This paper proposed a general probabilistic continuous review multi-item, multi-source inventory model with constraint for crisp and fuzzy environment. This constraint on the expected varying holding cost. The demand is a continuous random variable, the distribution of the lead time demand is known and the holding cost is varying. This model is formulated to analyze how the firm can deduce the optimal order quantity and the optimal reorder point for the item and source to reach the main goal of minimizing the expected total cost using a Lagrange multiplier technique. The lead time demand is follow some continuous distributions. Also, an application with real data is analyzed and the goal of minimization the expected total cost is achieved.