We analyze the use of caching of video frames at network routers for reducing average retransmission delay. We formulate an expression for the average retransmission delay using video caching routers. In turn, we use this expression to formulate a mathematical program to minimize the average retransmission delay. We find a dynamic programming solution to the resultant non-linear convex binary integer program. We compare the results obtained from the dynamic programming solution with those obtained via experimental exhaustive enumeration. The experimental results validate our models and dynamic programming solution. Finally, we use numerical analysis to quantify the retransmission delay difference between the best and worst caching router placements. Our findings show that the optimal placement of caching routers can significantly reduce cost by minimizing the number of caching routers required to meet a desired retransmission delay performance. Furthermore, our dynamic programming solution shows that such optimal placement can be efficiently determined from network parameters, without an exhaustive search.