In recent years, mining high-utility itemsets (HUIs) has become as a key topic in data mining. However, most of the developed algorithms assume the unrealistic situations that unit profits of items remain unchanged over time. But in real-life situations, the profit of an item or itemset varies as a function of cost prices, sales prices and sales strategies. In this paper, a novel framework for mining HUIs with two algorithms under various Discount strategies (HUID) are introduced. HUID-tp is based on various discount strategies and a novel downward closure property to mine the complete set of HUIs. HUID-Miner is an algorithm relying on a compact data structure (Positive-and-Negative Utility-list, PNU-list) and new pruning strategies to efficiently discover HUIs without candidate generation, while considerably reducing the size of the search space. Furthermore, a strategy named Estimated Utility Co-occurrence Strategy which stores the relationships between 2-itemsets is also adopted in the proposed improvement HUID-EMiner algorithm to speed up computation. An extensive experimental study carried on several real-life datasets shows the performance of the proposed algorithms.