ABSTRACT This paper addresses the Truck‐to‐dock Door Assignment Problem, an optimisation problem in supply chain management. The problem is characterized by two incommensurable business objectives: to maximise the volume of pallets transiting through the cross‐dock and to minimise the total transfer time required to perform the pallet transfer operations. Two single objective integer programming formulations introduced after 2009 in the literature are examined. Both formulations share the same objective function, which is composed of two parts made commensurable using coefficients of a monetary nature. However, these coefficients are inherently artificial, reflecting the impossibility of a pallet transfer through a penalty cost and a pallet transfer time through a transportation cost. To overcome this limitation, two bi‐objective lexicographic formulations, derived from these single‐objective formulations and free of any artificial cost coefficients, are proposed. The core of the paper is devoted to the analysis of the four formulations according to the two business objectives of the Truck‐to‐dock Door Assignment Problem. Mathematical formulations have been implemented in Julia, using the algebraic modelling language JuMP. Codes and datasets are available online on GitHub in open‐source. Reproducible numerical experiments on instances from the literature have been conducted using Gurobi Optimizer as IP solver. On the basis of results collected after intensive numerical experiments, the analysis carried out reveals that the bi‐objective lexicographic formulations outperform the two single‐objective formulations published in 2009 and 2016.
ABSTRACT Laplacian Ranking (LaRa) is a graph‐regularized multi‐criteria decision analysis method that incorporates relational geometry among alternatives into ranking while preserving convexity, interpretability and deterministic reproducibility. LaRa combines quantile normalization, metric‐weighted distances, a sparse similarity graph, a reference‐oriented prior and an optional quadratic pairwise target‐gap term. Its base score is the unique minimizer of a strictly convex quadratic objective, obtained by solving a symmetric positive definite linear system, with an optional deterministic dominance‐repair step. We evaluate LaRa on seven literature‐grounded real‐data problems spanning materials, manufacturing equipment, industrial robotics, renewable‐energy siting, and energy‐technology selection, together with a controlled synthetic pharmaceutical‐style benchmark. Five cross‐domain cases use one common fixed configuration and sensitivity grid rather than dataset‐specific tuning. Results show that the graph contribution is regime‐dependent. It is ordinally inert for cryogenic materials and clean‐energy technologies, measurable but non‐disruptive for flywheel selection, improves concordance with published rankings for CNC machine tools, arc‐welding robots and Colombian solar‐PV siting, and reduces concordance for gear‐material selection, which is retained as an explicit failure boundary. On the fixed synthetic benchmark, the high‐smoothing configuration attains Kendall's and Spearman's , reduces mean absolute rank error from 0.556 for TOPSIS to 0.111, and exactly recovers the Top‐3 set. These findings position LaRa as a relational refinement of pointwise MCDA whose usefulness depends on whether neighbourhood geometry is substantively meaningful and empirically supported. Accordingly, graph smoothing should be activated as a conditional modelling component and accompanied by sensitivity analysis rather than assumed beneficial in practical MCDA applications.
ABSTRACT In this paper, we present a systematic review of 103 peer‐reviewed studies published between 1991 and 2025 on the integration of multi‐criteria decision analysis (MCDA) and game theory (GT). Beyond synthesizing the literature, we introduce a structural criterion for evaluating the depth of MCDA–GT integration, focusing on whether multi‐criteria preferences remain active within the equilibrium formulation rather than being aggregated ex ante and introduced as fixed inputs. Applying this criterion, we find that most reviewed studies rely on relatively weak forms of integration: MCDA outputs typically enter game‐theoretic models as fixed payoff parameters while the strategic solution process remains largely unaffected by the multi‐criteria structure, and the literature is further dominated by static, perfect‐information game models combined with aggregated utility representations. By contrast, a smaller group of studies achieves deeper integration by preserving multi‐criteria preferences within the strategic solution process. Across these studies, two broad approaches emerge—some retain preference incomparability through order‐based representations and dominance relations on vector payoffs, while others embed trade‐offs directly within optimization and equilibrium structures—yet both allow multi‐criteria preferences to influence strategic outcomes throughout the solution process. Based on this assessment, we identify four recurring limitations: limited structural embedding of multi‐criteria preferences, underuse of imperfect‐information and adaptive game models, inadequate representation of stakeholder heterogeneity and limited attention to policy and governance settings. For each area we outline representative research directions that may support closer integration of multi‐criteria evaluation and strategic reasoning. Overall, the review suggests that the field has progressed beyond simple method combination but remains uneven in the depth of integration achieved, and this paper clarifies the modelling choices associated with deeper integration and highlights opportunities for future methodological development.
ABSTRACT We extend the non‐compensatory ELECTRE TRI‐B inspired sorting model with multiple evaluators with a two‐stage membership procedure to categorise 27 lower‐middle‐income countries (LMICs) based on their financial inclusion (FI) levels. By employing four access and four usage FI dimensions, we impose an ‘access‐first’ constraint and require the joint satisfaction of access and usage constraints for high, mid, and low FI classification. Unlike commonly used multivariate techniques and compensatory methods, this access‐first approach prevents an advantage in FI usage from offsetting a weakness in FI access, therefore providing a clearer picture for LMICs' FI levels. The results indicate that once the access condition is met, the usage FI dimensions decide whether to confirm or upgrade the category of a given country. Countries such as Nepal, Mauritania, and Nigeria show relatively better performance on some usage dimensions, but not in the access block; hence, they are sorted in mid or low FI categories.
ABSTRACT Several multicriteria methods have been created for use in problem situations that are considered complex because multiple actors and/or organisations are involved. Such methods are easily combined with problem shaping and structuring methods to reduce complexity when a situation is new, ill‐ or not well‐structured. These situations can also be dealt with by resorting to multiple criteria decision aiding MCDA approaches that use certain tools. Such tools are not only multicriteria methods but also logical and analytical models, interactive procedures and critical analyses of method results, which can be directly oriented towards activating mutual learning processes. Indeed, combining multicriteria methods with other tools, which are oriented more towards posing a decision problem than to solving it, can aid the perception and description of the nature and complexity of the situation in the initial phase of a decision aid process, orient a decision aid intervention and improve its effectiveness. An easy visualisation and understandability of the model components, of the used data and of the method application results facilitate a critical revision of the original problem formulation and modelling, and they can activate steps of mutual learning, improvements of the model and results, and of the generation of robustness, not only of the results but also of the model, and the decision and decision aid processes. This interpretation of how an integration of MCDA models, methods and other tools can be used to deal with complex decision problems is not new. Bernard Roy called this approach MCDA ‘description problematic’, but this methodological approach is rarely put into practice and still needs conceptual definition and structural clarity. An analysis framework is here presented to distinguish between some different MCDA situations where the outranking methods are oriented towards a description problem statement. Two complex cases are proposed to describe the main characteristics of four situations, which influence an analyst's behaviour and decision aid results, and suggest that some multicriteria models and methods should be used in complex situations first and foremost to facilitate understanding and communication.
