterjee: Delphi-FAHP and Promethee: An integrated Approach to Healthcare Facility..… TWP111_1505
3
2 An overview of FAHP, Delphi and PROMETHEE-GAIA approaches
2.1 Fuzzy AHP (FAHP)
Succeeding the work of Saaty (1980) several researchers used AHP in their studies that can be
illustrated using the following steps:
First the objective is identified and the overall hierarchy of the decision problem is designed.
This hierarchy reveals the various factors to be considered as well as the various alternatives
in the decision. There may be multiple levels within the hierarchy based on the sub factors
available under each factor.
Both qualitative and quantitative factors can be compared using pair wise comparisons and
processed through a comparison matrix, which generates factor weights. Factor weights are
numerical values quantifying the importance of the factor in the decision. The column average
of all these factor weights is used to check the consistency and is denoted by λaverage.
Check the consistency ratios of the pair wise comparison matrices to ensure consistency in
judgments. A response matrix failing to satisfy the consistency test is rejected. The consistency
index (CI) for each matrix of order n is computed by the formulae:
CI = (λaverage-n)/(n-1). The consistency ratio (CR) is then calculated using the formulae: CR =
CI/RI, where RI is a known Random Index. This consistency test validates the responses taken
into the model. A response is valid if the value of CR is found to be less than 0.1.
The alternatives are compared with respect to the factors or sub factors in the hierarchy and
the scores are aggregated to obtain overall rating of an alternative. Here each of the sub factor
weights are multiplied to the corresponding factor weights to generate overall weights of the
sub factors denoted by Sl. The overall score of mth alternative is obtained by Am in equation
(1.1)
1
........................(1.1)N
m l ml
l
A s a
where lsis the weight of lth sub factor and mla
is the weight of thm alternative with
respect to lth sub factor.
Since T. L. Saaty introduced AHP in 1980’s a number of researchers used this MCDM tool in
complex decision making situations with a good amount of success (Zahedi, 1986; Altay,
2008). However researchers also felt that this tool is not capable of handling subjectivity and
Debmallya Chatterjee: Delphi-FAHP and Promethee: An integrated Approach to Healthcare Facility..… TWP111_1505
4
vagueness inherent in human judgments. Zimmermann (1990) and then Chen and Mon (1994)
recommended the inclusion of fuzzy set theory (Zadeh, 1965) in AHP to address this issue.
Fuzzy AHP (FAHP) differs from AHP in terms of the linguistic scale and the computations
done in generating weights and importance. The linguistic scale consisting of five triangular
fuzzy numbers (TFN), proposed by Chen (2000) and further modified by Pan (2008) is used to
capture the expert responses. Normalization of geometric mean (NGM) method is used to
generate the fuzzy weights and further defuzzification is done using signed distance method
(Yao and Wu, 2000) to obtain non-fuzzy or crisp importance.
2.2 Delphi Technique
Delphi technique has evolved as an efficient and effective tool in qualitative decision making
since last couple of decades. The technique is widely used mainly in structuring processes and
generating consensus among responses (Okoli and Pawlowski, 2004; Azizollah, 2008). This
technique asks for reliable responses on problems or conflicting situations from the experts in
a panel. This tool helps the researchers in combining the reports or feedbacks of a group of
experts into one consolidated statement (Wanda and Tena, 2004). The process starts with
accumulating the expert responses and preparing a consolidated report. Though there is no
restriction on the number of experts in such a panel but Okoli and Pawlowski (2004)
recommended that 10-18 experts in such a panel may be adequate. In the next round the
consolidated report is sent to the experts along with their respective responses of the previous
round for modification or alteration, if any. After successive rounds the responses are expected
to converge. To avoid any sort of influence the anonymity of the experts are maintained
throughout the process.
2.3 PROMETHEE and GAIA
PROMETHEE is an interactive approach widely used in the context of multicriteria decision
making (MCDM) in different fields of study (Brans and Vincke, 1985; Hokkanen and
Saleminen, 1997; Athawale and Chakraborthy, 2010; Frikha et al., 2010; Rao and Patel, 2010;
Athawale et al., 2012; Jihen et al., 2012;). The backbone of PROMETHEE is the multicriteria
table containing the criteria, their importance or weights, details of the actions or alternatives
with respect to the criteria selected and the preference function. A preference function (Pj)
transforms the difference between scores obtained by two alternatives or actions with respect
to a particular criterion into a number between 0 and 1. Six different functions are proposed
Debmallya Chatterjee: Delphi-FAHP and Promethee: An integrated Approach to Healthcare Facility..… TWP111_1505
5
by Brans and Vincke (1985) which can be used in different criteria as deemed applicable
(Hokkanen and Salminen, 1997).
Another important aspect is the value function ϕ(a) corresponding to an alternative ‘a’. This is
also termed as net flow of alternative ‘a’. It is computed as the difference of ϕ+(a) and ϕ-(a)
where ϕ+(a) and ϕ-(a) represents the strength and weakness of vis-à-vis the other alternatives.
Where PROMETHEE I provides a partial ranking of the alternatives, a complete ranking with
respect to the net flow ϕ(a) can be obtained through PROMETHEE II.
GAIA is a multi-dimensional graphical representation which applies a principal component
analysis on the multi-dimensional space with respect to individual criterion net flow. It is a
visual descriptive analysis tool that helps in better understanding. Nemery et al. (2011) talked
about the usefulness of this method in MCDM.
3 Methodology
The methodology presented in this paper is divided into five sub sections. In the first section
Selection of experts, Identification of criteria and sub criteria, Shortlisting of alternative
locations are done. In the second section expert opinions are collected through questionnaire
framed using the fuzzy AHP scale. Further Delphi method is used to develop consensus among
expert opinions. In the third section criteria and sub criteria weights are generated using FAHP.
Data corresponding to all the alternative locations are fitted into PROMETHEE to generate net
flow of the alternatives and finally using the net flow the alternative locations are ranked.
4 Application
4.1 Selection of Experts
FAHP and PROMETHEE both being subjective decision making methods require consistent
inputs. In case of FAHP inconsistent responses may fail consistency test and the entire data
may be rejected (Saaty, 1980). This situation advocates for ‘expert opinion’ in criteria weight
generation through FAHP. In the present study 20 experts are selected for capturing responses.
The experts are medical doctors having more than fifteen years of experience in the field of
hospital or health care administration & projects and are quite acquainted of the heath
conditions of the district of Burdwan, West Bengal, India. Five of them are senior medical
practitioners having an average work experience of 36 years where as the other fifteen have in
between 20 to 35 years. A questionnaire is provided to the experts and are requested to do pair
Debmallya Chatterjee: Delphi-FAHP and Promethee: An integrated Approach to Healthcare Facility..… TWP111_1505
6
wise comparisons among criteria (or sub criteria) using the fuzzy linguistic scale (Pan, 2008).
Another questionnaire is also provided to capture information regarding the alternatives with
respect to four criteria using 9 point likert type scale ranging between very bad to very good.
4.2 Identification of criteria and sub criteria
Location selection criteria for health care facility are found to vary across different research
works in different country however in almost every piece of work researchers recommended
multi criteria evaluation of potential locations. Some of them talked about distance from arterial
routes, travel time, environmental issues, land cost and population density as the set of
important criteria (Vahidnia et al., 2009) where others opinioned for access to roads network,
distance to other medical centers, population density, environment and size of the land (Soltani
et al., 2011). Wu et al. (2007) considered population size, age, density, governmental policies,
land, labour and capital where Schuurman et al. (2006) considered socio demographics of the
service area, proximity to future expansion, space and population density while defining the
hospital catchment through travel time. Based on the prominence and repetitions of the criteria
in the available literature and on considering the valuable judgment of experts, this study
considers three major criteria and six sub criteria in the evaluation. The criteria and sub criteria
are summarized in Table 1.
Table 1: Criteria and sub criteria
Major Criteria Sub Criteria
Cost (CST) Cost of land (COL)
(Soltani et al., 2011; Vahidnia et al, 2009; Wu et al, 2007) Cost of construction (COC)
Population characteristics (PC) Population density (PD)
(Soltani et al., 2011; Schuurman et al, 2006;
Vahidnia et al, 2009; Wu et al, 2007) Economic condition (EC)
Location (L) Access to road network (ARN)
(Vahidnia et al, 2009; Soltani et al., 2011; Estill, 2006) Environment (ENV)
Debmallya Chatterjee: Delphi-FAHP and Promethee: An integrated Approach to Healthcare Facility..… TWP111_1505
7
4.3 Identification of the alternative locations for the study
The region of study consists of thirteen blocks within five sub divisions or clusters in the district
of Burdwan, West Bengal, India. An area covering more than 2755 square kilometers and a
total of more than two millions of populations without a hospital. From the medical facility and
population of these sub divisions of the district of Burdwan, West Bengal one can witness a
significant lacuna in terms of the availability of health care facilities. Table 2 provides us the
picture clearly. The number of hospital beds per 10000 populations is even poorer than the
nation’s average of 9. From Figure 1 the locations of these thirteen blocks can be identified.
Table 2: Health and population detail of the alternative locations
Cluster/
Sub
division
Blocks Area in
KM2
Population Density
(Persons per
KM2)
No. of hospital
Doctors
Male Female Total
C1 Ausgram-I 164.5 54623 52190 106813 649 0 8
Galsi-II 277.9 68641 65310 133951 482 0 6
C2
Jamalpur 267.88 123728 119746 243474 909 0 8
Raina-I 266.44 83633 79288 162921 611 0 4
Khandaghosh 256.13 87671 82639 170310 665 0 6
C3
Faridpur
Durgapur 144.6 59253 49366 108619 751 0 4
Pandabeswar 97.89 79992 66453 146445 1496 0 3
Kanksa 270.78 78669 72586 151255 559 0 7
C4
Purbasthali-II 188.18 97024 91125 188149 1000 0 7
Kalna-I 161.34 97903 92784 190687 1182 0 6
Monteshwar 305.4 109544 103718 213262 698 0 6
C5 Ketugram-I 189.86 74513 71500 146013 769 0 5
Katwa-II 164.45 61696 58618 120314 732 0 5
Total: 2755.35 1076890 1005323 2082213 0 75
Source: medical facility and population, bardhman.gov.in
Debmallya Chatterjee: Delphi-FAHP and Promethee: An integrated Approach to Healthcare Facility..… TWP111_1505
8
Figure 1: Map of the district of Burdwan, West Bengal, India
Source: NREGS, Bardhaman district1
4.4 Collecting expert responses and developing consensus using Delphi
The responses were collected to generate criteria weights and also to assess the alternative
locations with respect to some criteria for which data is not available. Six questions are
administered to compare the criteria and sub criteria using the fuzzy pair wise comparison scale
proposed by Pan (2008). Another four questions were administered to assess all the thirteen
alternatives with respect to four sub criteria using a 9 point likert type scale. After the data has
been collected a summary sheet is prepared and sent to the experts to have a relook at their
responses for possible alteration. Table 3, 4 and 5 respectively demonstrate the successive
rounds of Delphi and the associated convergence. The convergence process was terminated
after achieving eighty or more percentage of convergence to a point in the scale.
Table 3: Responses after first round of Delphi
Main criteria comparisons
Extremely un imp
Un imp
Equally imp Imp
Extremely imp
CST 15 5 PC
CST 7 12 1 L
PC 9 11 L
sub criteria comparison under cost
COL 11 9 COC
sub criteria comparison under population characteristics
PD 3 8 9 EC
sub criteria comparison under location
ARN 3 12 5 ENV
1 NREGS, Burdwan district (http://nregsburdwan.com)
Debmallya Chatterjee: Delphi-FAHP and Promethee: An integrated Approach to Healthcare Facility..… TWP111_1505
9
Table 4: Responses after second round of Delphi
Main criteria comparisons
Extremely un imp
Un imp Equally imp
Imp Extremely imp
CST 17 3 PC
CST 5 15 1 L
PC 4 16 L
sub criteria comparison under cost
COL 6 14 COC
sub criteria comparison under population characteristics
PD 1 5 14 EC
sub criteria comparison under location
ARN 3 15 2 ENV
Table 5: Responses after third round of Delphi
Main criteria comparisons
Extremely un
imp Un imp Equally imp Imp Extremely imp
CST 19 1 PC
CST 3 16 1 L
PC 2 18 L
sub criteria comparison under cost
COL 3 17 COC
sub criteria comparison under population characteristics
PD 1 1 18 EC
sub criteria comparison under location
ARN 1 17 2 ENV
4.5 Generation of criteria weights and scores for the alternatives
After the process of convergence by Delphi technique, the data is processed using the FAHP
to generate criteria weights. Each of the pair wise comparison table is tested for consistency
before considering them as inputs. These criteria weights are used to evaluate the alternatives
through PROMETHEE multicriteria table. Table 6 provides the detail of the multicriteria table
used to evaluate the alternatives by visual PROMETHEE software, version 1.4. GAIA is
further used to visually comprehend the conflicts among the alternatives with respect to each
criterion. The quantitative detail of the alternatives corresponding to population density and
economic condition are captured from Table 2.
Debmallya Chatterjee: Delphi-FAHP and Promethee: An integrated Approach to Healthcare Facility..… TWP111_1505
10
Table 6: Multicriteria table of PROMETHEE
Cost of
land
Cost of
construction
Population
density
Economic
condition
Access
to road
network Environment
Unit/ Scale 9-point 9-point
no. of people
/ sq. km.
livelihood
index(1000) 9-point 9-point
Preferences
Min/Max Min min Max Min max max
Weight 0.26 0.14 0.32 0.08 0.13 0.07
Preference Function Linear Linear Linear Linear Linear Linear
Thresholds absolute absolute Absolute Absolute absolute absolute
Statistics
Minimum 3 4 482 444 1 3
Maximum 7 7 1496 682 9 7
Average 5 5 808 506 6 5
Standard Dev. 1 1 268 61 2 1
5 Results and Discussions
The pair wise comparison using FAHP results in the determination of weights (both fuzzy and
crisp) for the criteria and sub criteria. See Table 7. Among the criteria, cost and population
characteristics have evolved as the most important criteria sharing equivalent importance.
Table 7: Criteria weights
Criteria Weight of main criteria Defuzzified
weight
(l m u) w
Cost (CST) 0.420 0.392 0.380 0.396
Population Characteristics (PC) 0.420 0.392 0.380 0.396
Location (L) 0.160 0.216 0.241 0.208
From the weights of the sub criteria in Table 8 one can witness that population density emerges
as the most important sub criteria with 31.6 % weight followed by cost of land with 25.5%.
Table 8: Sub criteria weights
Sub criteria L M U Weight within criteria Global weight
COL 0.710 0.634 0.600 0.645 0.2552
COC 0.290 0.366 0.400 0.355 0.1407
PD 1.000 0.750 0.691 0.798 0.3158
EC 0.000 0.250 0.309 0.202 0.0800
ARN 0.710 0.634 0.600 0.645 0.1341
ENV 0.290 0.366 0.400 0.355 0.0740
Debmallya Chatterjee: Delphi-FAHP and Promethee: An integrated Approach to Healthcare Facility..… TWP111_1505
11
The visual PROMETHEE software provides the partial ranking and the complete ranking of
the alternatives using PROMETHEE I and PROMETYHEE II. The indifference and preference
thresholds for the criteria can be observed from Table 9.
Table 9: Indifference and preference thresholds of the criteria
Sub Criteria Indifference threshold (q) Preference threshold (p)
Cost of land 1 2
Cost of construction 1 2
Population density 254 556
Economic condition 63 126
Access to road network 1 2
Environment 1 2
Table 10 demonstrates the rankings of the alternatives with respect to net dominance flow ϕ(a).
Table 10: Ranking of alternatives with respect to net flow
Rank Alternatives ϕ ϕ + ϕ -
1 Kalna-I 0.4452 0.4572 0.0119
2 Pandabeswar 0.3565 0.5412 0.1847
3 Kanksa 0.1700 0.2919 0.1219
4 Faridpur Durgapur 0.1446 0.2564 0.1118
5 Katwa-II 0.1393 0.1900 0.0508
6 Galsi-I 0.1023 0.2033 0.1011
7 Jamalpur -0.0824 0.0978 0.1802
8 Purbasthali-II -0.1267 0.1126 0.2393
9 Ausgram-I -0.1318 0.0800 0.2118
10 Khandaghosh -0.1751 0.0518 0.2269
11 Monteshwar -0.1818 0.0523 0.2341
12 Ketugram-I -0.277 0.0452 0.3222
13 Raina-I -0.3832 0.0524 0.4356
From the GAIA plane in Figure 2 one can visualize the conflicts among criteria very clearly.
Here the quality of information provided by the two dimensional GAIA plane is 89.1%.
Debmallya Chatterjee: Delphi-FAHP and Promethee: An integrated Approach to Healthcare Facility..… TWP111_1505
12
Figure 2: GAIA Plane
From figure 2 it is easy to identify that the alternative Pandabeswar (A7) is very strong in terms
of population density whereas Galsi-I (A2), Katwa II (A13) and to some extent Kanksa (A8)
are strong competitors in terms of access to road network. In the cost dimension Kalna I (A10)
and Faridpur-Durgapur (A6) are much stronger than the other competitors. A group of locations
including Monteshwar (A11), Jamalpur (A3), Khandaghosh (A5), Purbasthali II (A9),
Aushgram I (A1) and Ketugram (A11) are equivalently positioned with respect to environment,
however no location can be found strong enough with respect to economic conditions.
The sensitivity analysis shows that the alternative Pandabeswar, though in second position,
cannot be raised to the first position by changing the weights of the sub criteria cost of land,
Debmallya Chatterjee: Delphi-FAHP and Promethee: An integrated Approach to Healthcare Facility..… TWP111_1505
13
economic conditions, access to road network and environment. However by changing the
weight of cost of construction from 14% to 36% or population density from 36% to 46% may
revise the ranks of Kalna I and Pandabeswar. On critically analyzing the FAHP hierarchy one
can realize that raising either the weight of cost of construction to 36% or population density
to 46% are not feasible as they both asks for assigning more than 100% weightage on their
respective parent criteria.
6 Conclusion
This problem demonstrates an application of Delphi embedded FAHP and PROMETHEE -
GAIA approach in generating criteria weights and in evaluating potential health facility
locations in the district of Burdwan, West Bengal, India. The idea was to study how the strong
characters of Delphi embedded FAHP and PROMETHEE GAIA can be integrated successfully
to evaluate potential health facility locations. This integration helps us develop consensus
among expert opinions leading to better accuracy in results (Soltani et al., 2011). It also helps
us understand the similarities and conflicts among different criteria in the evaluation of
potential locations. The GAIA plane visually portrays the similarity of strengths of different
alternative locations with respect to different criteria. Sensitivity analysis performed on the
weights of the sub criteria through PROMETHEE shows that even after a reasonable alteration
of sub criteria weights, there is hardly any change in the first two positions of the alternative
rank list. This analysis certifies robustness of this integrated MCDM model.
This model can be used in similar real world applications in any field of study. In fact extension
of this work can be done by segmenting the locations with respect to sub divisions and
capturing the constraints existing within those sub divisions. Due to non-availability of reported
data within sub divisions and paucity of time in collecting data directly from field, the present
work was limited to the selection of a location representing a sub division. The work can be
more insightful if study can be done in selecting potential locations within sub divisions.
Though embedding Delphi resulted in better accuracy as reported by researchers, there is a
small glitch as well. The process of developing consensus among experts in Delphi may take a
lot of iterations to converge. In worst case it may also lead to divergence. The personal traits
of the experts may also shape the process of convergence.
Debmallya Chatterjee: Delphi-FAHP and Promethee: An integrated Approach to Healthcare Facility..… TWP111_1505
14
References
Altay, A. (2008) A Rating Approach to the Solutions of Istanbul Traffic in IEMC Europe 2008:
Proceedings of Engineering Management Conference, pp. 1-4. (Accessed on 26 Dec 2009,
http://ieeexplore.ieee.org)
Athawale, A.M and Chakraborthy, S. (2010) Facility Layout Selection Using PROMETHEE II
Method. The IUP Journal of Operations Management, 9(1), pp. 81-98.
Athawale, V.M., Chatterjee, P. and Chakraborty, S. (2012) Decision making for facility location
selection using PROMETHEE II method. International Journal of Industrial and Systems
Engineering, 11 (1/2), pp. 16 - 30.
Azizollah, J. (2008) Using Fuzzy Delphi Method in Maintenance Strategy Selection Problem. Journal
of Uncertain Systems, 2(4), pp. 289-298.
Bansal, A. and Kumar, P. (2013) 3PL selection using hybrid model of AHP-PROMETHEE.
International Journal of Services and Operations Management, 14 (3), pp. 373 - 397.
Brans, J.P. and Vincke, Ph. (1985) A preference ranking organization method.The PROMETHEE
method for MCDM. Management Science, 31(6), pp. 647-656.
Chen C.H. and Mon D.L. (1994) Evaluating weapon system by analytical hierarchy process based on
fuzzy scales. Fuzzy sets and systems, 63(1), pp. 1-10.
Chen C.T. (2000) Extension of the TOPSIS for group decision-making under fuzzy environment. Fuzzy
Sets and Systems, 114(1), pp. 1-9
Cheng-Ru, W., Chin-Tsai, L. and Chen H.C. (2007) Optimal selection of location for Taiwanese
hospitals to ensure a competitive advantage by using the analytic hierarchy process and
sensitivity analysis, Building and Environment, 42(3), pp. 1431-1444.
Estill and Associates (2006). Site Selection Community Consultation Report. Washington: Department
of Health
Frikha, H., Chabchoub, H. and Martel, J-M. (2011) An interactive disaggregation approach inferring
the indifference and the preference thresholds of PROMETHEE II. International Journal of
Multicriteria Decision Making, 1 (4), pp. 365 - 393.
Giannopoulos, D. and Founti, M. (2010) A fuzzy approach to incorporate uncertainty in the
PROMETHEE multicriteria method. International Journal of Multicriteria Decision Making,
1 (1), pp. 80 - 102.
Hanes, P. J. and McKnight, C.M. (1984) Criteria for selection of a practice location among senior dental
students at the University of Mississippi. Journal of Dental Education, 48(2), pp. 102-104.
Hokkanen, J. and Saleminen, P. (1997) Locating a Waste Treatment Facility by Multicriteria Analysis.
Journal of Multi-criteria decision analysis, 6(1), pp. 175-184.
Debmallya Chatterjee: Delphi-FAHP and Promethee: An integrated Approach to Healthcare Facility..… TWP111_1505
15
Jesuk, K. (2005) Solving distribution facility location problem using an analytic hierarchy process
approach. Paper presented at ISAHP, Honolulu, Hawaii, 8-10 July 2005.
Jihen, J., Mhamedi, A.EI. and Chabchoub, H. (2012) A fuzzy PROMETHEE II method for the selection
of reverse logistics provider. International Journal of Enterprise Network Management, 5
(3), pp. 304 - 315.
Kuo, R., Chi, S. and Kao, S. (1999) A decision support system for locating convenience store through
fuzzy AHP. Computers & Industrial Engineering, 37(3), pp. 323–326.
Macharis, C., Springael, J., Brucker, K.D. and Verbeke, A. (2004) PROMETHEE and AHP: The design
of operational synergies in multicriteria analysis. Strengthening PROMETHEE with ideas of
AHP. European Journal of Operational Research, 153(2), pp. 307-317.
Medical facility: Burdwan district. http://www.bardhaman.gov.in/health/medifaci.html (Accessed on
31st January 2013)
Nemery, Ph., Lidouh, K. and Mareschal, B. (2011) On the usefulness of taking the weights into account
in the GAIA visualisations. International Journal of Information and Decision Sciences, 3 (3),
pp. 228 - 251.
Okoli C., Pawlowski S. (2004) The Delphi method as a research tool: an example, design considerations
and applications. Information & Management, 42(1), pp. 15–29.
Pan N.F. (2008) Fuzzy AHP approach for selecting the suitable bridge construction method. Automation
in Construction, 17(8), pp. 958–965.
Paul, A.J. and Batta, R. (2008) Models for hospital location and capacity allocation for an area prone to
natural disasters. Intl. Journal of operations research, 3(5), pp. 473-496.
Paul, D.P. (1997) Dental practice location: Some aspects of the importance of selection of place. Health
Marketing Quarterly, 14(4), pp. 55–69.
Population: Burdwan district, http://www.bardhaman.gov.in/census/popliterate.html (Accessed on 31st
January 2013).
Rao, R.V. and Patel, B.K. (2010) Decision making in the manufacturing environment using an
Improved PROMETHEE method. International Journal of Production Research, 48(16), pp.
4665-4682.
Saaty, T.L. (1980) The Analytic Hierarchy Process, Planning, Priority Setting, Resource Allocation.
McGraw Hill, New York, 1980.
Schuurman, N., Fiedler, R.S., Grzybowski, S., and Grund, D. (2006) Defining rational hospital
catchments for non-urban areas based on travel-time. International Journal of Health
Geographics, http://www.ij-healthgeographics.com/content/5/1/43 (Accessed on 24th
December 2012)
Shim, J. P. (1989) Bibliographical research on the analytic hierarchy process (AHP). Socio-Economic
Planning Sciences, 23(3), pp. 161–16
Debmallya Chatterjee: Delphi-FAHP and Promethee: An integrated Approach to Healthcare Facility..… TWP111_1505
16
Soltani, A., Marandi, E.Z. (2011) Hospital site selection using two stage fuzzy multi-criteria decision
making process. Journal of Urban and environmental engineering, 5(1), pp. 32-43.
Vahidnia, M.H., Alesheikh, A. and Alimohammadi, A. (2009) Hospital site selection using fuzzy AHP
and its derivatives. Journal of environmental management, 90(10), pp. 3048-3056.
Venkatesan, S.P. and Kumanan, S. (2012) Supply chain risk prioritisation using a hybrid AHP and
PROMETHEE approach. International Journal of Services and Operations Management, 13
(1), pp. 19 - 41.
Walther, G., Spengler, T. and Queiruga, D. (2008) Facility location planning for treatment of large
household appliances in Spain. International Journal of Environmental Technology and
Management, 8(4), pp. 405 - 425.
Wanda L. and Tena BC. (2004) ‘The Delphi technique: A research strategy for career and technical
education’, Journal of Career and Technical Education, 20(2), pp. 55-67.
Wu, C.R., Lin, C. and Chen, H. (2007) Optimal selection of Taiwanese hospitals to ensure a competitive
advantage by using analytical hierarchy process and sensitivity analysis. Building and
environment, 42(3), pp. 1431-1444.
Yao, J-S. and Wu, K. (2000) ranking fuzzy numbers based on decomposition principle and signed
distance. Fuzzy Sets and Systems, 116(2), pp. 275-288.
Zahedi F. (1986) The analytic hierarchy process: A survey of the method and its application. Interfaces,
16(4), pp. 96-108.
Zimmermann H.J. (1990) Decision making in ill-structured environments and with multiple criteria,
Published in: Bana e costa, Ed., Readings in multiple criteria decision aid, Springer, Berlin, pp.
119-151.
Zedah, L.A. (1965) Fuzzy Sets. Information Control, 8(3), pp.338-353
Debmallya Chatterjee: Delphi-FAHP and Promethee: An integrated Approach to Healthcare Facility..… TWP111_1505
17
About Author
Dr. Debmallya Chatterjee
Associate Professor
Area: Operations Management
Education: M.Tech (NIT-D), MSc(Univ.of Burdwan), MIT(MAHE), PhD Telephone: +91-820-2701023
Email: [email protected]
Teaching: Operations Research, Application of Quantitative methods in Management, Business Statistics,
Discrete Mathematics, Business Mathematics, Mathematical Analysis, Problem solving and decision making.
Professional Activities: He obtained his Masters of Technology (Mtech) on ‘Operations Research in
Industry and Business management’ from NIT Durgapur. Prior to that he got his masters in Mathematics from
University of Burdwan and Masters of Information Technology from Manipal academy of higher education. He
is in academia for last eight years.
Research: Research interest is in the field of Fuzzy mathematics, Analytical hierarchy process and its
application in business, Systems thinking tools in creative decision making.
Publications:
1. Sinha, T.R., Chatterjee, D.and Iskanius, P. (2011) ‘Measuring stress among hospital nurses: an empirical
study using fuzzy evaluation’, Int. J. Logistics Economics and Globalisation, Vol. 3, Nos. 2/3, pp.142–
154.
2. Ghosh, A.,Chatterjee, D. and Ghosh, B.(2011), ‘Conceptual framework of faculty performance
evaluation’ Asian Journal of Management Research, Spl Issue 1, pp. 217-229
3. Chatterjee, D.(2010) ‘Fuzzy cognitive map of e-commerce customer satisfaction’, ICCS2010,
University of Burdwan
4. Chatterjee, D.(2010) ‘A Fuzzy Evaluation of service quality gap: A case study’, International Journal of
Advances in science and Technology, Volume. 1, Spl Issue 4, pp. 6-14
5. Chatterjee, D., Chowdhury, S. and Mukherjee, B., (2010), ‘Study of fuzzy-AHP model to search the
criterion in the evaluation of the best technical institutions: a case study’, International Journal of
Engineering Science and Technology, Vol. 2, No. 7, pp. 2499-2510
6. Chatterjee, D., Chowdhury, S. and Mukherjee, B., (2010), ‘A study of the application of fuzzy analytical
hierarchical process (FAHP) in the ranking of Indian banks’, International Journal of Engineering
Science and Technology, Vol. 2, No. 7, pp. 2511-2520
7. Chatterjee, D. (2008), ‘Understanding Cellular Automata: An Approach’, MID Journal of Computer
Application & Business Administration, Vol. 1, No. 1, pp 28-34.
Conference Presentations:
1. Presented a paper entitled “A Fuzzy-AHP evaluation of performance Appraisal: A case study on Peerless
general finance corps. ltd, kolkata” at the UGC sponsored National seminar at BB College, Asansol, W.B
on 19th – 20th Feb, 2010
2. Presented a paper entitled” Measuring service quality gap: A case study on City Residency Hotel,
Durgapur” at The Department of Business Administration, North Bengal University on 29th -30th
March, 2010
Awards & Recognitions
1. “Outstanding service 2010” Rahul Foundation, Rajbandh, Durgapur-12, West Bengal
2. “Best Faculty 2004-2005” Rahul Foundation, Rajbandh, Durgapur-12, West Bengal