الفهرس 
introduction
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Abstract
Inventories are materials stored, ordered these materials to face the demand of the customers and waiting for the processing. Because of their practical and economic importance, the subject of inventory control is a major consideration in many situations. If the most important questions must be constantly answered in the study of probabilistic inventory models as to when and how much raw material should be ordered?. So, we interested in this thesis to introduce some constraint probabilistic inventory models with new assumptions and considerations in order to get the optimal expected total cost. where, find the optimal results mathematically or numerically depending on the distribution of the lead time demand. The main model in our study is ”a constraint probabilistic continuous review inventory model when the holding cost is varying with considering that, the shortage cost is divided into backordered and lost sales”. We use the optimization to find the optimal decision variables involved in each proposed model. After analyzing every model and get his optimal values, the model is reintroduced by using the fuzziness to prove that the fuzzy optimal values are more reliability and gets minimum expected total cost less than the crisp case. The signed distance is the method which used to defuzzify the fuzzy values.