With the growing traffic of containerized shipping worldwide, container liners have seen increasing cooperation. Slot co-chartering has drawn wide attention as a way of cooperation within liner alliances. However, liners face the issue of finding proper measures to optimize alliance operations. In response to this, this paper comprehensively considers shipping capacity dispatch for containerized shipping companies within liner alliances. First, we explained the general rules of liner shipping dispatch and analyzed the interfering factors. Second, we created a liner shipping capacity dispatch model without consideration of slot co-chartering costs and a liner shipping capacity dispatch model with consideration of slot co-chartering costs and proposed a new column generation algorithm to solve both problems. Third, we tested our algorithm in a real case of a large Chinese containerized shipping company, which belongs to Ocean Alliance, and an optimal ship dispatch strategy on relevant routes and a decision on optimal slot chartering can be reached. Computational results indicate that the proposed column generation algorithm exhibits effective and efficient performance for large-scale slot co-chartering in liner shipping.