The work presented in this paper has been motivated primarily by Zadeh's idea of linguistic variables intended to provide rigorous mathematical modeling of natural language and CWW, Computing With Words. This paper reports some modeling of the linguistic inventory problems where CWW have been implemented: linguistic production inventory, linguistic inventory models under linguistic demand and linguistic lead time, linguistic production inventory models based on the preference of a decision maker, and linguistic inventory model for fuzzy reorder point and fuzzy safety stock. Only studies that focus on CWW, two linguistic inventory models and two linguistic backorder inventory models, which each model is combined by the heuristic fuzzy total inventory cost based on the preference of a decision maker, are proposed in this paper. The heuristic fuzzy total inventory cost of each model is modeled by linguistic values in natural language, fuzzy numbers, and crisp real numbers. It is also computed and defuzzified by using some fuzzy arithmetical operations by Function Principle and Graded k-preference integration representation method, respectively. In addition, Extension of the LaGrangean method is used for solving inequality constrain problem in the proposed linguistic inventory environments. Furthermore, we find that our heuristic optimal solutions of the new introduced modeling the linguistic inventory problems can also be specified to meet the classical inventory models, when all linguistic variables are crisp real numbers, such as the previous proposed linguistic inventory models.
