A Precedence Constrained Knapsack Problem with Uncertain Item Weights for Personalized Learning Systems

• Studies a novel educational context problem of personalized learning environments. Presents new precedence-constrained knapsack model with uncertain item weights. Provides efficient approximate cutting plane methods Taylor approximations. effective pre-processing procedures and cover cuts. This paper studies unique precedence constrained in which there are two available to place an the knapsack. Whether or not weight is depends on one selected. models students’ decisions choosing subjects study hybrid systems students can either under teacher supervision unsupervised self-study mode by using online tools. We incorporate uncertainty chance-constrained programming framework. Under assumption that weights independently normally distributed, we focus deterministic reformulation capacity constraint involves nonlinear convex function decision variables. By first-order linear approximations this function, propose exact method iteratively adds feasibility To supplement this, develop converge quickly high-quality feasible solutions. improve computational efficiency our methods, introduce eliminate items beforehand cuts refine space. Our experiments small large instances show optimality gaps very overall, they even able find solutions no as number increases instances. Moreover, demonstrate particularly when relations dense, may significantly speed up approach challenging