ELECTRE TRI is a well-known method to assign a set of alternatives to a set of predefined categories, considering multiple criteria. Using this method requires setting many parameters, which is often a difficult task. We consider the case where the decision makers (DMs) in the decision process are unsure of which values should each parameter take, which may result from uncertain, imprecise or inaccurately determined information, as well as from lack of consensus among them. This paper discusses the synergy between two approaches developed independently to deal with this difficulty. The first approach infers the value of parameters from assignment examples provided by the DMs, as an elicitation aid. Each assignment example originates mathematical constraints that the parameter values should satisfy. The second approach considers a set of constraints on the parameter values reflecting the imprecise information that the DMs are able to provide. Then, it computes the best and worst categories for each alternative compatible with constraints, in order to present robust conclusions. Both approaches avoid asking for precise values for the parameters. Rather, they proceed to solve the problem in a way that requires from the DMs much less effort. By integrating these two approaches, this paper proposes a new interactive approach, where the insight obtained during robustness analyses guides the DMs during the elicitation phase.

We consider a framework where decision makers (DMs) interactively define a multicriteria evaluation model by providing imprecise information (i.e., a linear system of constraints to the modelÕs parameters) and by analyzing the consequences of the information provided. DMs may introduce new constraints explicitly or implicitly (results that the model should yield). If a new constraint is incompatible with the previous ones, then the system becomes inconsistent and the DMs must choose between removing the new constraint or removing some of the older ones. We address the problem of identifying subsets of constraints which, when removed, lead to a consistent system. Identifying such subsets would indicate the reason for the inconsistent information given by DMs. There may exist several possibilities for the DMs to resolve the inconsistency. We present two algorithms to identify such possibilities, one using {0,1} mixed integer linear programming and the other one using linear programming. Both approaches are based on the knowledge that the system was consistent prior to introducing the last constraint. The output of these algorithms helps the DM to identify the conflicting pieces of information in a set of statements he/she asserted. The relevance of these algorithms for MCDA is illustrated by an application to an aggregation/disaggregation procedure for the Electre Tri method.

This paper makes a review of interactive methods devoted to multiobjective integer and mixed-integer programming (MOIP/MOMIP) problems. The basic concepts concerning the characterization of the non-dominated solution set are first introduced, followed by a remark about non-interactive methods vs. interactive methods. Then, we focus on interactive MOIP/MOMIP methods, including their characterization according to the type of preference information required from the decision maker, the computing process used to determine non-dominated solutions and the interactive protocol used to communicate with the decision maker. We try to draw out some contrasts and similarities of the different types of methods.

Dynamic routing, Communication networks, Mutiobjective Optimisation, Heuristics,

Brazil has an increasing rate of e-waste generation, but there are currently few adequate management systems in operation, with the largest share of Waste Electrical and Electronic Equipment (WEEE) going to landfill sites or entering informal chains. The National Solid Waste Policy (2010) enforces the implementation of reverse logistics systems under the shared responsibility of consumers, companies and governments. The objective of this paper is to assess sustainability and prioritise system alternatives for potential implementation in the metropolitan region of Rio de Janeiro. Sustainability criteria and decision alternatives were defined by elicitation of stakeholders. The adopted multicriteria approach combines Life Cycle Assessment with qualitative evaluations by a small sample of regional experts with knowledge of the problem. The recommended system consists of a hybrid WEEE collection scheme with delivery points at shops, metro stations and neighbourhood centres; a pre-treatment phase with the involvement of private companies, cooperatives and social enterprises; and full recycling of all components in the country.

MPLS (Multiprotocol Label Switching) enables the utilisation of explicit routes and other advanced routing mechanisms in multiservice packet networks, capable of dealing with multiple and heterogeneous QoS (Quality of Service) parameters. Firstly the paper presents a discussion of conceptual and methodological issues raised by multiobjective routing optimisation models for MPLS networks. The major contribution is the proposal of a multiobjective routing optimisation framework for MPLS networks. The major features of this modelling framework are: the formulation of a three-level hierarchical routing optimisation problem including network and service performance objectives, the inclusion of fairness objectives in the different levels of optimisation and a two-level stochastic representation of the traffic in the network (traffic flow and packet stream levels). A variant of the general model for two classes Work partially supported by programme POSI of the III EC programme cosponsored by FEDER and national funds. of traffic flows, QoS traffic and Best Effort traffic, is also presented. Finally a stochastic teletraffic modelling approach, underlying the optimisation model, is fully described.

This paper outlines a distributed GDSS suitable to be used over the Internet, based on the VIP Analysis methodology and software. VIP Analysis incorporates complementary approaches to deal with the aggregation of multicriteria performances by means of an additive value function under imprecise information. This proposed GDSS intends to support a decision panel forming a democratic decision unit, whose members wish to reach a final decision in a choice problem, based on consensus or on some majority rule. Its purpose is not to impose an aggregated model from the individual ones. Rather, the GDSS is designed to reflect to each member the consequences of his/her inputs, confronting them with analogous reflections of the group membersÕ inputs. We propose aggregation procedures to provide a reflection of the groupÕs inputs to each of its members, and an architecture for a GDSS implementing these procedures.

We consider the aggregation of multicriteria performances by means of an additive value function under imprecise information. The problem addressed here is the way an analysis may be conducted when the decision makers are not able to (or do not wish to) fix precise values for the importance parameters. These parameters can be seen as interdependent variables that may take several values subject to constraints. First, we briefly classify some existing approaches to deal with this problem. We will argue that they complement each other, each one having its merits and shortcomings. Then, we present a new decision support software-VIP Analysis-which incorporates approaches belonging to different classes. It proposes a methodology of analysis based on the progressive reduction of the number of alternatives, introducing a concept of tolerance that lets the decision makers use some of the approaches in a more flexible manner.