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Assigning priorities for maintenance, repair and refurbishment in managing a municipal housing stock
European Journal of Operational Research 138 (2002) 380–391 www.elsevier.com/locate/dsw
Assigning priorities for maintenance, repair and refurbishment in managing a municipal housing stock Carlos A. Bana e Costa a
b
a,*
, Rui Carvalho Oliveira
b
Instituto Superior T ecnico (SAEG/CEG-IST), Technical University of Lisbon and Department of Operational Research, London School of Economics (LSE), Houghton Street, London WC2A 2AE, UK Instituto Superior T ecnico (DEC/CESUR), Technical University of Lisbon, Av. Rovisco Pais, 1049-001 Lisbon, Portugal
Abstract The municipality of Lisbon owns a large housing stock that requires maintenance, repair and refurbishment. Taken together, these activities imply a financial effort each year that clearly exceeds the available budget, and therefore it is critical that the decisions on which sub-set of potential activities should be carried out in each coming year are based on sound analysis and evaluation. The design and construction process of a model to assist the Lisbon Municipality to assign priorities to these activities is described. The M A C B E T H approach was extensively used, in an interactive and constructive process, to derive the value functions associated with each criterion and their respective weights, reflecting municipal policies and their officials preferences and attitudes. The paper also presents the procedure used to determine multidimensional reference-profiles that define urgency categories, enabling to assign each potential action to one of these categories. Finally, a specific model was defined to aggregate elemental building jobs in ‘‘packages’’, when there are arguments (in terms of cost reduction, action coherence, urban environment impact synergies, etc.) that favour their joint execution under a single contract. 2002 Published by Elsevier Science B.V. Keywords: Assignment; Multiple criteria analysis;
MACBETH;
Municipal management
1. Introduction The municipality of Lisbon owns a large housing stock of over 22,000 dwellings, many of which are quite old and require maintenance, repair and refurbishment. ‘‘Departamento de Conservacß~ ao de Edificios e Obras Diversas’’
*
Corresponding author. E-mail addresses: [email protected] (C.A. Bana e Costa), [email protected] (R.C. Oliveira).
(DCEOD) is the municipal department that manages this housing stock. DCEOD regularly receives requests from tenants asking for building work to be done on their dwellings. These requests impose a financial burden each year that clearly exceeds the budget available. Therefore it is critical that decisions on priorities for these works are based on sound and objective criteria which reflect policies defined and pursued by the municipality. There is a clear need for a decision support tool that avoids the pitfalls and drawbacks associated with ‘‘adhoc’’ decisional processes where the pressures
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that are subjectively perceived at the moment and/ or conjuncture restrictions determine choices. In this context, the Director of DCEOD asked for our expertise to develop a multicriteria system to support decisions on the establishment of a programme for maintenance, repair and refurbishment in the buildings owned by the Lisbon municipality. At the initial meetings with DCEOD, it was agreed that this system should: • be conceived and developed interactively not only with DCEOD technicians, but also directly with the CML politicians responsible for determining municipal housing policies; and • bring objectivity, transparency and consistency into the process of allocating scarce resources to building works. Since allocation of public funds is a sensitive political issue, equity and the fair treatment of tenants’ requests must be ensured. There is also a need for legitimacy, in the sense that decisions made should be politically defensible, so such a system should provide the means of objectively and unambiguously justifying the chosen courses of action. The preliminary study of multicriteria applications in similar contexts – see, for example, Roy et al. (1986) and Vansnick (1989) – offered insights which lead to the development of an effective approach to the problem. This paper describes the process of designing the system that itself consists of two stages: • the definition of a priority index, reflecting the degree of urgency of each potential building job (PJ), and the assignment, based on its priority value, of the PJ to a category for action: absolute urgency, urgent, medium priority, and low priority; and • the aggregation of PJs into ‘‘packages of jobs’’ when there are arguments (in terms of cost reduction, action coherence, urban environment impact, etc.) that justify their joint execution under a single contract. The paper is organised as follows. Section 2 presents the structure of the multicriteria assignment model developed to determine the priority index for each PJ. Section 3 describes the procedure used to define the four urgency categories and to assign each PJ to one of these categories. The specific model, based on a synergy scoring system,
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for aggregating elemental PJs into ‘‘packages of jobs’’, is presented in Section 4, and this is followed by the conclusions section.
2. The priority assignment model 2.1. General overview and structuring From the very beginning of the process, and in the face of the budget constraint, it was clear to all the key actors involved, by invoking equity arguments, that the full set of defects (‘‘pathologies’’) in a building should not be taken as a single action. Therefore, a PJ was formally defined as a minimal set of actions to correct defects, identified in a dwelling or building, that satisfies two conditions. Firstly the actions have to be carried out together, and secondly it is considered technically, socially and economically acceptable that they are undertaken independently of other possible actions in the same building. Therefore, the full set of defects of a given building might generate one or more PJs, defined by the DCEOD engineers. Fig. 1 depicts an overview of the structure of the multicriteria value model. The model starts by defining the degree of urgency of every single PJ, and, later on, to assign it to one, and only one, of four ordered urgency categories: ‘‘absolute urgency’’, ‘‘urgent’’, ‘‘medium priority’’, and ‘‘low priority’’. The definition of these categories is presented in Section 3.1. The multicriteria model is of the additive type (cf. Belton, 1999). The corresponding value tree, shown in Fig. 2, was constructed through intensive interaction (interviews and work sessions) with technical officials (the Director and senior engineers of DCEOD) and political staff (the town councillor responsible for this area and two of his principal advisers). The value tree comprises a coherent (i.e., consensual, operational, exhaustive, and non-redundant) family of nine fundamental points of view (FPsV) – the criteria to evaluate the urgency of each PJ. They are grouped in three ‘‘areas of concern’’, and two of them (FPV6 and FPV7) are specified by more elementary concerns. The cost was not considered by the technical officials as a criterion in the
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Fig. 1. General overview of the priority assignment model.
evaluation of the urgency of the PJs. This was quite convenient for us, as analysts, because it avoided significant preference dependency
problems. Indeed, the costs were only incorporated later, in the model for package construction (see Section 4). As far as possible to appraise objectively the impacts of the PJs in terms of the nine FPsV, a descriptor (i.e., an ordered set of plausible impact levels) was associated with each FPV. The descriptors of FPsV 1–7 are qualitative constructed scales (see the example in Table 1), whereas the descriptors of the FPsV 8 and 9 are direct quantitative attributes.
Table 1 Constructed scale of ‘‘Historical and cultural values’’ (FPV4) Impact level
Description
N4 N3
PJ in a classified building PJ in a building located within the area of protection of a classified building PJ in a building located in an area of high historical or architectonic interest PJ in a common building
N2 Fig. 2. Value tree.
N1
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2.2. Construction of the value model To measure how attractive (or unattractive) each PJ is, in terms of a relative priority for action, for each FPV a 0–100 cardinal value function was constructed for its descriptor. A value function serves to translate impacts into value scores, so indicating the attractiveness relative to each other of the impacts within a FPV. The M A C B E T H approach (Bana e Costa and Vansnick, 1997, 1999) was extensively used. Its use is illustrated for FPV4; the full process is described in detail in Bana e Costa et al. (1997). The DCEOD Director was asked to consider the four levels of impact in Table 1, and to judge qualitatively the difference in attractiveness between each two levels x and y, such that x is preferred to y in terms of priority for action because of historical and cultural values. This was done by asking her to choose one of the six M A C B E T H semantic categories ‘‘very weak’’, ‘‘weak’’, ‘‘moderate’’, ‘‘strong’’, ‘‘very strong’’, or ‘‘extreme’’ as a qualitative measure of the difference of attractiveness between x and y. Her answers are shown in the matrix of Fig. 3, together with the value scale proposed by M A C B E T H and
Fig. 3. Matrix of judgements and the respective scale.
MACBETH
the differences in value corresponding to the qualitative judgements. Then, a discussion was launched about the cardinality of the scale, by visually comparing proportions between intervals (differences of values) in the thermometer scale (see Fig. 4). The DCEOD Director considered that equal distances between N4 and N3, on one hand, and N2 and N1, on the other hand, adequately represent her feeling that there is a similar difference in attractiveness between those two pairs of impact levels. However, she felt that the distance between N3 and N2 should be smaller, when compared with the
Fig. 4. Discussing the cardinality of the scale.
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difference between N4 and N3. When appropriately questioned about the proportion between these two differences, she answered that the increase in value from N3 to N4 was about twice the increase in value from N2 to N3. Consequently, the values of N2 and N3 were adjusted to 40 and 60, respectively, as shown in Fig. 4. Note that M A C B E T H shows the limits within which a value can be changed without violating the consistency of the matrix of qualitative judgements. The group process of weighting the criteria was held in a two day ‘‘decision conferencing’’ (Phillips, 1988) type session, supported by M A C B E T H . Although we cannot divulge the weights, for confidentiality reasons, we think that it is worthwhile to describe the main phases of the assessment. The group of key players (the town councillor, his two advisors, and our DM) was asked first to consider nine reference PJs, each one corresponding to the swing from the least attractive to the most attractive impact levels in each criterion, and rank them in terms of urgency for action. Once an agreement on the ranking of the swings was reached, the group was then asked to pair-wise compare the difference of overall attractiveness (‘‘very weak’’, ‘‘weak’’, . . ., or ‘‘extreme’’) of each two swings in terms of urgency for action. Finally, the consistency of the full matrix of judgements was tested, the corresponding M A C B E T H weights presented to the group and adjusted interactively until an agreement was obtained on a final weighting scale. With the value functions and the weights, the additive evaluation model could then be used to associate an overall score – the priority index – to any PJ. However, a validation of the model was required; this is discussed in the last paragraph of Section 3.2 and more thoroughly in Section 3.3.
priority; C) – low priority. The first of these categories (absolute urgency) covers situations where there is a high risk of structural collapse of the building and/or of serious physical injury to the tenants, or the housing conditions are extremely bad. In this case, the corresponding PJs are directly assigned to the absolutely urgent category, as there is no need to go through the multicriteria evaluation model (described in Section 2) since it is imperative to act immediately to correct these extremely serious cases. For the other three categories, the assignment is based on the priority index associated with each PJ by the evaluation model described in the previous section. To separate the urgency categories and define the assignment rule, the following thresholds, expressed in terms of the priority index, were adopted: Priority index > 45 ) UrgentðCþþ Þ 35 6 Priority index 6 45 ) Medium PriorityðCþ Þ Priority index < 35 ) Low PriorityðC Þ:
The methodology, to establish these thresholds, is based on the identification of ‘‘reference profiles’’ (defined in terms of the levels of impact on all the nine FPsV) for which the DM hesitates in deciding to which category the profile should be assigned. To identify these ‘‘reference profiles’’, fictitious PJs, as close as possible to real situations, were constructed. A committee of experts, formed by the Director and senior engineers of DCEOD, thereafter called the DM, were asked to assign (holistically) each of them to one of the urgency categories. Two alternative procedures, bottom-up and top-down, were used and are described below.
3.2. Identifying reference-profiles 3. Assigning PJs to urgency categories 3.1. Urgency categories and assignment rule As mentioned in Section 2.1, four pre-defined ordered categories of action priority (‘‘urgency categories’’) were considered (see Fig. 1): C" – absolutely urgent; C++ – urgent; C+ – medium
The Bottom-up procedure consists of the following stages (see also Fig. 5): • Start with the fictitious PJ (A0) characterised by the lowest level of impact in every FPV. • At each stage, select a new FPV and raise the corresponding impact of A0 to its highest level. . .
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Fig. 5. Two procedures to identify reference profiles.
. . .until the DM assigns the resulting profile to the urgency category above the previous assignment category. . . . . .then, lower the impact level for the last added FPV until the DM hesitates about deciding to which category the PJ should be assigned. The priority index, computed by the evaluation model, of the resulting PJ defines the threshold separating the two urgency categories. The Top-down procedure consists of the following stages (see also Fig. 5): • Start with a fictitious PJ (B0) characterised by the highest level of impact in every FPV. • At each stage, select a new FPV and lower the corresponding impact of B0 to its lowest level. . .
. . .until the DM assigns the resulting profile to the urgency category below the previous assignment category. . . . . .then, raise the impact level for the last added FPV until the DM hesitates about deciding to which category the PJ should be assigned. The priority index to the resulting PJ defines the threshold separating the two urgency categories. Several reference profiles were constructed using these two procedures through various combinations of the FPsV. Not all these reference profiles led to the same threshold values but, whenever discrepancies occurred, the reflections and discussions about the reasons were very enlightening and served to broaden our views of the problem and to fine-tune some formulations and
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parameters of the multicriteria evaluation model. As a result of these exercises, the numerical values of the thresholds were finally adopted and proved to be quite robust.
Holistic Assignment
8 (62)
8
2
3.3. Validation As a final stage, the whole assignment model consisting of the priority index evaluation model and the rule for assignment to an urgency category, was submitted to a validation test. Seventeen PJs (real cases selected from among DCEOD’s portfolio of requests for building works) were submitted to the committee of experts who were asked to rank them, in terms of urgency of action, and to assign each of them to one of the urgency categories. The committee was also asked to assess the impact of each PJ in every FPV (using the corresponding descriptors) and the model was run to compute the priority index and to assign each PJ to one of the urgency categories. The results of the experts and model assignments are depicted in Fig. 6, where each PJ is represented by a circle (with an identification number inscribed) and their relative position represents (from bottom to top) an increasing level of urgency. The figures in brackets represent the priority index computed by the evaluation model. As can be observed in Fig. 6, the model assignment and ranking compares quite favourably with the experts assignment and ranking, the only exceptions being for the PJs 14, 15, 16 and 17, indicated with darkened circles in the picture. After some discussion about these discrepancies, we concluded that the low priority assigned by the experts to these PJs (particularly in the case of PJ number 15) was because the experts did not take into proper consideration some political issues. The experts had a natural tendency to overlook political issues and to concentrate on the technical and social aspects. After due consideration of all the aspects, it was agreed that the model assignments were probably more appropriate particularly if town councillors were involved in the decision process. Thus, the model was considered to be a valid decision support tool.
Model Assignment (scores)
2 (53)
++
Urgent C
12
12 (49)
9 7
45 11 5
Medium Priority
13
C
6
7
11 (45)
9
5 (43)
13
6 (41)
+
15 (43
17 (37) 16 (36)
4 3
4
3 (35)
14 (35)
35 1 (34)
14
1 10
15 16
Low Priority C-
10 (31)
17
Fig. 6. Validating the assignment model.
4. Model for package construction 4.1. Overview ‘‘Package’’ is understood to be a set of PJs that are carried out under a single contract. This aggregation of PJs into a package can be justified whenever it results in advantages, particularly: • cost reduction, because of economies of scale that the contractors are presumed to incorporate into their tenders; • reduction of administrative effort by CML departments (associated with the whole process of preparing, launching, awarding and controlling contracts) and an increase in inspection and monitoring efficiency; • rationalisation of PJs within the same building; • promotion of fair treatment among tenants; and • a contribution to improving city’s image resulting from improvements to several nearby buildings. Also this encourages improvements by private owners to neighbouring buildings.
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It is not an easy task to evaluate these advantages when forming a package of PJs. The simple issue of cost reduction cannot be evaluated directly and immediately. In the DCEOD’s budgeting procedure, the estimated costs are merely the result of multiplying quantities of work by the corresponding standard unit prices since there is no information which will enable an estimate of the cost reduction resulting from the effects of scale. We therefore opted to make an indirect evaluation of the advantages of aggregating the PJs into packages. This indirect evaluation uses a score allocation system which evaluates the degree of synergy resulting from the aggregation. This ‘‘synergy scoring’’ system is described later. At this stage, it is sufficient to understand that if a pair of PJs is awarded a given number of synergy points, this means that there are advantages in aggregating those PJs into a single package, and the greater the advantage, the higher the synergy score. Nevertheless, there are also factors that may work against the aggregation of PJs into a single package. Such as, for example, when the PJs are located in different areas (geographical divisions governed by DCEOD) or when the total cost of the package is too high (with regard to budget restrictions or other considerations). This issue of the disadvantages of aggregation is discussed later, and is dealt with in the model through ‘‘veto conditions’’ which prevent the aggregation of PJs into packages. The process of constructing packages of PJs seeks to deal with both the advantages and disadvantages of aggregation. It is an iterative process that starts from an initial seed of the most urgent PJ. At each stage, from the set of unallocated, non-vetoed PJs, the PJ with the greatest synergy index with respect to the package being formed is added to the package. Once a package is complete, the processes is re-started using a new initial nucleus and continued until either all PJs have been allocated or there is no gain to be made in allocating the remaining PJs into packages. This process is generically represented in Fig. 7, and its fundamental aspects are described below.
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Fig. 7. Package-formation procedure.
4.2. Selection of candidate PJs During the first stage, a selection of the candidate PJs for the formation of packages is made from amongst all the PJs for which an estimate of cost already exists. This procedure is justified when budget constraints (or other types of restrictions) make it impossible to carry out all the PJs and therefore it is possible right from the start to exclude low-priority PJs, thereby simplifying the package-formation process. This selection is based on the urgency categories. When budget constraints (or other types of restrictions) apply, the first PJs to be excluded are those assigned to the low priority category (C)). Other criteria also may be used during this selection stage. For example, if it is intended that packages will only be formed for
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a given geographical area, only the PJs in this area will be selected. Selection may be even further restricted if, for example, in addition to the previous criteria, PJs must be of the same theme (type of works to be undertaken). Using this selection process, a set of candidate PJs is created, and it is important to note that each one will be given a level of urgency by the application of the multicriteria evaluation model, thereby making it possible to rank the PJs in decreasing order of urgency. The set of candidate PJs (to form packages) resulting from this process may be further reduced by eliminating the PJs which must remain isolated (in what we will call ‘‘absolute veto analysis’’). This absolute veto may result from: • the application of one of the pre-defined veto criteria (which are presented in the following section). For example, if the budget for the isolated PJ already exceeds the maximum value fixed for the budget of the packages to be formed, it is evident that the PJ cannot be aggregated with any other; • the (discretionary) imposition of isolating this PJ for reasons which are not considered in the model, but which may assume a particular relevance within specific contexts.
4.3. Veto analysis At any stage of the package-formation process, veto analysis is used to prevent the addition of a given PJ to a package (made up of one or more PJs during a previous stage) when this aggregation results in disadvantages that appear to outweigh any potential advantages. The following factors are veto conditions: (a) The maximum value of the total budget for a package; this parameter, defined (from the start) for each run of the model, may result from a range of conditions such as: • levels of autonomy for launching invitations to tender; • questions of opportunity linked to seasonal or one-off availability of funds; • the (remaining) capacity of contractors to submit tenders (because of actual workload).
(b) PJs belonging to different DCEOD’s geographical areas. (c) Filling of the quota for PJs in each DCEOD’s area and/or project inspection and monitoring capacity. (d) Thematic incompatibility between the candidate PJ and those which already belong to the package being formed. (e) Other types of incompatibility (type of construction, age of building, etc.). (f) The aggregation to the package of the candidate PJ leads to unfair treatment among tenants. It is intended that there should be flexibility in the way values are given to the parameters that define the veto conditions, so that different scenarios can be analysed and sensitivity tests may be performed. This is the case, for example, for the maximum value of the global budget for the package which, depending on the context, may be defined at different levels.
4.4. Evaluation of synergies As stated in Section 4.1, the desirability of adding a given PJ to a package being formed is evaluated by means of allocating ‘‘synergy points’’. These points are intended to reflect the advantages resulting from the aggregation. The scoring system is based on the definition of some typified situations (A–G, in Table 2). Each situation has been attributed a certain number of synergy points, as set out in Table 2. This scoring system was obtained using the M A C B E T H method. It is based on assessments, made by the Director and senior engineers of DCEOD, of the relative desirability of each of the situations set out in the table. It is important to highlight that these synergy scores are cumulative. Thus, if for example, a candidate PJ is located in the same building, has the same theme, and contributes towards inspection and monitoring efficiency, the total synergy score (which we will call synergy index) is 247ð¼ 100 þ 100 þ 47Þ. At each stage of the process for forming the packages, the synergy that results from adding
C.A. Bana e Costa, R.C. Oliveira / European Journal of Operational Research 138 (2002) 380–391 Table 2 Scoring system Description of situation
Synergy points
A. The candidate PJ is located in the same building as at least one PJ already included in the package B. The candidate PJ has the same theme as at least one PJ already included in the package C. The addition of the candidate PJ to the package contributes significantly to equitable treatment among tenants D. The candidate PJ is located in the same street as at least one PJ already included in the package E. The candidate PJ is located in the same urban area as at least one PJ already included in the package F. The addition of the candidate PJ to the package contributes significantly to increasing inspection and monitoring efficiency G. The addition of the candidate PJ to the package contributes significantly to the image of the city, and has didactic and catalytic effects by inducing private owners to intervene in neighbouring buildings (only applicable when the PJ is on the exterior of a building)
100
100
100
79
63
47
37
each one of the (still isolated) candidate PJs to the package being formed, is evaluated with the scoring system. The PJ with the highest synergy index is selected. In the event of a tie (an equal synergy index), preference will be given to the PJ with the greatest urgency, and in the case that there is still a tie, to the one with the highest ratio: priority score/ cost. When the selected PJ has been included in the package being formed, it may be necessary to reevaluate the synergy index associated to the remaining candidate PJs, since the contents of the package being formed have changed and so the synergy index needs to be updated. Prior to this updating of the synergy index, it is also envisaged that a forced aggregation of a candidate PJ to the package being formed may be made to, without checking whether this PJ has the highest synergy index. This procedure (called ‘‘analysis of absolute acceptance’’) will enable the
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model to handle situations that are not defined in the scoring system. For example, the case of a candidate PJ which corresponds to the ‘completion’ of a building (or street, or neighbourhood) that is, if it covers, together with the other PJs already included in packages, all the defects in that building (or street, or neighbourhood). At any stage, if none of the candidate PJs has a positive synergy index, which means that there are no advantages in adding any of the remaining PJs to the package being formed, the process for constructing the package is terminated. A new package will therefore be formed, starting with the remaining isolated PJ with the greatest priority index. It should be stressed that, when budget constraints become active, the procedure above described may lead to the selection of PJs (through their inclusion in a package) with priority indexes lower than others that are excluded. This is justified by the fact that additional dimensions of the problem (such as economies of scale, or thematic or geographic proximity) have been incorporated in the model. These complexities could not be handled within the priority assignment model that deals only with individual PJs. However, when the decision maker thinks this is inappropriate or unfair, the veto condition f) comes into play and avoids the aggregation, to the package being formed, of a PJ with a lower priority index that those that will be excluded by the addition of the candidate PJ. Furthermore, since this is a heuristic procedure, there is no assurance that the resulting packages constitute the ‘‘most desirable’’ solution. By varying the procedure parameters (namely those that define the veto conditions), different scenarios can be analysed therefore reducing the risk of adopting less attractive courses of action. A full validation of the package construction procedure could not be carried out since there was not a sufficiently large and comprehensive computer database of PJs with which to perform the tests. Nevertheless, the experiments carried out with a limited database showed that the procedure performed satisfactorily, producing what were considered good solutions. We look forward to the implementation of a Municipal
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Information System that will provide data on PJs to fully validate (or to adjust and fine tune) the procedure.
5. Conclusions We have presented in this paper a real-world application, in Municipal Management, of Decision Analysis concepts, techniques, methodological issues, and, above all, modelling creativity (cf. Clemen, 1996, Chapter 6). Our work as facilitators was a rich interactive consulting path throughout: • the structuring of the problem, • the design of a multicriteria sorting model, including an innovative questioning procedure enabling to determine multidimensional reference-profiles that define urgency categories, and finally, to complete the resource allocation model, • the design of a specific assignment model, to aggregate elemental PJs in ‘‘packages’’, involving the design of a synergy scoring system combined with a particular type of veto analysis. Throughout the various stages of this decisionanalysis process, we were pleased and motivated by the positive reactions of the technical and political actors involved, and by their enthusiastic participation. At the end, they emphasised the learning capabilities of the methodology, and said that the discussions offered them a deeper insight about the various features of the problem that would change their way of making choices in the future. Indeed, the meta-model developed is already informally used for deciding which requests for building works should be given priority in each year. It has not yet been implemented as a decision support system because the development of a Municipal Information System is required to provide the indispensable inputs for automatic assignment. The implementation of this information system will create the necessary conditions to complete the validation of the model, namely in what concerns the package construction procedure that could not be fully tested due to the unavailability of a large enough and comprehensive database on PJs. This constitutes the main limitation of the work produced.
This paper does not aim to introduce new fundamental or theoretical advances. It focuses on the analyst’s ability to capture the main features of the decision process and to develop an approach well suited to the decisional context. It also illustrates the value of exploring established concepts, methodologies and techniques with a creative and innovative spirit. As a final conclusion, and based upon Phillips’ conceptualisation, we want to stress that we are convinced that we have supported the construction of a requisite decision model: ‘‘{. . .} requisite in the sense that everything required to solve the problem is either included in the model or can be simulated in it {. . .}. The process of building the model is iterative and consultative, and when no new intuitions emerge about the problem, the model is considered to be ‘requisite’ {. . .}. In short, requisite decision modelling treats problem solving as a dynamic process in which all relevant actors become clearer about the problem and develop a deeper understanding of it over time’’ (Phillips, 1982, p. 304). Acknowledgements The work described in this paper was developed under a contract between Instituto Superior Tecnico and the Lisbon Municipality. The authors are indebted to the former DCEOD’s Director, Maria de Lourdes Alvarez, for her agreement to report the case and her commitment all throughout its development. Last but not the least, the authors thank Susan Powell and two anonymous referees for their valuable comments on an earlier version of this paper. References Bana e Costa, C.A., Vansnick, J.C., 1997. Applications of the M A C B E T H approach in the framework of an additive aggregation model. Journal of Multi-Criteria Decision Analysis 6 (2), 107–114. Bana e Costa, C.A., Vansnick, J.C., 1999. The M A C B E T H approach: Basic ideas, software and an application. In: Meskens, N., Roubens, M. (Eds.), Advances in Decision Analysis. Kluwer Academic Publishers, Dordrecht, pp. 131– 157.
C.A. Bana e Costa, R.C. Oliveira / European Journal of Operational Research 138 (2002) 380–391 Bana e Costa, C.A., Oliveira, R.C., Alvarez, M.L., 1997. ~es SMAI: Sistema multicriterio de avaliacß~ao de intervencßo num parque habitacional municipal. In: Bezelga, A., Borges Leit~ ao, A. (Eds.), A Avaliacß~ao do Imobiliario. APAE, ~es de Engenharia, LisAssociacß~ ao Portuguesa de Avaliacßo bon, pp. enharia–122. Belton, V., 1999. Multi-criteria problem structuring and analysis in a value theory framework. In: Gal, T., Stewart, T., Hanne, T. (Eds.), Multicriteria Decision Making, Advances in MCDM – Models, Algorithms, Theory, and Applications. Kluwer Academic Publishers, Dordrecht, pp. 12-1–12-32. Clemen, R., 1996. Making Hard Decisions: An Introduction to Decision Analysis, second ed. Duxbury Press, Boston. Phillips, L.D., 1982. Requisite decision modelling: A case study. Journal of the Operational Research Society 33 (4), 303–311.
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Assigning priorities for maintenance, repair and refurbishment in managing a municipal housing stock Carlos A. Bana e Costa a
b
a,*
, Rui Carvalho Oliveira
b
Instituto Superior T ecnico (SAEG/CEG-IST), Technical University of Lisbon and Department of Operational Research, London School of Economics (LSE), Houghton Street, London WC2A 2AE, UK Instituto Superior T ecnico (DEC/CESUR), Technical University of Lisbon, Av. Rovisco Pais, 1049-001 Lisbon, Portugal
Abstract The municipality of Lisbon owns a large housing stock that requires maintenance, repair and refurbishment. Taken together, these activities imply a financial effort each year that clearly exceeds the available budget, and therefore it is critical that the decisions on which sub-set of potential activities should be carried out in each coming year are based on sound analysis and evaluation. The design and construction process of a model to assist the Lisbon Municipality to assign priorities to these activities is described. The M A C B E T H approach was extensively used, in an interactive and constructive process, to derive the value functions associated with each criterion and their respective weights, reflecting municipal policies and their officials preferences and attitudes. The paper also presents the procedure used to determine multidimensional reference-profiles that define urgency categories, enabling to assign each potential action to one of these categories. Finally, a specific model was defined to aggregate elemental building jobs in ‘‘packages’’, when there are arguments (in terms of cost reduction, action coherence, urban environment impact synergies, etc.) that favour their joint execution under a single contract. 2002 Published by Elsevier Science B.V. Keywords: Assignment; Multiple criteria analysis;
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Municipal management
1. Introduction The municipality of Lisbon owns a large housing stock of over 22,000 dwellings, many of which are quite old and require maintenance, repair and refurbishment. ‘‘Departamento de Conservacß~ ao de Edificios e Obras Diversas’’
*
Corresponding author. E-mail addresses: [email protected] (C.A. Bana e Costa), [email protected] (R.C. Oliveira).
(DCEOD) is the municipal department that manages this housing stock. DCEOD regularly receives requests from tenants asking for building work to be done on their dwellings. These requests impose a financial burden each year that clearly exceeds the budget available. Therefore it is critical that decisions on priorities for these works are based on sound and objective criteria which reflect policies defined and pursued by the municipality. There is a clear need for a decision support tool that avoids the pitfalls and drawbacks associated with ‘‘adhoc’’ decisional processes where the pressures
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that are subjectively perceived at the moment and/ or conjuncture restrictions determine choices. In this context, the Director of DCEOD asked for our expertise to develop a multicriteria system to support decisions on the establishment of a programme for maintenance, repair and refurbishment in the buildings owned by the Lisbon municipality. At the initial meetings with DCEOD, it was agreed that this system should: • be conceived and developed interactively not only with DCEOD technicians, but also directly with the CML politicians responsible for determining municipal housing policies; and • bring objectivity, transparency and consistency into the process of allocating scarce resources to building works. Since allocation of public funds is a sensitive political issue, equity and the fair treatment of tenants’ requests must be ensured. There is also a need for legitimacy, in the sense that decisions made should be politically defensible, so such a system should provide the means of objectively and unambiguously justifying the chosen courses of action. The preliminary study of multicriteria applications in similar contexts – see, for example, Roy et al. (1986) and Vansnick (1989) – offered insights which lead to the development of an effective approach to the problem. This paper describes the process of designing the system that itself consists of two stages: • the definition of a priority index, reflecting the degree of urgency of each potential building job (PJ), and the assignment, based on its priority value, of the PJ to a category for action: absolute urgency, urgent, medium priority, and low priority; and • the aggregation of PJs into ‘‘packages of jobs’’ when there are arguments (in terms of cost reduction, action coherence, urban environment impact, etc.) that justify their joint execution under a single contract. The paper is organised as follows. Section 2 presents the structure of the multicriteria assignment model developed to determine the priority index for each PJ. Section 3 describes the procedure used to define the four urgency categories and to assign each PJ to one of these categories. The specific model, based on a synergy scoring system,
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for aggregating elemental PJs into ‘‘packages of jobs’’, is presented in Section 4, and this is followed by the conclusions section.
2. The priority assignment model 2.1. General overview and structuring From the very beginning of the process, and in the face of the budget constraint, it was clear to all the key actors involved, by invoking equity arguments, that the full set of defects (‘‘pathologies’’) in a building should not be taken as a single action. Therefore, a PJ was formally defined as a minimal set of actions to correct defects, identified in a dwelling or building, that satisfies two conditions. Firstly the actions have to be carried out together, and secondly it is considered technically, socially and economically acceptable that they are undertaken independently of other possible actions in the same building. Therefore, the full set of defects of a given building might generate one or more PJs, defined by the DCEOD engineers. Fig. 1 depicts an overview of the structure of the multicriteria value model. The model starts by defining the degree of urgency of every single PJ, and, later on, to assign it to one, and only one, of four ordered urgency categories: ‘‘absolute urgency’’, ‘‘urgent’’, ‘‘medium priority’’, and ‘‘low priority’’. The definition of these categories is presented in Section 3.1. The multicriteria model is of the additive type (cf. Belton, 1999). The corresponding value tree, shown in Fig. 2, was constructed through intensive interaction (interviews and work sessions) with technical officials (the Director and senior engineers of DCEOD) and political staff (the town councillor responsible for this area and two of his principal advisers). The value tree comprises a coherent (i.e., consensual, operational, exhaustive, and non-redundant) family of nine fundamental points of view (FPsV) – the criteria to evaluate the urgency of each PJ. They are grouped in three ‘‘areas of concern’’, and two of them (FPV6 and FPV7) are specified by more elementary concerns. The cost was not considered by the technical officials as a criterion in the
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Fig. 1. General overview of the priority assignment model.
evaluation of the urgency of the PJs. This was quite convenient for us, as analysts, because it avoided significant preference dependency
problems. Indeed, the costs were only incorporated later, in the model for package construction (see Section 4). As far as possible to appraise objectively the impacts of the PJs in terms of the nine FPsV, a descriptor (i.e., an ordered set of plausible impact levels) was associated with each FPV. The descriptors of FPsV 1–7 are qualitative constructed scales (see the example in Table 1), whereas the descriptors of the FPsV 8 and 9 are direct quantitative attributes.
Table 1 Constructed scale of ‘‘Historical and cultural values’’ (FPV4) Impact level
Description
N4 N3
PJ in a classified building PJ in a building located within the area of protection of a classified building PJ in a building located in an area of high historical or architectonic interest PJ in a common building
N2 Fig. 2. Value tree.
N1
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2.2. Construction of the value model To measure how attractive (or unattractive) each PJ is, in terms of a relative priority for action, for each FPV a 0–100 cardinal value function was constructed for its descriptor. A value function serves to translate impacts into value scores, so indicating the attractiveness relative to each other of the impacts within a FPV. The M A C B E T H approach (Bana e Costa and Vansnick, 1997, 1999) was extensively used. Its use is illustrated for FPV4; the full process is described in detail in Bana e Costa et al. (1997). The DCEOD Director was asked to consider the four levels of impact in Table 1, and to judge qualitatively the difference in attractiveness between each two levels x and y, such that x is preferred to y in terms of priority for action because of historical and cultural values. This was done by asking her to choose one of the six M A C B E T H semantic categories ‘‘very weak’’, ‘‘weak’’, ‘‘moderate’’, ‘‘strong’’, ‘‘very strong’’, or ‘‘extreme’’ as a qualitative measure of the difference of attractiveness between x and y. Her answers are shown in the matrix of Fig. 3, together with the value scale proposed by M A C B E T H and
Fig. 3. Matrix of judgements and the respective scale.
MACBETH
the differences in value corresponding to the qualitative judgements. Then, a discussion was launched about the cardinality of the scale, by visually comparing proportions between intervals (differences of values) in the thermometer scale (see Fig. 4). The DCEOD Director considered that equal distances between N4 and N3, on one hand, and N2 and N1, on the other hand, adequately represent her feeling that there is a similar difference in attractiveness between those two pairs of impact levels. However, she felt that the distance between N3 and N2 should be smaller, when compared with the
Fig. 4. Discussing the cardinality of the scale.
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difference between N4 and N3. When appropriately questioned about the proportion between these two differences, she answered that the increase in value from N3 to N4 was about twice the increase in value from N2 to N3. Consequently, the values of N2 and N3 were adjusted to 40 and 60, respectively, as shown in Fig. 4. Note that M A C B E T H shows the limits within which a value can be changed without violating the consistency of the matrix of qualitative judgements. The group process of weighting the criteria was held in a two day ‘‘decision conferencing’’ (Phillips, 1988) type session, supported by M A C B E T H . Although we cannot divulge the weights, for confidentiality reasons, we think that it is worthwhile to describe the main phases of the assessment. The group of key players (the town councillor, his two advisors, and our DM) was asked first to consider nine reference PJs, each one corresponding to the swing from the least attractive to the most attractive impact levels in each criterion, and rank them in terms of urgency for action. Once an agreement on the ranking of the swings was reached, the group was then asked to pair-wise compare the difference of overall attractiveness (‘‘very weak’’, ‘‘weak’’, . . ., or ‘‘extreme’’) of each two swings in terms of urgency for action. Finally, the consistency of the full matrix of judgements was tested, the corresponding M A C B E T H weights presented to the group and adjusted interactively until an agreement was obtained on a final weighting scale. With the value functions and the weights, the additive evaluation model could then be used to associate an overall score – the priority index – to any PJ. However, a validation of the model was required; this is discussed in the last paragraph of Section 3.2 and more thoroughly in Section 3.3.
priority; C) – low priority. The first of these categories (absolute urgency) covers situations where there is a high risk of structural collapse of the building and/or of serious physical injury to the tenants, or the housing conditions are extremely bad. In this case, the corresponding PJs are directly assigned to the absolutely urgent category, as there is no need to go through the multicriteria evaluation model (described in Section 2) since it is imperative to act immediately to correct these extremely serious cases. For the other three categories, the assignment is based on the priority index associated with each PJ by the evaluation model described in the previous section. To separate the urgency categories and define the assignment rule, the following thresholds, expressed in terms of the priority index, were adopted: Priority index > 45 ) UrgentðCþþ Þ 35 6 Priority index 6 45 ) Medium PriorityðCþ Þ Priority index < 35 ) Low PriorityðC Þ:
The methodology, to establish these thresholds, is based on the identification of ‘‘reference profiles’’ (defined in terms of the levels of impact on all the nine FPsV) for which the DM hesitates in deciding to which category the profile should be assigned. To identify these ‘‘reference profiles’’, fictitious PJs, as close as possible to real situations, were constructed. A committee of experts, formed by the Director and senior engineers of DCEOD, thereafter called the DM, were asked to assign (holistically) each of them to one of the urgency categories. Two alternative procedures, bottom-up and top-down, were used and are described below.
3.2. Identifying reference-profiles 3. Assigning PJs to urgency categories 3.1. Urgency categories and assignment rule As mentioned in Section 2.1, four pre-defined ordered categories of action priority (‘‘urgency categories’’) were considered (see Fig. 1): C" – absolutely urgent; C++ – urgent; C+ – medium
The Bottom-up procedure consists of the following stages (see also Fig. 5): • Start with the fictitious PJ (A0) characterised by the lowest level of impact in every FPV. • At each stage, select a new FPV and raise the corresponding impact of A0 to its highest level. . .
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Fig. 5. Two procedures to identify reference profiles.
. . .until the DM assigns the resulting profile to the urgency category above the previous assignment category. . . . . .then, lower the impact level for the last added FPV until the DM hesitates about deciding to which category the PJ should be assigned. The priority index, computed by the evaluation model, of the resulting PJ defines the threshold separating the two urgency categories. The Top-down procedure consists of the following stages (see also Fig. 5): • Start with a fictitious PJ (B0) characterised by the highest level of impact in every FPV. • At each stage, select a new FPV and lower the corresponding impact of B0 to its lowest level. . .
. . .until the DM assigns the resulting profile to the urgency category below the previous assignment category. . . . . .then, raise the impact level for the last added FPV until the DM hesitates about deciding to which category the PJ should be assigned. The priority index to the resulting PJ defines the threshold separating the two urgency categories. Several reference profiles were constructed using these two procedures through various combinations of the FPsV. Not all these reference profiles led to the same threshold values but, whenever discrepancies occurred, the reflections and discussions about the reasons were very enlightening and served to broaden our views of the problem and to fine-tune some formulations and
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parameters of the multicriteria evaluation model. As a result of these exercises, the numerical values of the thresholds were finally adopted and proved to be quite robust.
Holistic Assignment
8 (62)
8
2
3.3. Validation As a final stage, the whole assignment model consisting of the priority index evaluation model and the rule for assignment to an urgency category, was submitted to a validation test. Seventeen PJs (real cases selected from among DCEOD’s portfolio of requests for building works) were submitted to the committee of experts who were asked to rank them, in terms of urgency of action, and to assign each of them to one of the urgency categories. The committee was also asked to assess the impact of each PJ in every FPV (using the corresponding descriptors) and the model was run to compute the priority index and to assign each PJ to one of the urgency categories. The results of the experts and model assignments are depicted in Fig. 6, where each PJ is represented by a circle (with an identification number inscribed) and their relative position represents (from bottom to top) an increasing level of urgency. The figures in brackets represent the priority index computed by the evaluation model. As can be observed in Fig. 6, the model assignment and ranking compares quite favourably with the experts assignment and ranking, the only exceptions being for the PJs 14, 15, 16 and 17, indicated with darkened circles in the picture. After some discussion about these discrepancies, we concluded that the low priority assigned by the experts to these PJs (particularly in the case of PJ number 15) was because the experts did not take into proper consideration some political issues. The experts had a natural tendency to overlook political issues and to concentrate on the technical and social aspects. After due consideration of all the aspects, it was agreed that the model assignments were probably more appropriate particularly if town councillors were involved in the decision process. Thus, the model was considered to be a valid decision support tool.
Model Assignment (scores)
2 (53)
++
Urgent C
12
12 (49)
9 7
45 11 5
Medium Priority
13
C
6
7
11 (45)
9
5 (43)
13
6 (41)
+
15 (43
17 (37) 16 (36)
4 3
4
3 (35)
14 (35)
35 1 (34)
14
1 10
15 16
Low Priority C-
10 (31)
17
Fig. 6. Validating the assignment model.
4. Model for package construction 4.1. Overview ‘‘Package’’ is understood to be a set of PJs that are carried out under a single contract. This aggregation of PJs into a package can be justified whenever it results in advantages, particularly: • cost reduction, because of economies of scale that the contractors are presumed to incorporate into their tenders; • reduction of administrative effort by CML departments (associated with the whole process of preparing, launching, awarding and controlling contracts) and an increase in inspection and monitoring efficiency; • rationalisation of PJs within the same building; • promotion of fair treatment among tenants; and • a contribution to improving city’s image resulting from improvements to several nearby buildings. Also this encourages improvements by private owners to neighbouring buildings.
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It is not an easy task to evaluate these advantages when forming a package of PJs. The simple issue of cost reduction cannot be evaluated directly and immediately. In the DCEOD’s budgeting procedure, the estimated costs are merely the result of multiplying quantities of work by the corresponding standard unit prices since there is no information which will enable an estimate of the cost reduction resulting from the effects of scale. We therefore opted to make an indirect evaluation of the advantages of aggregating the PJs into packages. This indirect evaluation uses a score allocation system which evaluates the degree of synergy resulting from the aggregation. This ‘‘synergy scoring’’ system is described later. At this stage, it is sufficient to understand that if a pair of PJs is awarded a given number of synergy points, this means that there are advantages in aggregating those PJs into a single package, and the greater the advantage, the higher the synergy score. Nevertheless, there are also factors that may work against the aggregation of PJs into a single package. Such as, for example, when the PJs are located in different areas (geographical divisions governed by DCEOD) or when the total cost of the package is too high (with regard to budget restrictions or other considerations). This issue of the disadvantages of aggregation is discussed later, and is dealt with in the model through ‘‘veto conditions’’ which prevent the aggregation of PJs into packages. The process of constructing packages of PJs seeks to deal with both the advantages and disadvantages of aggregation. It is an iterative process that starts from an initial seed of the most urgent PJ. At each stage, from the set of unallocated, non-vetoed PJs, the PJ with the greatest synergy index with respect to the package being formed is added to the package. Once a package is complete, the processes is re-started using a new initial nucleus and continued until either all PJs have been allocated or there is no gain to be made in allocating the remaining PJs into packages. This process is generically represented in Fig. 7, and its fundamental aspects are described below.
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Fig. 7. Package-formation procedure.
4.2. Selection of candidate PJs During the first stage, a selection of the candidate PJs for the formation of packages is made from amongst all the PJs for which an estimate of cost already exists. This procedure is justified when budget constraints (or other types of restrictions) make it impossible to carry out all the PJs and therefore it is possible right from the start to exclude low-priority PJs, thereby simplifying the package-formation process. This selection is based on the urgency categories. When budget constraints (or other types of restrictions) apply, the first PJs to be excluded are those assigned to the low priority category (C)). Other criteria also may be used during this selection stage. For example, if it is intended that packages will only be formed for
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a given geographical area, only the PJs in this area will be selected. Selection may be even further restricted if, for example, in addition to the previous criteria, PJs must be of the same theme (type of works to be undertaken). Using this selection process, a set of candidate PJs is created, and it is important to note that each one will be given a level of urgency by the application of the multicriteria evaluation model, thereby making it possible to rank the PJs in decreasing order of urgency. The set of candidate PJs (to form packages) resulting from this process may be further reduced by eliminating the PJs which must remain isolated (in what we will call ‘‘absolute veto analysis’’). This absolute veto may result from: • the application of one of the pre-defined veto criteria (which are presented in the following section). For example, if the budget for the isolated PJ already exceeds the maximum value fixed for the budget of the packages to be formed, it is evident that the PJ cannot be aggregated with any other; • the (discretionary) imposition of isolating this PJ for reasons which are not considered in the model, but which may assume a particular relevance within specific contexts.
4.3. Veto analysis At any stage of the package-formation process, veto analysis is used to prevent the addition of a given PJ to a package (made up of one or more PJs during a previous stage) when this aggregation results in disadvantages that appear to outweigh any potential advantages. The following factors are veto conditions: (a) The maximum value of the total budget for a package; this parameter, defined (from the start) for each run of the model, may result from a range of conditions such as: • levels of autonomy for launching invitations to tender; • questions of opportunity linked to seasonal or one-off availability of funds; • the (remaining) capacity of contractors to submit tenders (because of actual workload).
(b) PJs belonging to different DCEOD’s geographical areas. (c) Filling of the quota for PJs in each DCEOD’s area and/or project inspection and monitoring capacity. (d) Thematic incompatibility between the candidate PJ and those which already belong to the package being formed. (e) Other types of incompatibility (type of construction, age of building, etc.). (f) The aggregation to the package of the candidate PJ leads to unfair treatment among tenants. It is intended that there should be flexibility in the way values are given to the parameters that define the veto conditions, so that different scenarios can be analysed and sensitivity tests may be performed. This is the case, for example, for the maximum value of the global budget for the package which, depending on the context, may be defined at different levels.
4.4. Evaluation of synergies As stated in Section 4.1, the desirability of adding a given PJ to a package being formed is evaluated by means of allocating ‘‘synergy points’’. These points are intended to reflect the advantages resulting from the aggregation. The scoring system is based on the definition of some typified situations (A–G, in Table 2). Each situation has been attributed a certain number of synergy points, as set out in Table 2. This scoring system was obtained using the M A C B E T H method. It is based on assessments, made by the Director and senior engineers of DCEOD, of the relative desirability of each of the situations set out in the table. It is important to highlight that these synergy scores are cumulative. Thus, if for example, a candidate PJ is located in the same building, has the same theme, and contributes towards inspection and monitoring efficiency, the total synergy score (which we will call synergy index) is 247ð¼ 100 þ 100 þ 47Þ. At each stage of the process for forming the packages, the synergy that results from adding
C.A. Bana e Costa, R.C. Oliveira / European Journal of Operational Research 138 (2002) 380–391 Table 2 Scoring system Description of situation
Synergy points
A. The candidate PJ is located in the same building as at least one PJ already included in the package B. The candidate PJ has the same theme as at least one PJ already included in the package C. The addition of the candidate PJ to the package contributes significantly to equitable treatment among tenants D. The candidate PJ is located in the same street as at least one PJ already included in the package E. The candidate PJ is located in the same urban area as at least one PJ already included in the package F. The addition of the candidate PJ to the package contributes significantly to increasing inspection and monitoring efficiency G. The addition of the candidate PJ to the package contributes significantly to the image of the city, and has didactic and catalytic effects by inducing private owners to intervene in neighbouring buildings (only applicable when the PJ is on the exterior of a building)
100
100
100
79
63
47
37
each one of the (still isolated) candidate PJs to the package being formed, is evaluated with the scoring system. The PJ with the highest synergy index is selected. In the event of a tie (an equal synergy index), preference will be given to the PJ with the greatest urgency, and in the case that there is still a tie, to the one with the highest ratio: priority score/ cost. When the selected PJ has been included in the package being formed, it may be necessary to reevaluate the synergy index associated to the remaining candidate PJs, since the contents of the package being formed have changed and so the synergy index needs to be updated. Prior to this updating of the synergy index, it is also envisaged that a forced aggregation of a candidate PJ to the package being formed may be made to, without checking whether this PJ has the highest synergy index. This procedure (called ‘‘analysis of absolute acceptance’’) will enable the
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model to handle situations that are not defined in the scoring system. For example, the case of a candidate PJ which corresponds to the ‘completion’ of a building (or street, or neighbourhood) that is, if it covers, together with the other PJs already included in packages, all the defects in that building (or street, or neighbourhood). At any stage, if none of the candidate PJs has a positive synergy index, which means that there are no advantages in adding any of the remaining PJs to the package being formed, the process for constructing the package is terminated. A new package will therefore be formed, starting with the remaining isolated PJ with the greatest priority index. It should be stressed that, when budget constraints become active, the procedure above described may lead to the selection of PJs (through their inclusion in a package) with priority indexes lower than others that are excluded. This is justified by the fact that additional dimensions of the problem (such as economies of scale, or thematic or geographic proximity) have been incorporated in the model. These complexities could not be handled within the priority assignment model that deals only with individual PJs. However, when the decision maker thinks this is inappropriate or unfair, the veto condition f) comes into play and avoids the aggregation, to the package being formed, of a PJ with a lower priority index that those that will be excluded by the addition of the candidate PJ. Furthermore, since this is a heuristic procedure, there is no assurance that the resulting packages constitute the ‘‘most desirable’’ solution. By varying the procedure parameters (namely those that define the veto conditions), different scenarios can be analysed therefore reducing the risk of adopting less attractive courses of action. A full validation of the package construction procedure could not be carried out since there was not a sufficiently large and comprehensive computer database of PJs with which to perform the tests. Nevertheless, the experiments carried out with a limited database showed that the procedure performed satisfactorily, producing what were considered good solutions. We look forward to the implementation of a Municipal
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Information System that will provide data on PJs to fully validate (or to adjust and fine tune) the procedure.
5. Conclusions We have presented in this paper a real-world application, in Municipal Management, of Decision Analysis concepts, techniques, methodological issues, and, above all, modelling creativity (cf. Clemen, 1996, Chapter 6). Our work as facilitators was a rich interactive consulting path throughout: • the structuring of the problem, • the design of a multicriteria sorting model, including an innovative questioning procedure enabling to determine multidimensional reference-profiles that define urgency categories, and finally, to complete the resource allocation model, • the design of a specific assignment model, to aggregate elemental PJs in ‘‘packages’’, involving the design of a synergy scoring system combined with a particular type of veto analysis. Throughout the various stages of this decisionanalysis process, we were pleased and motivated by the positive reactions of the technical and political actors involved, and by their enthusiastic participation. At the end, they emphasised the learning capabilities of the methodology, and said that the discussions offered them a deeper insight about the various features of the problem that would change their way of making choices in the future. Indeed, the meta-model developed is already informally used for deciding which requests for building works should be given priority in each year. It has not yet been implemented as a decision support system because the development of a Municipal Information System is required to provide the indispensable inputs for automatic assignment. The implementation of this information system will create the necessary conditions to complete the validation of the model, namely in what concerns the package construction procedure that could not be fully tested due to the unavailability of a large enough and comprehensive database on PJs. This constitutes the main limitation of the work produced.
This paper does not aim to introduce new fundamental or theoretical advances. It focuses on the analyst’s ability to capture the main features of the decision process and to develop an approach well suited to the decisional context. It also illustrates the value of exploring established concepts, methodologies and techniques with a creative and innovative spirit. As a final conclusion, and based upon Phillips’ conceptualisation, we want to stress that we are convinced that we have supported the construction of a requisite decision model: ‘‘{. . .} requisite in the sense that everything required to solve the problem is either included in the model or can be simulated in it {. . .}. The process of building the model is iterative and consultative, and when no new intuitions emerge about the problem, the model is considered to be ‘requisite’ {. . .}. In short, requisite decision modelling treats problem solving as a dynamic process in which all relevant actors become clearer about the problem and develop a deeper understanding of it over time’’ (Phillips, 1982, p. 304). Acknowledgements The work described in this paper was developed under a contract between Instituto Superior Tecnico and the Lisbon Municipality. The authors are indebted to the former DCEOD’s Director, Maria de Lourdes Alvarez, for her agreement to report the case and her commitment all throughout its development. Last but not the least, the authors thank Susan Powell and two anonymous referees for their valuable comments on an earlier version of this paper. References Bana e Costa, C.A., Vansnick, J.C., 1997. Applications of the M A C B E T H approach in the framework of an additive aggregation model. Journal of Multi-Criteria Decision Analysis 6 (2), 107–114. Bana e Costa, C.A., Vansnick, J.C., 1999. The M A C B E T H approach: Basic ideas, software and an application. In: Meskens, N., Roubens, M. (Eds.), Advances in Decision Analysis. Kluwer Academic Publishers, Dordrecht, pp. 131– 157.
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