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Int. J. Mathematics in Operational Research, Vol. 1, No. 3, 2009

An interactive decision support system for implementing sustainable relocation strategies for adaptation to climate change: a multi-objective optimisation approach Sajjad Zahir* Decision Sciences and Information Systems, Faculty of Management, University of Lethbridge, Lethbridge, Alberta T1K 3M4, Canada Fax: +1 403 329 2038 E-mail: [email protected] *Corresponding author

Ruhul Sarker School of Information Technology and Electrical Engineering, University of New South Wales, Australian Defence Force Academy, Northcott Drive, Canberra 2600, Australia Fax: +61 2 626 88581 E-mail: [email protected]

Ziaul Al-Mahmud Lethbridge Community Network, Lethbridge, Alberta T1J 4C9, Canada Fax: +1 403 329 2038 E-mail: [email protected] Abstract: Global warming may cause low-lying areas to be inundated because of frequent flooding and rising sea levels. It may further intensify dehydration of semi-arid zones. Such environmental impacts may require planned relocation of a section of population and force others to adapt to these evolving situations. In this article, we discuss a multi-objective optimisation approach for deciding what fraction of a population will be relocated to another location and what fraction of it may be retained for effective adaptation to climate change. We consider various costs, people’s preferences and priorities of planning objectives in a goal programming model and illustrate the concept with the design of a decision support system for interactive analysis of complex multifaceted environmental decisions. Keywords: adaptation; AHP; analytic hierarchy process; climate change; DSS; decision support system; goal programming; interface; multi-objective; optimisation; planned relocation.

Copyright © 2009 Inderscience Enterprises Ltd.

A multi-objective optimisation approach

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Reference to this paper should be made as follows: Zahir, S., Sarker, R. and Al-Mahmud, Z. (2009) ‘An interactive decision support system for implementing sustainable relocation strategies for adaptation to climate change: a multi-objective optimisation approach’, Int. J. Mathematics in Operational Research, Vol. 1, No. 3, pp.326–350. Biographical notes: Sajjad Zahir is a Professor of Management (Decision Sciences and Information Systems) at the University of Lethbridge, Alberta, Canada. He received his PhD and two Masters Degrees from the University of Oregon, Eugene, USA. In addition, he obtained a B Sc (Honours) and an MSc from the University of Dhaka, Bangladesh. His current research interests are in the analytic hierarchy process, DSS and intelligent systems, and the internet technologies. He has published in European Journal of Operational Research, Canadian Journal of Administrative Sciences, Journal of the Operational Research Society, Journal of American Society for Information Science, Int. J. Information Technology and Decision Making, Internet Research: Electronic Networking Applications and Policy, Journal of Computer and Information Systems, Int. J. Operations and Quantitative Management, INFOR, Int. J. Management and Decision Making, Asia-Pacific Journal of Operational Research, Int. J. Logistics Systems and Management, Journal of American Academy of Business and also in several physics journals. Ruhul A. Sarker obtained his PhD in Operations Research (1991) from DalTech (former TUNS), Dalhousie University, Halifax, Canada. Currently, he is a Senior Lecturer in Operations Research at the School of Information Technology and Electrical Engineering (ITEE), University of New South Wales (UNSW), ADFA Campus, Canberra, Australia. Before joining UNSW@ADFA in 1998, he worked with Monash University and Bangladesh University of Engineering and Technology. He has published 150+ refereed technical papers in international journals, edited reference books and conference proceedings. He is the lead author of the book ‘Optimization Modelling: A Practical Approach’ published by Taylor and Francis in 2007. He has edited six reference books and several proceedings, and served as Guest Editors and Technical Reviewers for a number of international journals. He is the Editor of the Bulletin of the Australian Society for Operations Research. His research interests include applied operations research and evolutionary optimisation. Ziaul Al-Mahmud obtained his BSc in Computer Science from the University of Lethbridge, Alberta, Canada in 2007 and presently is working as the System Support Associate with the Lethbridge Community Network. Previously, he worked with Industry Canada and as a Student Research Assistant at the Faculty of Management, University of Lethbridge. He co-authored a paper (on wireless network simulation) which was published in Journal of Computer and Information Systems.

1

Introduction

Various activities undertaken by humanity have been affecting the ecosystem over a long period of time. However, nothing has been more serious than the emission of greenhouse gases (GHG) and deforestation that have been causing global warming to a degree that threatens to change the terrestrial climate for many years to come. The potential impact

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S. Zahir, R. Sarker and Z. Al-Mahmud

of climate change has been extensively studied by many local, national and international experts and concerned public groups, resulting in the latest document produced by Intergovernmental Panel on Climate Change (IPCC, 2007). Numerous studies (see Munasinghe and Swart (2005) and references therein) have documented the probable impacts due to climate change on various parts of the world and have suggested steps for mitigating GHG emission and adapting to environmental conditions due to climate change. Although mitigation measures are vitally important for controlling emissions, in this article we focus on specific adaptation strategies (Munasinghe and Swart, 2005) to enable sustainable development efforts. The environmental policy makers have to understand the limitations of mitigation and need novel approaches in actions and ideas for successful adaptation to climate change (Pielke et al., 2007). Global warming may cause vast low-lying coastal areas, many densely populated, to be inundated; some areas become frequently prone to flooding; reduce precipitation in some already arid and semi-arid lands. These phenomena inevitably will adversely affect the socio-economic conditions of many communities exerting additional stress on their health and welfare. Among a wide variety of strategies discussed in various forums, documents and publications, relocation and planned retreat/migration have been mentioned as well as an adaptation strategy. A large-scale cross-boundary migration may not be a feasible solution mainly due to continued debate about the societal costs and benefits of labour mobility (Brown, 2007). Such an idea of relaxed immigration for environmental refugees is likely to face strong resistance from developed countries. However, partial redistribution/relocation of settlements within a country (or region) should be seriously considered as a sustainable approach as opposed to total migration. It promotes continued efforts in pursuit of new or existing opportunities for the common good of a society by a section of the population who would adapt to climate change with added global support in a sustainable manner. Mathematical and operational research techniques have been used in analysing, understanding and solving environmental problems. Recently, Wang, Fang and Hipel (2008) applied a mathematical programming technique to a large-scale water allocation problem in the South Saskatchewan River Basin located in southern Alberta, Canada. They combined two approaches called, the priority-based maximal multi-period network flow method and lexicographic minimax water shortage ratios technique with game theoretic approaches to achieve optimal economic reallocation of water resources. Leightner and Inoue (2008) used a new analytic technique, bi-directional reiterative truncated projected least squares method, to assess climate’s effect on pollution abatement. Yin, Cohen and Huang (2000) focuses on methodological developments in research for studying climate change impacts and regional sustainable development in the Mackenzie basin impact study in Canada using analytic hierarchy process (AHP) and goal programming. They also incorporated inputs from various stakeholder groups such as environmental activists, industries, natives, agricultural interest groups and transport representatives. In this article, we use goal programming and the AHP for analysing optimal relocation strategies for adaptation to climate change by incorporating various costs, preferences and priorities of planning objectives. We present the mathematical modelling techniques within the framework of a sustainable relocation decision support system (SRDSS). Research interests in environmental issues have evolved from the mathematical modelling approaches into computer-based decision support system (DSS) as well


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(Turban, Aronson and Liang, 2004). Blecic, Cecchini and Pusceddu (2008) recently presented a multi-objective evaluation model and its related software tool for project selection and prioritisation in strategic urban and territorial planning. Körner and Van Starten (2008) discussed a DSS for helping GHG emission management. Sullivan, Gitten and Moskowitz (1997) recently evaluated some other selected environmental DSS software. For a detailed survey of numerous DSS applications, see Eom and Kim (2006). Rest of the article is organised as follows. A brief literature review of AHP and goal programming approach is presented in Section 2. A short background to climate change, adaptation and relocation strategies are given in Section 3; Section 4 describes system design issues including the mathematical model, database and user interface in which the SRDSS is demonstrated with selected screen shots and by explaining various functionalities of the system and future research directions and conclusions are presented in Section 5.

2

Multi-objective optimisation: goal programming and analytic hierarchy process approach

We formulate the problem as a goal programming model (Schniederjans, 1995) using the AHP (Saaty, 1980, 1990) for assigning cardinal weights for goal objectives. Recently, Vaidya and Kumar (2006) provided literature review of many AHP applications while critically analysing 27 of 150 referred application papers published in highly reputed international journals. Liberatore and Nydick (2008) reviewed 50 articles that used the AHP in medical and healthcare decision-making applications. After reviewing articles published in international journals from 1997 to 2006, Ho (2008) identified five tools (mathematical programming, quality function deployment, meta-heuristics, SWOT analysis and data envelopment analysis) that are commonly combined with the AHP in applications. He asserted that the integrated AHPs were better than the stand-alone AHP. The AHP and variations of linear programming techniques have been used together since the 1980s to solve various problems. Srinivasan (1973) used paired comparisons to produce weights for a multi-attribute problem. Sinuany-Stern (1984) used the AHP for determining preferences in a multi-goal budget allocation problem for a university. Gass (1986, 1987) and Gass et al. (1988) also used the AHP for determining priorities and weights for large-scale linear goal programmes applied to military personal planning. Arbel (1993) presented a multiobjective linear programming algorithm using the AHP to generate ‘locally relevant scaling coefficients’. Then, he applied them to the projected gradients produced by a variant of Karmarkar’s interior-point algorithm known as the affine-scaling primal algorithm. Stannard, Zahir and Rosenbloom (2006) formulated and solved an airlift capacity planning problem of the Canadian Air Force combining a sequential multiobjective mixed integer programming model with the AHP by extending the earlier work by Stannard (1993). Recently, there are several applications (Pan, 1996; Pan and Yan, 1999; Badri, 1999, 2001; Sylla and Wen, 2002) of the AHP in the context of goal programming to solve problems such as facility location-allocation, quality control and information technology investment evaluation. The AHP also has been used with linear programming in human

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resource allocation decisions (Saaty and Peniwati, 1996). Korpela and Lehmusvaara (1999) and Korpela et al. (2001) considered a customer-service oriented supply chain design problem in which the AHP and mixed integer programming are used together. They considered an environment where the customers had access to a number of facilities implying that the facilities were in close proximity. In their approach, they first calculated customers’ priorities that are later used as inputs to the integer programming model. Radasch and Kwak (1998) used the AHP in a zero-one goal programming model for a large-scale military sales decision with offset planning. Kwak, Lee and Kim (2005) developed a mixed integer goal programming model in which the pre-emptive priority ordering is established by the AHP in order to facilitate the advertising media selection process. Combined goal programming–AHP approach has been applied in myriad of other domains such as sustainable urban energy-environment management (Bose and Anandalingam, 1996), cost drivers selection in activity-based costing (Schniederjans and Garvin, 1997), information resource planning for a health care system (Lee and Kwak, 1999), supply chain optimisation with sustainability (Zhou, Cheng and Hua, 2000), maintenance strategy selection (Bertolini and Bevilacqua, 2006), optimal nuclear fuel cycle selection (Kim, Lee and Lee, 1999) and computer-integrated manufacturing cycle selection (Yurdakul, 2004). Zahir and Sarker (2008, in press) recently used a combined AHP–goal programming approach for optimising location decisions in environmental planning and supply chain management. Many recent applications of AHP in environmental studies have been reported as well. For example, in the mitigation of GHG study, Yedla and Shrestha (2003) considered three alternative transport options (4-stroke 2-wheelers, CNG cars and CNG buses) for Delhi, India and prioritised them taking into account different stakeholders through an AHP analysis based on six different criteria – energy saving potential, emission reduction potential, cost of operation, availability of technology, adaptability of the option and barriers to implementation. Santisirisomboon et al. (2005) investigated 15 research areas of impact, adaptation and vulnerability to global climate change as well as GHG mitigation that have been proposed for Thailand in order to strengthen its research basis to cope with climate change problems. The AHP was applied to calculate the importance index of each area with respect to four judgmental criteria. Individual inputs from each stakeholder group were aggregated using the weighted geometric mean method and determined the overall ratings for the research areas.

3

Climate change, adaptation and relocation

3.1 Global warming and challenges for human living conditions Vulnerability of a population is determined by its exposure to an environmental risk and its adaptive capacity (Adger et al., 2003). While climate change can affect the Earth (Houghton et al., 2001) in many forms (see IPCC, 2007); in the present research, we specifically focus on three types of risks impacted by climate change: worsening environmental conditions in arid and semi-arid zones due to warmer temperatures and reduced precipitation (type A), worsening sustainability in flood-prone zones due to frequent and irregular occurrence of flooding (type B) and prolonged periods of


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inundation of the coastal zones due to rising sea levels (type C). Historically, people have resorted to migration as a strategy for adaptation to each of types A–C risks (see McLeman and Smit (2006) for a brief review and references therein for a better understanding of migration behaviours). In the context of the Indian subcontinent, Gupta et al. (2006) recently investigated how extended periods of aridity and droughts at 5000– 4000 cal years budget objective seemed to have triggered human migration eastward towards the Ganga plain. Other scenarios of temporary labour migration during climatic stress (e.g. drought) have been discussed by Hampshire and Randall (1999) and Deshingkar and Start (2003). In the recent context of climate change, some researchers (McLeman and Smit, 2006; Brown, 2007) have suggested that climate change will become an increasingly important driver of migration in the coming decades. One oftquoted source estimates that as many as 200 million people will be displaced by 2050 (Myers, 2002, 2005).

3.2 Migration and planned resettlement Most of these studies mentioned unplanned migration of population as a means of escaping degrading living conditions. McLeman and Smit (2006) developed a conceptual model of the relationship between climate change and household migration decisionmaking. Their model was meant for unplanned migration and it combined the ‘vulnerability approach’ with a concept based on household endowments of cultural, economic and social capital (Adger, 2000; Adger et al., 2002). However, in this article we focus on planned relocation (resettlement or retreat) of population groups as a sustainable strategy applicable to types A–C risks. In some extreme cases, full-scale migration may sooner or later become the only adaptive option (Hay and Beniston, 2001). We emphasise that in many situations an entire affected population may not have to be moved en masse; rather a selective resettlement of sections of populations may enhance the adaptive capacity of the remaining part of the population. Not only so, with the passage of time, such an approach may even encourage the return of migrants to the affected locations as the adaptation technologies and processes become more accepted and institutionalised. Reduced population load on a community will lighten the pressure on limited resources and enhance manageability of the adaptive capacity of a community. Each affected location may not have to be totally abandoned as new economic opportunities will emerge. For example, increased fishing (in a cage or using traditional means) may replace lost agricultural opportunities when low-lying coastal areas are inundated by rising sea levels; growing ducks, instead of chickens, may be a better choice (types B and C). Different species of livestock may be available for breeding and farming as temperature rises and water sources and land become further stressed (type A) due to climate change. Human beings have been adapting to such prolonged climatic variations for thousands of years. Pandey, Gupta and Anderson (2003) reported that during prolonged weakening of the monsoon during the Holocene were coincident with initial developments of ponds, reservoirs and other rainwater harvesting structures that might have served as an adaptation to climate change in northern India.

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Table 1

Some adaptation strategies applicable to situations of types A, B and C

Barriers against rising sea levels Elevated housing infrastructure (e.g. on pillars) Creating islands of high land segments and protecting them from erosion Redesigning crop mixes Using biotechnology to produce new types of drought- and salt-resistant plants and domestic animals Innovative aquaculture technology Producing multi-purpose fuel-efficient marine vehicles Using renewable energy for irrigation, temperature controlled housing Rainwater harvesting and storage facilities Water conserving utility systems

3.3 Conceptual foundation of the planned relocation model Our objective is to devise an optimal relocation plan to determine the number of families (‘who’ and ‘how many’) that have to be resettled at which locations (‘to where’). We consider several types of costs and incorporate family preferences (obviously influenced by social and cultural capitals) in the plan in a multi-criteria decision-making approach. Such an investigative study does not exist in current literature and is expected to encourage further research. Therefore, we expect that relocation strategies will become necessary and will require appropriate planning for achieving optimal objectives. We study a two-stage strategy. In the first stage, we optimise how many families will be resettled to which target areas from which affected locations. Then, in the second stage the plan will determine which particular families will be selected taking into various human and social–cultural considerations. In the latter stage, composition of a family in respect of number of elderly members, health condition of family members and number of children need to be considered in determining the priority for selecting a family for relocation. Each of the adaptation strategies (Table 1) will require investing resources (hence costs) to make them feasible and successful. In addition, to be successful, these strategies are supposed to be implemented within an adaptation policy framework (Burton and Lim, 2001). Similarly, relocation of any group to a new location will need resources for new housing, schooling, health care support; planning for retraining and financial support for setting up businesses or trades. Keeping these factors in mind, we design the SRDSS with detailed structures for its model base, database and user interface.

4

Designing the sustainable relocation decision support system: model base, database and user interface

The goal of this research was to build a DSS to help manage the relocation strategies for adaptation to climate change as discussed above. SRDSS is expected to suggest a ‘good’ feasible solution fulfilling multiple objectives. Hence, it would require integration with an optimising tool (i.e. for solving goal programming models) with a database containing socio-economic data, human preferences (HP), objective priorities and other model parameters. There should be a friendly user interface for facilitating navigation, solution generation, interactive change/update of data plus ‘what if’ and sensitivity analyses.


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The system was designed using the standard (Sprague, 1980) framework, where the key components are model base, database and user interface.

4.1 Mathematical model As stated earlier, we formulate the problem as a multi-objective optimisation problem using an AHP enhanced goal programming approach (Schniederjans, 1995). In a goal programming, we have deviational variables and aspiration levels for the goal objectives in addition to familiar decision variables and constraints of a linear programme. We consider the human relocation problem concerning N affected locations from where part of the population may have to be relocated to M target areas/sites (Figure 1). While relocating, in general, families have to be kept together. From the beginning, we consider average size of a family to be f in order to keep the problem simple. Current population (in number of average families) in ith affected location is popi; jth target location will be able to accommodate up to rcj new families. Socio-economic planners have estimated that the ith affected location will be able to sustain si average families based on new and possibly some existing opportunities where presumably si < popi. So as to make the planned relocation benefit all types of community members according to their common interests and professional objectives, we divide them into C categories. A category may be defined as a group of families having common interests for a particular type of job or business. Note that a relocated area may require more than one category of families. Let xicj be the number of families of category c relocated from location i to area j. Figure 1

Schematic diagram of the relocation problem

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Capacity limit at the target areas. For a given category, the total number of families relocated to any target area will be up to its capacity (climate change (CCcj)) in that category. So, we need the following constraint. N

¦x

icj

d CCcj ( j M , c C ).

(1)

i 1

Here,

¦

C c 1

rc j ( j M ) as we defined rcj earlier. It needs to be noted that some of

CC cj

the CCcj may be zeroes. Minimum requirements C

M

¦¦ x

icj

t MR i (i PL)

(2)

c 1 j 1

here, MRi, minimum number of families that must be relocated from location i; PL, a set of priority locations among the N locations set by the authority. This constraint ensures that the number of families (all categories) that would be relocated from priority location i to all areas j is at least equal to the minimum number set by the authority for that location. The value of MRi obviously cannot exceed (popi–si). Limit on number relocated. Not all families will be required (or even allowed) to relocate, as some should remain for exploring new opportunities and contributing to the local economy. There is an opportunity loss cost for having fewer than si families left at location i. This opportunity objective (OP) is given by, M

C

¦¦ x

icj

sdi sd i

popi si

i.

(3)

j 1 c 1

Here, sdi and sdi are deviational variables, and popi si is the aspiration level for this goal objective. Assuming this to an equality constraint, both the deviational variables are undesirable and thus will be minimised in the objective function. Limit on the number of available families. The affected population is also identified into the categories with PCic defined as number of people of category c at the affected location i. Obviously, N

C

¦¦ PC

ic

popi .

(4)

i 1 c 1

The following constraint guarantees the total number of people relocated from affected locations in different categories does not exceed the number of people in each category at the affected locations. M

¦x

icj

d PCic (i N , c C ).

j 1

It needs to be noted that some of the PCic may be zeroes.

(5)


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Preferences. We are interested in planned relocation or retreat of a community as a whole. Each affected location will produce a collective score for the target areas in order of preference for resettlement regarding their own judgment as to how well they will fit in a target location to the best of their liking, employability, skill-utilisation and future viability. Each family belonging to a particular category may score the target areas based on its preference, but all scores from each family belonging to a particular category will be aggregated and the target areas will be assigned a combined score representing the choices of the group as a whole. We define picj as the normalised preference of category c in location i for relocating to target area j. M

¦p

icj

1 (i N , c C ).

j 1

We define total number of people that are targeted to be relocated as G, N

¦ (pop

G

i

si ) .

(6)

i 1

Total preference should be a goal constraint (i.e. HP objective) 1 G

N

M

C

¦¦¦ x

icj

picj pd pd

P

(7)

i 1 j 1 c 1

such that the expected preference is at least equal to P and thus pd– is the undesirable deviational variable which will be minimised. P is estimated as follows. Let pic = average of top three priorities assigned by the people of category c at the affected location i to three of the possible target areas (we assume M 3). We identify them as ( picj )*** , ( picj )** and ( picj )* ( j M ) , and therefore, pic P

1ª ( picj )*** ( picj )** ( picj )* º¼ 3¬ 1 (NC)

N

C

¦¦ p

ic .

(8)

i 1 c 1

In an earlier application of the AHP to goal programming, Badri (2001) took the sum of three top priorities as the aspiration levels. We are softening the requirement here because it may not be possible to satisfy all requests for relocating to the most preferred locations due to lack of space and facilities. Costs tcij = transportation cost per average family from location i to target area j scij = settlement cost for settling each average family from location i to target area j aci = adaptation cost for enabling each family staying back at location i for adaptation. lci = loss of opportunity cost at location i per family is inflicted if any family is relocated from location i in excess of (popi–si).

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This is also equal to opportunity gain contributed by any family who decide to stay back at location i in excess of si families as initially planned. This is calculated as net additional contribution that a family would be able to make due to adaptation above their normal contribution that they could have made at the target areas if relocated. That is, if rc is the average economic contribution made by a family after being relocated to a target area, and nci is the economic contribution that can be made by a family at location i, then lci § nci – rc. Such a definition of the loss of opportunity cost is chosen for simplifying the formulation. Total cost is the sum of transportation, settlement, adaptation and loss of opportunity costs (i.e. if more than initially planned (popi–si) are relocated from location (i) minus any opportunity gain (i.e. if more than si families end up staying back at location (i). This budget objective (BP) is given by, N

M

C

¦¦¦

N

xicj (tcij scij )

i 1 j 1 c 1

¦ (sd

i

¦

aci (popi

i

sdi ) lci bd bd

M

C

j

c 1

¦¦ x

icj )

(9)

B

Our target is to keep the total cost less than or equal to the budgeted amount B and therefore bd+ is the undesirable deviational variable that will be minimised in the goal programming objective function. The budgeted amount B is estimated by taking into consideration the potential opportunity gain contributed by the si families who have initially planned to stay back at the affected location i. While trying to determine the optimum relocation decision with the above described multiple objectives, we emphasise that different objectives may have different priorities as in any goal programming problem. Let W1, W2, W3 be the relative priorities for HP, OP and BP, respectively. The deviational variables in Equations (3), (7) and (9) have different units and scales of magnitude. So as to bring them at par with each other, we divide them by P, B and G, respectively, in the goal programming objective function. The objective function is N

Min Z

W1 pd

/ P W2 bd

/ B W3

¦ (sd

i

sd i ) / G.

(10)

i 1

The AHP is a popular multi-criteria decision-making tool that is ideally suited for setting priorities for the goal objectives. It has been used in many applications in environmental and climate change research (Kiker et al., 2005). By searching ABI/INFORM and Web of Science™, authors have identified at least 50 articles published during the last few years in various areas of environmental research using the AHP. We consider the hierarchy (Figure 2) in respect of three criteria: human considerations (HC), economic considerations (EC) and technical considerations (TC). We use Expert Choice™ for computing the overall priorities of the alternatives (i.e. HP, OP and BP) after inputting ratio judgments via pairwise comparisons either by a single decision-maker or by a group of decision-makers that include all possible stakeholders.


337

Complete formulation of the relocation model N

Min Z W1 pd

/ P W2 bd

/ B W3

¦ (sd

i

sdi ) / G

(F1)

i 1

N

M

C

¦¦¦

N

¦

xicj (tcij scij )

i 1 j 1 c 1

¦ (sd

1 G

N

i

M

aci (popi

i

icj

picj pd pd

sd i )lci bd bd

M

C

j

c 1

¦¦ x

icj )

(F2)

B

C

¦¦¦ x

P

(F3)

i 1 j 1 c 1

M C

¦ ¦ xicj sd i sdi

j 1c 1

C

popi si

(i N )

(F4)

M

¦¦ x

t MR i (i PL)

(F5)

d CCcj ( j M , c C )

(F6)

d PCic (i N , c C )

(F7)

icj

c 1 j 1 N

¦x

icj

i 1 M

¦x

icj

j 1

Figure 2

Analytic hierarchy process for computing priorities of the goal objectives

4.2 Sample database: inputs to sustainable relocation decision support system Priorities are set by the planners for the three types of objectives preferably via a group decision-making environment. They were obtained via pairwise comparisons as per the

338


AHP and using Expert Choice™. For example, the ratio judgments about the objectives with respect to human consideration criteria are entered into Expert Choice™ as follows (Table 2). The criteria weights and the local priorities are given in Table 3. The numbers in the last column are used in the objective function of the goal programming model. SRDSS allows changing these weights interactively for ‘what if’ analysis. In the sample database used in SRDSS, we considered five affected locations from where families can be relocated to six target areas (i.e. N = 5, M = 6). The affected number of families (in thousands) are broken into three categories (i.e. C = 3) at the five locations and the accommodating capacities at the six target areas under different categories are given in Figure 3. This sample database is used as the default dataset. However, each input data element can be changed interactively for analysing any similar relocation decision problem via the user interface (Table 4). Table 2

Pairwise compare the relative importance of objectives with respect to human consideration HP

OP

BP

HP

–

3.0

2.0

OP

–

–

0.5

Incon: 0.01 Table 3

Criteria weights, local priorities and the aggregate relative priorities Criteria

Objectives

HC (0.547)

EC (0.190)

TC (0.263)

Aggregate

HP

0.540

0.413

0.460

0.495

OP

0.163

0.327

0.221

0.210

BP

0.297

0.260

0.319

0.295

Figure 3

Input sample data for sustainable relocation decision support system (see online version for colours)

Each number can be changed and saved in separate files.

A multi-objective optimisation approach Table 4

339

Default data used as sample data: category-wise breakdown of number of families at affected locations and target area capacities Categories (c)

Locations (i)

1

Categories (c) Total (popi) Areas (j)

2

3

1.5

2.5

5

Total

1

2

3

1

4

3

0

7

1

1

2

1.5

2

3.5

7

2

1

1

1

3

3

1

1.5

2.5

5

3

2

1

1

4

4

2.5

2

4.5

9

4

3

2

3

8

5

1

3

0

4

5

5

0

4

9

6

1

1

3

Total number families (thousands)

30

Table 5

5

Total number families (thousands)

36

Other parameters at the affected locations Affected location (i) 1

2

3

4

5

aci

18.5

25.5

32.5

19.5

27.5

million $ per 1000 families

lci

19

18

17

16.5

21

million $ per 1000 families

si

0.5

1.0

0.5

1.5

1.0

thousands

MRi

0

5.5

0

7.0

2.75

thousands

Table 6

Transportation and settlement costs (in parentheses) from affected locations to target areas

Affected location (i)

Target areas (j) 3

4

5

1

0.5 (13)

1

2 (20)

2

0.5 (12)

1 (10)

0.25 (18)

1 (17)

6

2

0.85 (14)

0.75 (9)

1.5 (16)

2 (25)

3 (30)

2 (25)

3

0.5 (16)

2.5 (21)

1.2 (18)

0.5 (19)

2.5 (15)

2 (25)

4

2.1 (12)

2 (31)

1 (21)

2.1 (20)

2 (21)

0.75 (14)

5

2.1 (20)

2 (22)

2 (19)

0.9 (11)

1.3 (17)

0.25 (17.5)

The adaptation cost (aci), loss of opportunity cost (lci), the number of families (si) planned to stay at location i, and the minimum number of families (MRi) that have to be relocated from location i are given in Table 5. N

G

¦ (pop i 1

i

si )

25.5 (thousands).

340 Table 7

S. Zahir, R. Sarker and Z. Al-Mahmud Relocation preferences of affected families Target area (j)

Categories (c)

Affected locations (i)

1

2

3

4

5

6

1

0.16

0.31

0.2

0.12

0.09

0.12

2

0.17

0.3

0.23

0.12

0.08

0.1

3

0.14

0.33

0.26

0.12

0.06

0.09

4

0.33

0.06

0.09

0.27

0.13

0.12

5

0.09

0.12

0.23

0.28

0.11

0.17

1

0.33

0.06

0.09

0.26

0.14

0.12

2

0.21

0.11

0.12

0.16

0.09

0.31

3

0.32

0.12

0.24

0.13

0.09

0.1

4

0.17

0.35

0.11

0.19

0.07

0.11

5

0.12

0.26

0.06

0.1

0.14

0.32

1

0.21

0.08

0.11

0.19

0.31

0.1

2

0.28

0.17

0.12

0.23

0.09

0.11

3

0.14

0.12

0.09

0.33

0.26

0.06

4

0.16

0.37

0.22

0.1

0.07

0.08

5

0.34

0.12

0.26

0.14

0.06

0.08

1

2

3

The transportation costs and settlement costs (in parentheses) from affected area i to target area j are given in Table 6 (in million $ per 1000 families). They are entered as sample inputs in the database as the default dataset and as noted earlier they can be interactively changed via the user interface. The preferences picj are obtained from the affected families are given in Table 7. From these preferences, P was calculated to be 0.236667 using Equation (8). The user interface was designed in VB.NET and the data were stored in text data files. We used LINGO 10 for optimising the model goal programming as it provided a library module for interfacing VB.NET application with LINGO 10 (we had to modify some part of the module to make our system to work properly). Data were read in from database into multi-dimensional arrays which were passed into LINGO 10 via pointers.

4.3 User interface Various controls of VB.NET were very useful in designing effective interface with excellent functionalities. The introductory screen of the interface is shown in Figure 4. The various sub-menu items of the menu tabs display the default data and various model parameters as they are loaded from the database. These screens also allow changing the input data before generating optimal decisions meeting various goal objectives subject to given objective priorities. For example, selecting ‘Affected area categories’ sub-menu item from ‘population’ menu item will open the screen in Figure 3 where each of the input data values can be changed (and later saved). The weights of the goal objectives can also be changed using the interface screen of Figure 5. SRDSS automatically readjust other weights if one is changed such that sum of all weights remain equal to one.


341

Figure 4

Introductory screen of sustainable relocation decision support system with menu and sub-menu items and buttons (see online version for colours)

Figure 5

Editable objective priorities obtained via an analytic hierarchy process analysis (see online version for colours)

Changing one priority automatically changes others such that total sum remains unity.

Selecting the button ‘Run Lingo’ from the mail screen (Figure 4), will opens a screen with solution-numbers using the updated input data as in Figure 6.

342 Figure 6

S. Zahir, R. Sarker and Z. Al-Mahmud Detailed output from sustainable relocation decision support system after optimisation by LINGO 10 (see online version for colours)

Each tab in the top bar opens further outputs.

The numbers in Figure 6 correspond to SRDSS using LINGO 10.0 to solve the goal programming problem assuming B = 200 (million $) and other default datasets as inputs. The goal programming solutions are as follows. Non-zero deviational variables are: pd– = 0.014, bd+= 277.38 and sd 4 0.50 . Total cost was $477.38 million. Selecting the tab XICJ, opens a screen with detailed optimal decisions of the relocation numbers. Selecting ‘RIJ’ from the screen in Figure 5, opens screen in Figure 7 giving the total number of families (all categories together) relocated with the following breakdown (total number was 25.00 thousand).

A multi-objective optimisation approach Figure 7

343

RIJ tab gives summarised results of the number of families relocated for all categories from each location to all target areas (see online version for colours)

4.4 Sensitivity analysis Selecting the ‘sensitivity’ button on the introductory screen (Figure 4) opens the screen in Figure 8. The various tools are for performing sensitivity analysis. The user can vary various costs incrementally (increasing or decreasing all costs of each type by a common factor, e.g. 10%). Also the goal reference values for the budget (B) and the target collective preference of the group of people (P) can be varied to see how sensitive the solutions are with respect such changes. All outputs are saved in clearly identified data files and are available for use (e.g. graphical analysis) in other software tools like MS Excel™. For example, in order to investigate the sensitivity of the solution with respect to various costs, we vary the transportation, adaptation, settlement and loss of opportunity costs one at a time by a common percentage and report the results in Figures 9 and 10 for the number of families relocated and the total cost, respectively. The results seem to

344


behave as expected. The given transportation, adaptation, loss of opportunity and settlement costs in the above example are termed as the base costs of each category. In our sensitivity analysis, we vary each category one at a time by changing all costs belonging to a category by a certain factor (say 90%) of the base costs. Figure 8

Screen for sensitivity analysis (see online version for colours)

All the costs of each category can be increased (decreased) by adjusting numbers in the pull-down item-list controls. For example changing 1.0 to 1.25 (0.75) implies increasing (decreasing) the costs by 25%. Similarly input values for B and P can be changed as well for ‘what if’ analysis. Figure 9

Variation of the total number of families relocated (see online version for colours)

A multi-objective optimisation approach Figure 10

345

Variation of the total cost (see online version for colours)

In Figure 9, we plot the total number of families transported against the change in base costs. The target (G) line represents the targeted number G (= 25.5 thousand). We see that as the transportation and loss of opportunity costs are increased, number of families relocated is decreased below the target (G) line (i.e. more families (i.e. greater than some si) are retained for adaptation as some of the sdi s become non-zeroes). But, as the adaptation cost increases, the number of families relocated is increased (as some of the sdi s become non-zeroes). We also note similar variation of total cost and number relocated with respect to transportation, settlement and adaptation cost changes (Figure 10). To be specific, for example, we notice that as the settlement cost is increased, more families are relocated and the total cost is increasing as well. Similarly, as the transportation cost increases, both the total cost and the number of families relocated go down slowly. However, for the loss of opportunity cost variation, the behaviour is opposite. If the loss of opportunity cost is increased, both the number of families relocated and the total cost decreases (i.e. more families stay back). It should be noted that in our example the average transportation, settlement, adaptation and loss of opportunity costs are 1.44, 18.28, 24.70 and 18.30 thousands of $ per family, respectively, and their relative magnitudes are important for setting optimal policies. However, the most interesting result from this example is that if we can make families adapt so that they can contribute more economically (i.e. increased loss of opportunity cost), more families would stay and at the same time the total overall cost will be lower. This is a strong case for more efforts for adaptation strategies as far as this numerical example is concerned.

346


This observed sensitivity of the optimal solutions for the objectives with respect to various model parameters justifies the need for the computer-based interactive SRDSS so that the decision-makers can perform ‘what if’ analysis before recommending any relocation strategy.

5

Future research and conclusions

We have discussed the potential impacts of climate change to human livability and economic conditions in areas (e.g. low-lying and semi-arid regions in the world) that might be adversely affected by climate change. To maintain sustainable economic development, we propose adaptation to climate change in the present locations (for some) and relocation to other potential areas with different environment and opportunities (for others) as a long-term solution for the people of the affected regions. To make adaptation a success, part of the population must be prepared to adapt to new or different work opportunities and living conditions and others may have to be relocated in a planned way to new locations that require accepting different working and environmental conditions. In this article, we have developed a methodology to find the fraction of people who would be relocated and who would stay in an optimal manner. The methodology considers the preference of individual families so as to reduce social costs, preferences of authority for meeting the planning objectives, and accommodation capacities at the present locations and new areas in order to determine which group of families will be relocated and where. It also incorporates various costs such as relocation cost, adaptation cost, transportation cost, settlement cost and loss of opportunity costs. A combined goal programming and AHP approach is used to formulate the multi-objective optimisation problem. The concept was illustrated with the design of SRDSS. Using a sample dataset, the system generated optimal solutions suggest that the level of relocation is dependent on new opportunities and costs of relocation, settlement, transportation and adaptation. In this article, we have proposed a methodology to make the relocation decisions for the future adaptation to climate change. As we cannot collect data from real world scenarios yet, we may continue to study the model by applying this methodology to various types of simulated data using the SRDSS. This work can be further extended by imposing new constraints such as family-wise accommodation needs, profession, job type and schooling preferences for children. Similarly, more criteria and conditions can be considered for overall preference calculation. Since the problem is expected to be sensitive to the actual values of many parameters involved, we have highlighted our research by designing the SRDSS, an interactive software tool. It will be extremely useful in practical and dynamic situations.

Acknowledgements One of the authors (SZ) was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC). We express thanks to anonymous reviewers for their useful comments.


347

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