Implementing Mixed Integer Programming for Forced-Choice Questionnaire Assembly: An R-Based Tutorial with ROI

Forced-choice questionnaires (FCQs) mitigate social desirability bias in personnel selection, yet their optimal assembly—equating item desirability within blocks while satisfying scale-level constraints—remains computationally challenging. This paper presents a mixed integer programming (MIP) framework that identifies globally optimal FCQ assemblies under structural constraints including factor balance, factor-pair representation, and mixed-keyed block proportions. Unlike heuristic approaches such as simulated annealing or genetic algorithms, the proposed MIP formulation guarantees optimality when both objective functions and constraints admit linear representations. We detail a two-stage procedure: (1) generation of a restricted candidate block pool via top-N selection to mitigate combinatorial explosion, and (2) set-partitioning optimization using the ROI R package with commercial or open-source solvers. Simulation studies show that MIP consistently identified the best solutions observed in our comparisons within practical timeframes, whereas the heuristic methods did not match those solutions within 600 seconds. The tutorial provides complete R implementations, enabling researchers to construct psychometrically optimized FCQs for high-stakes assessment contexts.