Discussion Papers In Economics
And Business

PROMETHEE Multicriteria Analysis for Evaluation of Recycling
Strategies in Malaysia

Santha Chenayah
Eiji Takeda
Discussion Paper 05-01

Graduate School of Economics andOsaka School of International Public Policy (OSIPP)
Osaka University, Toyonaka, Osaka 560-0043, JAPANPROMETHEE Multicriteria Analysis for Evaluation of Recycling
Strategies in Malaysia

Santha Chenayah
Eiji Takeda
Discussion Paper 05-01

February 2005

この研究は「大学院経済学研究科・経済学部記念事業」
基金より援助を受けた、記して感謝する。

Graduate School of Economics andOsaka School of International Public Policy (OSIPP)
Osaka University, Toyonaka, Osaka 560-0043, JAPANPROMETHEE Multicriteria Analysis for Evaluation of Recycling
Strategies in Malaysia
Santha Chenayah
Faculty of Economics and Administration, University of Malaya
50603 Kuala Lumpur, Malaysia
andEiji Takeda
Graduate School of Economics, Osaka University
Toyonaka, Osaka 560-0043, Japan
Abstract
At present, the per capita generation of solid waste in Malaysia varies from 0.45 to 2kg/day dependingon the economic status of an area. In general, the per capita generation rate is about 1kg/day. Even though
17,000 tonnes/day of solid waste is being generated, only 5% is being recycled. If this particular scenariocontinues without appropriate mitigation, Malaysia will be facing a serious problem in municipal solid waste
management. Hence, government has targeted 22% of waste to be recycled by 2020. Various strategies havebeen formulated in achieving this figure.
In Malaysia, research is being done vastly on recycling but very few related to multicriteria. As a firststep, we propose here an evaluation of various recycling strategies and ranking them based on multicriteria
to provide an insight on increasing the recycling activities among residents. Since values of alternatives
are imprecise, ambiguous and/or uncertain, the multicriteria outranking analysis is particularly useful inorder to facilitate further detailed consideration. The problem of the selection or the ranking of alternatives
submitted to a multicriteria evaluation is not an easy problem economically or mathematically. We propose
a modified PROMETHEE analysis for treating multicriteria problems.

JEL Classification: C44, C61, Q53
Keywords: solid waste management, recycling, multicriteria decision-aid (MCDA), PROMETHEE, outranking relations

1

1

Introduction

The rapid growth in the urban population due to rural-urban migration and natural growth as well as changing
consumption patterns contributed to an increase in the generation and composition of solid waste. The estimatedamount of waste generated by the urban population in 2000 was 11,940 tonnes per day or 0.8 kilogram per
capita per day(EPU,2001). This large amount of solid waste strained existing landfill sites, and the majorities
of disposal grounds were considered unsanitary landfills or merely open dumps.
The problem was compounded by cases of open burning being reported at dumpsites. To ensure a more
efficient waste management system, the privatization of solid waste management was started on an interim
basis. Two of the four consortia involved started collection of solid waste in 26 of the 145 local authorities by
the end of the plan period. As a whole, a total of 23 municipal disposal sites were upgraded to ensure proper
disposal. The government also conducted awareness campaigns to encourage the reduction, reuse and recyclingof waste materials.
In the Seventh Malaysia Plan (1995-2000), the Malaysian government introduced a new law on solid waste
management. In general, the principal processes options available and being recognized as hierarchy for integrated waste management are listed as follows: waste minimization, reuse, material recycling, energy recovery
and landfill. During the Eighth Malaysian Plan (2001-2005) period, government will consider the adoption of
a comprehensive waste management policy to address issues of waste reduction, reuse and recycling (EPU, 2001).

Figure 1: An integrated waste management system
Source: Integrated Waste Management and Thermal Oxidation Plant(MINT: NST Quaterly, 2000)

An integrated waste management system (Figure 1)would include waste collection and sorting, followed by
one or more of the following :1. Waste reduction and recovery of secondary materials (recycling): this will require adequate sorting andaccess to reprocessing facilities.
2. Biological treatment of organic materials: this will produce marketable compost or reduce volume for2disposal. Anaerobic digestion produces methane that can be burned to release energy.
3. Thermal treatment: this will reduce volume, render residues inert and may recover energy.
4. Landfill: this can increase amenity via land reclamation but will at least minimize pollution and loss ofamenity.
The purpose of the paper is to analyze various recycling strategies in order to increase recycling of Municipal
Solid Waste (MSW) by the year 2020. In achieving the above objective, we have enlisted two sub-objectives:
1. increase the awareness among people/ educate them on recycling and the benefits
2. increase the infrastructures related to recycling
In this paper, we propose a multicriteria evaluation of alternatives, followed by ranking to provide an insightto the decision makers on which alternative/s they should focus in achieving the objective. First, we will lookat the present scenario of solid waste management and recycling in Malaysia. Next, we will examine various
criteria and recycling strategies for evaluation. In section 3, we propose a modified PROMETHEE analysis todeal with outranking relation with discordance. In section 4, we will further analyze and rank the recycling
strategies using this approach. Lastly, we conclude with a few recommendations.

2

Formulation of Problem

Malaysians generate about 72% compostable waste, comprising organic waste, paper, textile/leather and wood.
The amount of plastic waste accounts for 16% and is considered very high and is typical of a fast developing
nation. The amount of solid waste generated shows an increasing trend (Table 1). An average annual generation
rate increase of 4% is predicted (2.5% attributed to population increase, 1.5% due to increase of waste production
per capita). It has been estimated that the average Klang Valley resident produced 1.56kg of garbage every day
in 1998 (The Star, 2000), enough to fill all 88 floors of the Twin Towers in nine days.

3

TABLE 1: SOLID WASTE GENERATED, 1996-2000 (’000 tonnes)
1996

1997

1998

1999

2000∗

Kuala Lumpur

na

na

1058

1070

1082

Selangor

na

na

1169

1204

1240

Pahang

na

na

202

206

210

Kelantan

na

na

123

126

129

Terengganu

na

na

119

122

125

Negeri Sembilan

245

250

267

278

291

Malacca

192

200

208

216

225

Johore

854

890

927

956

1005

Perlis

26

27

28

28

29

Kedah

507

538

569

560

631

Penang

570

591

611

630

648

Perak

672

696

719

741

736

Total

3066

3192

6000

6137

6378

Area

Source: Eight Malaysian Plan 2001-2005, EPU, 2001.
Note:∗ Estimates, n.a.= not available

The generation of solid wastes presents challenges to solid waste managers and town and country planners,
due to lack of available landfill space, and also because solid waste management represents every significant
increases in collection and disposal facilities and functions, which will affect the manpower needed to manage
them. The majority of dump sites in Malaysia have no leachate or gas management facilities, and no daily earth
covering of the piles, so they are leaching chemicals into the groundwater, poisoning the air with toxic gases
and generally being health hazards. To compound the problem, most of the dumpsites are almost full.

Collection methods and landfills
Waste collection involves the gathering of waste by collection trucks that transport it to intermediate processing
plants, transfer stations or landfills. Collection is the most expensive activity and is both capital-and laborintensive, accounting for some 60-75% of the cost of waste management (Nasir et. al, 1998). In Malaysia, themost widely-practiced collection methods are the door-to-door front curbside method, for accessible households,
while for the relatively inaccessible areas, collection is from communal bins.
After collection, most wastes are transported to landfills. There are 230 official dumping sites in Malaysia,
the majority of which are crude landfills, with only 10% providing leachate treatment ponds and gas ventilation
systems and with most having no control mechanisms and supervision (Zaman, 1992). Steps are being taken
to upgrade the landfills, and this includes fence installation, weighbridge and site-office wheel washing troughs,
and gas disposal pipes.
4

In almost all landfills, there are sorting activities by scavengers for cardboard, plastics, bottles and metals,
with the remaining pile levelled by bulldozers. At the end of the day, the pile is supposed to be covered by alayer of soil and compacted to reduce infestation by vermin (flies, rats, birds), fire and odor problems, although
this is frequently not done.

Waste management hierarchy and 3R
Presently, about 17,000 tonnes of solid waste is being discarded daily, of which only 70 percent is collected anddisposed. The remaining 30 percent is either disposed of illegally or is recycled. However, it is estimated that
only about 5% is being recycled. The waste management hierarchy (Figure 2) states that wastes should be
prevented or reduced at the source whenever feasible and safe disposal is the option of last resort.
Source reduction or waste prevention, which includes reuse, is the best approach, followed by recycling.
Waste that cannot be prevented or recycled can be incinerated or landfilled according to proper regulations.
Source reduction at the top of the hierarchy because the best approach to managing solid waste is to avoid
creating it in the first place. This means reducing the amount of trash being discarded and reusing containers
and products instead of throwing them away. Once waste is created, recycling, which includes composting, is
one of the most effective methods of reducing the amount of material in the waste stream. If waste cannot berecycled, incineration or sanitary landfilling are the next preferred methods of treatment.

Figure 2: The waste management hierarchy
Source: US Environmental Protection Agency website

Why Recycle?
With 17,000 tonnes of rubbish produced everyday, it is only a matter of time before we run out of space todispose of them. Recycling reduces waste, which in turn reduces the need for landfills and dumpsites. Recycling
reduces pollution and saves energy. Making products from virgin or raw materials results in pollution and uses
more energy. Recycling is cheaper in the long run compared to maintaining landfills and other systems. Whenrecycling programmes become more efficient, there will be less rubbish to dispose of. Recycling creates up to 55times more jobs than waste disposal alone. It will create jobs for engineers, machine specialists, environmental
personnel, general workers and many more. Recycling improves cleanliness and quality of life. Breakdown ofsolid waste created by Malaysians are as shown in Table 2.

Table 2: Breakdown of Solid Waste
Typespercentage %
Paper

27%

Household waste

36.5%

Steel

3.9%

Glass

3.7%

Plastic

16.4%

Others12.5%

Source:www.kitarsemula.com

Experts believe a landfill can last 10 years longer if Malaysians recycled 50% of their garbage. Recycling ofsolid wastes, especially the non-combustible waste (glass and metal); combustible but hazardous waste (plastic)
and paper, reduces the amount of waste introduced into the environment and the need for disposal capacity. The
benefits of recycling are two-hold. Firstly, recycling cuts down the need for disposal capacity, lowers emission
from landfills and incinerators and reduces litter. Secondly, the use of recycled materials in industries reduces
energy use and emissions; lessens impacts when raw material is extracted or manufactured and conserves raw
materials (Agamuthu, 2001).
However, three important elements of integrated solid waste management hierarchy (source reduction, waste
recycling and waste transformation) are not officially and legally incorporated into the Malaysian waste management practice. In the year 2000, the Malaysian government has targeted 22% of waste to be recycled by theyear 2020. Various strategies are being formulated in achieving this figure. These strategies form a guideline
for all local authorities in implementing the recycling program.

Recycling alternatives and multi-criteria for consideration
Alternatives/ Action plans
The Ministry of housing and local authorities of Malaysia has outlined several existing action plans toincrease the recycling activities throughout the nation. These alternatives have been divided into two maingroups; awareness creation program and increasing infrastructure program. With the outline given by ministry,each local authority can act independently to achieve the recycling objective.

6

Group 1: awareness creation program (66% of government budget allocation for recycling)
Under this program, there are 5 alternatives/action plans to increase awareness among the public. The alternatives are as listed below. We propose an evaluation to derive a proposal on which one of this action plan/s
can contribute in increasing the awareness among the public.
1. Billboard advertisement (a1 )2. Carnival, exhibition and briefing (a2 )3. Printed matters: posters, pamphlets and bulletins (a3 )4. Electronic medium; television, radio, websites (a4 )5. Transportation (a5 ): consists of- public transportation such as light rail transit (LRT), commuters, public bus- school bus
Group 2: increase the infrastructure program: recycling-friendly facilities (29% of government budget allocation
for recycling)
Under this program, 5 alternatives/ action plans has been formulated. Some have been practiced longer thanothers.
1. Recycling bin (b1 ): 240 Lt, 360 Lt, 660Lt; - 7080 units of 240Lt and 3675 units of 360Lt bins are locatedat public places all over Malaysia - 3950 units of 660Lt is located at collection centers
2. Silverbox (b2 ): only 44 units are distributed to some of the local municipalities/ city councils as Silverboxes
are costly
3. Recycling Lorry (5 tonne)(b3 ): to collect recyclable items from collection center, schools, residential association, kerb side collection
4. Recycling van (b4 ): house to house collection (on-call basis)
5. Recycling center/Collecting centers(b5 ): there are 718 collection centers to enable residents to bring therecyclable items. More are being built. However, there are only a limited number of recycling center.
We propose an evaluation of these alternatives to provide an understanding on how to encourage the public
to recycle by answering the following question:• is it achieved by providing/ placing more recycling bins in a way that the public cannot avoid but utilizeit?
• is it achieved by having lesser bins but provide more collection vehicles?
• is it achieved by having more recycling/ collection centers at every residential area (every “Taman”)?
The best method to answer these questions is the evaluation based on multicriteria.
7

Decision makers/Stakeholders
Decision makers are the local authorities and city councils. However, the ranking of these plans vary according
to the stakeholders and their interest. In this paper, we concentrate our analysis and rank the recycling
alternatives focusing on the local authorities and city councils as the decision maker. However, there are manyother stakeholders with different interest in recycling. Ranking of alternatives depend on these stakeholders andtheir objectives. The stakeholders are the education institutions, NGO’s, concessionary companies, recyclable
waste collectors and association, residence association, private sector: corporate, shopping malls, restaurants
and others [hotels, hospitals, religious institutions].

Criteria for consideration
From the interview with the government officers involved in recycling in Malaysia, we have listed some of thecriteria for consideration:
1. cost (c1 )2. maintenance (c2 )3. efficiency (c3 )4. targeted result (c4 )These criteria can further be described:
1. Cost refers to all the cost directly involved in starting the strategy such as planning and engineering andcost of the equipments and building. Cost is a minimizing objective. A higher score is more desirable
than a lower one. We use the following score:
Category

Score

Low

5

Relatively low

4

Fair

3

Relatively high

2

High

1

2. Maintenance refers to the maintenance and operational cost of each action (includes cost of employing
workers): a score of 1 - 5 indicate the degree of maintenance cost:8DegreeScore

low maintenance cost5

relatively low maintenance cost4

fair maintenance cost3

relatively high maintenance cost2

high maintenance/ continuous maintenance cost

1

3. Efficiency: refers to the efficiency of each plan to date. The score is between 1 (0% - 20%) and 5 (80% 100%).
RatingScore

80% - 100%560% - 80%440% - 60%3

20% - 40%20% - 20%

1

4. Targeted result: This target refers to the expected result from each action plan and is given in percentage.
The following table presents a summary of the alternatives and criteria for consideration:
Group 1: Creating awareness
Alternatives/criteria

Cost (c1 )Maintenance (c2 )Efficiency (c3 )Target (c4 )

(min)

(min)

(max)

(max)

Billboard Advertisement (a1 )

1

1

2

50%

Carnival , exhibition, briefing (a2 )

2

3

3

70%

Printed matters (a3 )

3

4

2

40%

Electronic media (a4 )

1

2

4

80%

Transportation (a5 )

2

2

3

60%

Group 2: Recycling facilities
Alternatives/criteria

Cost (c1 )Maintenance (c2 )Efficiency (c3 )Target (c4 )

(min)

(min)

(max)

(max)

Recycling bin (b1 )

3

2

3

40%

Silverbox (b2 )

3

2

2

20%

Recycling Lorry (b3 )

1

3

4

60%

Recycling Van (b4 )

2

3

5

80%

Recycling/ collection center (b5 )

1

1

2

50%

9

3

PROMETHEE Multiple Criteria Analysis

The outranking analysis has been frequently used to deal with the complex decisions involving quasi-criterion
and pseudo-criterion (see Roy and Vincke, 1984, Vincke, 1992). So far, PROMETHEE (Preference Ranking
Organization METHod for Enriching Evaluations)have been proposed for the outranking analysis(see Brans
and Vincke, 1985). PROMETHEE methods have taken an important place among the existing outranking
multicriteria methods (Keyser and Peeters, 1996). A particularly user-friendly Decision Lab software makes
it easier to conduct the PROMETHEE analysis. PROMETHEE is based on the positive (out-) and negative(in-) preference flows for each alternative in the valued outranking relation to elicit the ranking of alternatives
according to the decision maker’s preferences. The positive flow is expressing how much an alternative isdominating the other ones, and the negative flow how much it is dominated by the other ones. Based on
the preference flows, PROMETHEE I provides a partial preorder. PROMETHEE II is also introduced toobtain a complete preorder by using a net flow, though, it loses much information of preference relations (seeBrans, and Mareschal, and Vincke, 1986). It is not possible to take discordance into account when constructing
the outrank relations of PROMETHEE (Keyser and Peeters, 1996). Discordance is however considered as arealistic concept in multiple criteria decision aid and is considered as one of the reasons for developing outranking
methods (Vincke, 1992).
In this paper, we propose a modified procedure using the “weighted” preference flows to get a partial preorderin a PROMETHEE context. It reduces to the eigenvalue problem. An advantage of the modified procedureis that the ranking of alternatives is relatively stable in the change of components in the outranking relation
matrix. Therefore, it is useful for the outranking relations which take discordance into account.
Let us consider the set A of n alternatives:
A = {ai , a2 , . . . , an }.
Let g1 , g2 , . . . , gm be m-criteria. Thus, each alternatives ai is characterized by a multiattribute outcome
denoted by a vector(g1 (ai ), g2 (ai ), . . . , gm (ai )) .
The valued outranking relation is constructed from the notions of quasi-criterion and pseudo-criterion.
In particular, PROMETHEE constructs it using a preference function which represents the decision maker’s
preference for an alternative ai with regard to aj . Several types of preference functions are considered for thecriteria such as usual criterion, quasi-criterion, criterion with linear preference, level criterion, pseudo-criterionwith linear preference and indifference area, and Gaussian criterion (see, Brans and Vincke, 1985 and Brans,
and Mareschal, and Vincke, 1986). To be precise, let
Pk (ai , aj ) = f [gk (ai ) − gk (aj )]10

be the preference function associated with the criterion gk (·). As f (·), six types of functions are proposed tocover most of the cases in practical applications. Then, the valued outranking relation π(ai , aj ) of ai over aj
is defined as the weighted sum of the preference functions Pk :π(ai , aj ) =X

Pk (ai , aj )wk ,kwhere wk is a weight for criterion k. Thus, π(ai , aj ) represents the intensity of the preference of ai over aj for
all the criteria: the closer to 1, the greater the preference. We now introduce the weighted sum of preference(out-) flows.
λψ + (ai ) =nXπ(ai , aj )ψ + (aj ),i = 1, 2, . . . , n,

(1)

j=1

where λ is a constant.
This implies that, if ai outranks aj having a high value of ψ + (aj ), it should reflect a higher attractivenessthan ai over aj having a low value of ψ + (aj ).
Similarly, we define the weighted sum of preference (in-) flows
λψ − (ai ) =nXπ(ai , aj )ψ − (aj ),i = 1, 2, . . . , n,

(2)

j=1

Thus, using the weighted sum of preference flows reduces the eigenvalue problem:Πψ + = λψ +(3)ψ − Π = λψ −(4)where Π = (π(ai , aj )), ψ + = (ψ + (ai )) and ψ − = (ψ − (ai )).
In what follows, to assure that the eigenvectors ψ + = (ψ + (ai )) and ψ − = (ψ − (ai )) corresponding to the
maximum eigenvalue of any valued outranking relation have positive components, for calculation, we replaceπ(ai , aj ) = 0 by π(ai , aj ) = ε where ε is a sufficiently small positive number.

Theorem. If the outranking relation Π = (π(ai , aj )) is a complete preorder, ψ + (·) and − [ψ − (·)] are strategically equivalent value functions which represent the decision maker’s preferences.

Proof : see Appendix

11

4

A Modified PROMETHEE Analysis of the Recycling Strategies

Setting weights
Weights are set based on the interview with several government officials involved in recycling in Malaysia.
From these officials point of view, cost criteria is more important than all other criteria as all local authorities have to formulate their strategies within the budget allocated to them. With PROMETHEE, no specificguidelines are provided to determine the weights. PROMETHEE assumes that the decision-maker is able toweigh the criteria appropriately, at least when the number of criteria is not too large. This may be difficult toto achieve by an inexperienced user. Macharis (2004) suggested to utilize Analytic Hierarchy Process (AHP).
From the interview, we constructed the following reciprocal matrix:
c1

c2

c3

c4

c1

1

E

B(W-S)

B(D-S)

c2

1/E

1

B(W-S)S

c3

1/B(W-S)

1/B(W-S)

1

B(W-E)c4

1/B(D-S)

1/S

1/B(W-E)

1∗E=equal, W=weak, S=strong, D=demonstrated, A=absolute, B(.-.)between values indicated in parentheses.
From this, the priority vector is derived:(0.422, 0.397, 0.081, 0.1).
From this priority vector, we find that the cost criteria (c1 ) is more important, followed by the maintenancecriteria (c2 ), target (c4 ) and efficiency (c3 ). λmax = 4.1327, C.I.=0.043, thus, a consistency ratio (C.R.) of 0.048(≤ 0.1) is considered acceptable.

Group1: Creating AwarenessAs for alternatives, we have the following ,criteria

c1

c2

c3

c4

0.422

0.397

0.081

0.1

a1

1

1

2

50

a2

2

3

3

70

a3

3

4

2

40

a4

1

2

4

80

a5

2

2

3

60

weight (wi )alternatives

Since, scores are imprecise and ambiguous, we employ the outranking method. Therefore, it is important12

to determine the preference (p), indifference (q) and veto (v ) thresholds. It is as given in the table below.
Threshold

c1

c2

c3

c4

p

2

2

2

20

q

1

1

1

10

v

10

10

10

100

From this, we have an outranking relation matrix.
a1

a2

a3

a1  1

a2 
 1

a3 
 1


a4  1

a5
1

0.503

0.181 0.819



a4

1

1

1

0.9

1

0.819

1

0.181

1

1

0.603

0.9

a5


1 

1 


0.9 



1 

1

From a modified PROMETHEE, we have:ψ + = (0.676, 1, 0.922, 0.825, 0.896)
ψ − = (1, 0.872, 0.547, 0.912, 0.987)
λmax = 4.318

Descending:
a2 → a3 → a5 → a4 → a1
Ascending:a3 → a2 → a4 → a5 → a1
and thus:
a2

-

a3

¡
µ
@
¡
R
@
-

a4

H
j
H
a1

a5

*
©
©

Interpretation of the result:From the ranking, alternatives a2 (carnival, exhibition, briefing) and a3 (printed matters) are preferred to
the rest. These two alternatives contributes more in creating awareness among the public. The local authorities
organize exhibitions at well-known shopping complexes during the ‘Environment Week’ or some other events.
One of the television station, TV3, organized a carnival to create awareness among the public. Usually during
such events, the organizers incorporate other features to attract the crowd. For example, during ‘Environment
Week’, they organize ‘treasure hunt’, various contest to attract the children and medical check-ups for a minimumfee. Some events emphasizes the need for recycling directly, while others, indirectly. The posters on the need13

to recycle and other information related to recycling are usually found at all public spots.
Alternative (a1 ) is the least preferred. From the analysis, we find that billboard advertisement contributeless in creating awareness among the public. Furthermore, it involves very high initial cost and maintenancecost. So far, the efficiency is quite low. Electronic media and transportation contribute less but are better
alternative in increasing awareness compared to billboard advertisement.

Group 2: Recycling Facilities
As for alternatives, we have the following ,criteria

c1

c2

c3

c4

0.422

0.397

0.081

0.1

b1

3

2

3

40

b2

3

2

2

20

b3

1

3

4

60

b4

2

3

5

80

b5

1

1

2

50

weight (wi )alternatives

The preference (p), indifference (q) and veto (v ) thresholds are as given in the table below.
Threshold

c1

c2

c3

c4

p

2

2

2

20

q

1

1

1

10

v

10

10

10

100

From this, we have an outranking relation matrix:b1

b1  1

b2 
 0.9

b3 
 0.578
b4  1
b5 0.578

b2

b3

b4

1

0.9

0.819

1

0.819 0.819

0.578

1

0.9

1

1

1

0.578 0.522 0.422

b5


1 

0.9 


1 



1 

1

From a modified PROMETHEE, we have:ψ + = (0.938, 0.887, 0.793, 1, 0.589)
ψ − = (0.814, 0.834, 0.851, 0.791, 1)
λmax = 4.207
14

Descending:b4 → b1 → b2 → b3 → b5
Ascending:b4 → b1 → b2 → b3 → b5
and thus:
b4

-

b1

-

b2

-

b3

-

b5

Interpretation of the result:
In Group 2, we evaluate 5 strategies on how to increase recycling among the residents by providing thenecessary infrastructure. From the ranking, alternatives b4 is preferable to alternatives b1 , b2 , b3 and b5 .
Recycling van is preferred to other alternatives. Recycling lorry is the fourth mode that can initiate interestof recycling among the residents. Recycling van is more effective in increase the recycling interest among theresidents because residents can call for this van to collect the recyclable items. Whereas, the recycling lorry isavailable only on certain days for certain areas.
Recycling center is the least preferred because most center are away from individual housing units andresidents prefer if the segregated waste are collected from house to house. Apart from the recycling van,recycling bins can contribute in creating awareness. However, the public must have complete information on
the location of the bins and complete knowledge on the usage before expecting them to utilize recycling bins.
The location of the recycling bins are important to encourage the public to recycle. Only those who are awareof the location of these bins can utilize it. There have been complaints as well about bins being stolen. As
Silverboxes are made of steel a few had been stolen as well. Therefore, every municipality is provided with only
a limited number to be placed at pedestrian walks.
With these evaluation, it is possible to answer the questions raised earlier. The results from ranking based
only multicriteria suggests that public can be encouraged to practice recycling by providing more recycling vans
at more frequent use and by providing them on more information on the location of bins. For example, theSubang Jaya City Council has a website that also updates the residents on recycling.

5

Concluding Remarks

We have proposed a slightly different eigenvector procedure in the context of PROMETHEE using the weighted
sum of preference in-flow and out-flow to deal with outranking relation with discordance. Advantages of it arethat the eigenvector is easy to understand and to calculate and that it is relatively robust in the change ofcomponents in the valued outranking relation. We demonstrated its application on the evaluation of recycling
strategies in Malaysia.
To achieve the recycling objective, creating awareness and providing the necessary facilities have to be done
simultaneously. From one of the surveys done by the Ministry of Housing and Local Authority in the year 2003,15

there is awareness among the public but not many are applying it.
In our analysis, the decision maker is the city council/ local authority. From the modified PROMETHEE
analysis, the most effective way to create awareness among the public is by having exhibitions, carnival, briefing
and through printed matters. People generally like carnivals. During exhibitions, the public can see hands-on
some benefits from recycling. The most effective way of encouraging the public to recycle is by collecting thewaste from house to house. Compared to recycling bins and recycling centers, recycling van is a new strategy andhas proved to be more successful in luring the public to recycle. People seem more comfortable with recyclingvans as they can utilize it simply by making a call. Many are not aware the location of recycling centers andsome are too lazy to make the trip themselves.
As a first step in achieving the recycling objective, we have done an evaluation on how to create awarenessamong public and on how to increase the infrastructure to encourage the public to recycle. We hope thisevaluation will provide some insight to the local authorities on how to tackle the lack of interest in recycling
among the public. However, we would like to emphasize here that what we have proposed here is a preliminary
step towards achieving the objective by the year 2020.
There are many stakeholders with different interest in recycling and have to be taken into consideration.
Ranking of alternatives depend on the stakeholders and their objectives. As the stakeholders vary, the emphasison the objectives also varies and this will result in the difference of ranking in alternatives. This matter will beelaborated in detail in our further research. In addition, our research will look at recycling in Subang Jaya andits successfulness.

Appendix
Proof of Theorem:
From (1), we have for any ai , aj ,n¡
¢ X
λmax ψ + (ai ) − ψ + (aj ) =(π(ai , ak ) − π(aj , ak )) ψ + (ak )

(5)

k=1

Note that, either (i) ai P aj or (ii) aj P ai or (iii) ai Iaj exclusively holds.
We shall prove, if ai P aj , then ψ + (ai ) > ψ + (aj ).
Since ai P aj implies not [aj P ai ] by asymmetry of P , we get
π(ai , aj ) = 1 and π(aj , ai ) = ε(6)It follows from the reflexivity of I thatπ(ai , ai ) = 1 and π(aj , aj ) = 1.

(7)

From (6) and (7), we haveπ(ai , aj ) = π(aj , aj ),(8)π(ai , ai ) > π(aj , ai ).

(9)For any ak (k 6= i, j; k = 1, 2, . . . , n), we have either aj P ak or ak P aj or aj Iak exclusively.

16

(a) If aj P ak , then ai P ak as P is transitive. That is,π(ai , ak ) = π(aj , ak ) = 1.

(10)(b) If ak P aj , which implies not [aj P ak ], thenπ(aj , ak ) = ε.

(11)

Since π(ai , ak ) ≥ ε, we have from (11)π(ai , ak ) ≥ π(aj , ak ) = ε.

(12)(c) If aj Iak , then ai P ak . Thus, we haveπ(ai , ak ) = π(aj , ak ) = 1.

(13)

From (8), (9), (10), (12) and (13), we haveπ(ai , ak ) ≥ π(aj , ak ),k = 1, 2, . . . , n,andπ(ai , ai ) > π(aj , ai ).
Since, from the well-known Perron’s theorem (Saaty, 1990) , for a positive matrix, λmax > 0 and ψ + (ak ) > 0, k =1, 2, . . . , n, it follows from (5) that
ψ + (ai ) > ψ + (aj ).
Thus, it is shown that
if ai P aj , then ψ + (ai ) > ψ + (aj )(14)

Similarly, we haveif aj P ai , then ψ + (aj ) > ψ + (ai )(15)Finally, let us assume (iii) ai Iaj . It follows thatπ(ai , aj ) = π(aj , aj ) = 1,

(16)π(ai , ai ) = π(aj , ai ) = 1.

(17)

For any ak , (k 6= i, j; k = 1, 2, . . . , n), we have either aj P ak or ak P aj or aj Iak exclusively.
(a) If aj P ak , then ai P ak . Therefore,
π(ai , ak ) = π(aj , ak ) = 1.

(18)(b) If ak P aj , then ak P ai . Thus
π(ai , ak ) = π(aj , ak ) = ε.

(19)

17

(c) If aj Iak , then ai Iak . Thus we haveπ(ai , ak ) = π(aj , ak ) = 1.

(20)

From (16), (17), (18), (19), and (20)we haveπ(ai , ak ) = π(aj , ak ),k = 1, 2, . . . , n.

It follows from (5) that
if ai Iaj , then ψ + (ai ) = ψ + (aj ).

(21)

Since, for any ai , aj , only one of the following cases: ai P aj , aj P ai , ai Iaj occurs, it follows from (14), (15), and (21)thatai P a j

if and only if ψ + (ai ) > ψ + (aj ),aj P a i

if and only if ψ + (ai ) < ψ + (aj ),ai Iajif and only if ψ + (ai ) = ψ + (aj ).

In a similarly way, we haveai P a j

if and only if ψ − (ai ) < ψ − (aj ),aj P a i

if and only if ψ − (ai ) > ψ − (aj ),ai Iajif and only if ψ − (ai ) = ψ − (aj ).

which ends the proof.

18

References[1] Agamuthu, P., 2001. Solid Waste: Principles and Management, University of Malaya Press.
[2] Brans,J.P., Mareschal,B., Vincke,Ph., 1986. How to select and how to rank projects: The PROMETHEE method
for MCDM, European Journal of Operational Research 24, 228-238.
[3] Brans,J.P., and Vincke,Ph., 1985. A preference ranking organization method: The PROMETHEE method, Management Science 31, 647-656.
[4] EPU, 2001. Eight Malaysia Plan 2001-2005, Percetakan Nasional Malaysia Berhad, Kuala Lumpur Branch, Malaysia.
[5] Keyser,W.De., and Peeters,P., 1996. A note on the use of PROMETHEE multicriteria methods, European Journalof Operational Research 89, 457-461.
[6] Macharis,C., Springael, J., Brucker, K., and Verbeke,A., 2004. PROMETHEE and AHP: The design of operational synergies in multicriteria analysis. Strengthening PROMENTHEE with ideas of AHP, European Journal ofOperational Research 153, 307-317.
[7] MINT, 2000. Integrated Waste Management and Thermal Oxidation Plant, NST Quaterly, Malaysian Institute For
Nuclear Technology Research (MINT), Bangi, Malaysia.
[8] Nasir, H., Sulaiman, W., and Rakmi A.R., 1998. Issues and Problems of Solid Waste Management in Malaysia.
Towards the Next Two Decades, Ed. Nordin,H., Lizuryaty Azrina Abd. and Ibrahim Komoo. UKM, Bangi.
[9] Roy, B. and Vanderpooten, D., 1997, An Overview on The European school of MCDA: Emergence, basic featuresand current works, European Journal of Operational Research 99, 26-27.
[10] Roy, B. and Vincke,Ph., 1984. Relational systems of preference with one or more pseudo-criteria: Some new concepts
and results, Management Science 30, 1323-1335.
[11] Saaty,T.L., 1990. The Analytic Hierarchy Process, RWS Publications, Pittsbugh.
[12] The Star, 2000. Incinerators, a Burning Question, Daily News, Malaysia.
[13] USEPA, 2004. Municipal Solid Waste, US Enviromental Protection Agency, http://www.epa.gov/epaoswer/nonhw/muncpl/faq.htm[14] Vincke,Ph., 1992. Multicriteria Decision-Aid, John Wiley and Sons, Chichester, New York.
[15] Zaman, H.Z, 1992. Actual Siltation of Landfill Site and Improvement Design for Sanitary Landfill in Malaysia,
National Seminar on Municipal and Industrial Waste and Industrial Management and Technology, 18-19 February
1992, Kuala Lumpur. Cited in Abdul et al. 1996.

19