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Unpredictable behavior of cache memory makes it difficult to statically analyze the worst-case performance of real-time systems. This problem is exacerbated in case of preemptive multitask systems due to intertask cache interference, called Cache-Related Preemption Delay (CRPD). This paper proposes an approach to analysis of the tight upper bound on CRPD which a task might impose on lower-priority tasks. Our method determines the program execution path of the task which requires the maximum number of cache blocks using an integer linear programming technique. Experimental results show that our approach provides up to 69% tighter bounds on CRPD than a previous approach.