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Abstract The facility location of a competing firm in a market has great importance in supply chain management. The two-stage competitive location model formulates the decision process of an entrant firm facing both location and price competition. In this paper, we incorporated the facility quantity as a decision variable into a two-stage competitive location model with the objective of maximized profit. Sequential location mode and simultaneous location mode were applied to simulate different location behavior. We developed an approximate branch and bound method to accelerate optimal location searching speed under the premise of accuracy. Greedy algorithm and approximate branch and bound method were used in two location modes. From algorithm evaluation, we found that the approximate branch and bound method is an ideal supplement of the traditional branch and bound method, especially for location problems with large-scale potential locations. Compare the results of the two modes, we found when a new firm is going to enter a market with both price and location competition, sequential location mode is an advantage strategy, since it can gain more profit than simultaneous location mode.