Techniques for test-case prioritization re-order test cases to increase their rate of fault detection. When there is a fixed time budget that does not allow the execution of all the test cases, time-aware techniques for test-case prioritization may achieve a better rate of fault detection than traditional techniques for test-case prioritization. In this paper, we propose a novel approach to time-aware test-case prioritization using integer linear programming. To evaluate our approach, we performed experiments on two subject programs involving four techniques for our approach, two techniques for an approach to time-aware test-case prioritization based on genetic algorithms, and four traditional techniques for testcase prioritization. The empirical results indicate that two of our techniques outperform all the other techniques for the two subjects under the scenarios of both general and version-specific prioritization. The empirical results also indicate that some traditional techniques with lower analysis time cost for test-case prioritization may still perform competitively when the time budget is not quite tight.