This paper introduces an interactive framework to guide decision-makers in a multi-criteria supplier selection process. State-of-the-art multi-criteria methods for supplier selection elicit the decision-maker’s preferences among the criteria by processing pre-collected data from different stakeholders. We propose a different approach where the preferences are elicited through an active learning loop. At each step, the framework optimally solves a combinatorial problem multiple times with different weights assigned to the objectives. Afterwards, a pair of solutions among those computed is selected using a particular query selection strategy, and the decision-maker expresses a preference between them. These two steps are repeated until a specific stopping criterion is satisfied. We also introduce two novel fast query selection strategies, and we compare them with a myopically optimal query selection strategy. Computational experiments on a large set of randomly generated instances are used to examine the performance of our query selection strategies, showing a better computation time and similar performance in terms of the number of queries taken to achieve convergence. Our experimental results also show the usability of the framework for real-world problems with respect to the execution time and the number of loops needed to achieve convergence.

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In a decision-making problem, there is often some uncertainty regarding the user preferences. We assume a parameterised utility model, where in each scenario we have a utility function over alternatives, and where each scenario represents a possible user preference model consistent with the input preference information. With a set $$A$$ A of alternatives available to the decision-maker, we can consider the associated utility function, expressing, for each scenario, the maximum utility among the alternatives. We consider two main problems: firstly, finding a minimal subset of $$A$$ A that is equivalent to it, i.e., that has the same utility function. We show that for important classes of preference models, the set of possibly strictly optimal alternatives is the unique minimal equivalent subset. Secondly, we consider how to compare $$A$$ A to another set of alternatives $$B$$ B , where $$A$$ A and $$B$$ B correspond to different initial decision choices. This is closely related to the problem of computing setwise max regret. We derive mathematical results that allow different computational techniques for these problems, using linear programming, and especially, with a novel approach using the extreme points of the epigraph of the utility function.

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