We discussed two different cases of the probabilistic continuous review mixture shortage inventory model with varying and constrained expected order cost, when the lead time demand follows some different continuous distributions. The first case is when the total cost components are considered to be crisp values, and the other case is when the costs are considered as trapezoidal fuzzy number. Also, some special cases are deduced. To investigate the proposed model in the crisp case and the fuzzy case, illustrative numerical example is added. From the numerical results we will conclude that Uniform distribution is the best distribution to get the exact solutions, and the exact solutions for fuzzy models are considered more practical and close to the reality of life and get minimum expected total cost less than the crisp models.