This paper addresses a mixed integer programming (MIP) formulation for the multi-item uncapacitated lot-sizing problem that is inspired from the trailer manufacturer. The proposed MIP model has been utilized to find out the optimum order quantity, optimum order time, and the minimum total cost of purchasing, ordering, and holding over the predefined planning horizon. This problem is known as NP-hard problem. The model was presented in an optimal software form using LINGO 13.0.

Learning concepts via instruction and expository texts is an important problem for modeling human learning and for making autonomous AI systems. This paper describes a computational model of the self-explanation effect, whereby conceptual knowledge is repaired by integrating and explaining new material. Our model represents conceptual knowledge with compositional model fragments, which are used to explain new material via model formulation. Preferences are computed over explanations and conceptual knowledge, along several dimensions. These preferences guide knowledge integration and question-answering. Our simulation learns about the human circulatory system, using facts from a circulatory system passage used in a previous cognitive psychology experiment. We analyze the simulation’s performance, showing that individual differences in sequences of models learned by students can be explained by different parameter settings in our model.