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A complete bipartite graph with the number of two partitions s and t is denoted by \(K{s,t}\). For a positive integer s and two bipartite graphs G and H, the s-bipartite Ramsey number \(BR_s (G, H)\) of G and H is the smallest integer t such that every 2-coloring of the edges of \(K_{s,t}\) contains the a copy of G with the first color or a copy of H with the second color. In this paper, by using an integer linear program and the solver Gurobi Optimizer 8.0, we determine all the exact values of \(BR_s (K_{2,3}, K_{3,3})\) for all possible \(s\). More precisely, we show that \(BR_s (K_{2,3}, K_{3,3})=13\) for \(s\) \(\in\) {8,9}, \(BR_s (K_{2,3}, K_{3,3})=12\) for \(s \in \{10,11\}\), \(BR_s (K_{2,3}, K_{3,3})=10\) for \(s = 12\), \(BR_s (K_{2,3}, K_{3,3})=8\) for \(s \in \{13,14\}\), \(BR_s (K_{2,3}, K_{3,3})=6\) for \(s \in \{15,16,…, 20\}\), and \(BR_s (K_{2,3}, K_{3,3})=4\) for s ≥ 21. This extends the results presented in [Zhenming Bi, Drake Olejniczak and Ping Zhang, “The s-Bipartite Ramsey Numbers of Graphs \(K_{2,3}\) and \(K_{3,3}\)” , Journal of Combinatorial Mathematics and Combinatorial Computing 106, (2018) 257-272].